Daily Papers

Anti-Money Laundering (AML) is a crucial task in ensuring the integrity of financial systems. One keychallenge in AML is identifying high-risk groups based on their behavior. Unsupervised learning, particularly clustering, is a promising solution for this task. However, the use of hundreds of features todescribe behavior results in a highdimensional dataset that negatively impacts clustering performance.In this paper, we investigate the effectiveness of combining clustering method agglomerative hierarchicalclustering with four dimensionality reduction techniques -Independent Component Analysis (ICA), andKernel Principal Component Analysis (KPCA), Singular Value Decomposition (SVD), Locality Preserving Projections (LPP)- to overcome the issue of high-dimensionality in AML data and improve clusteringresults. This study aims to provide insights into the most effective way of reducing the dimensionality ofAML data and enhance the accuracy of clustering-based AML systems. The experimental results demonstrate that KPCA outperforms other dimension reduction techniques when combined with agglomerativehierarchical clustering. This superiority is observed in the majority of situations, as confirmed by threedistinct validation indices.

We propose a novel method, LoLep, which regresses Locally-Learned planes from a single RGB image to represent scenes accurately, thus generating better novel views. Without the depth information, regressing appropriate plane locations is a challenging problem. To solve this issue, we pre-partition the disparity space into bins and design a disparity sampler to regress local offsets for multiple planes in each bin. However, only using such a sampler makes the network not convergent; we further propose two optimizing strategies that combine with different disparity distributions of datasets and propose an occlusion-aware reprojection loss as a simple yet effective geometric supervision technique. We also introduce a self-attention mechanism to improve occlusion inference and present a Block-Sampling Self-Attention (BS-SA) module to address the problem of applying self-attention to large feature maps. We demonstrate the effectiveness of our approach and generate state-of-the-art results on different datasets. Compared to MINE, our approach has an LPIPS reduction of 4.8%-9.0% and an RV reduction of 73.9%-83.5%. We also evaluate the performance on real-world images and demonstrate the benefits.

There is a growing gap between the impressive results of deep image generative models and classical algorithms that offer theoretical guarantees. The former suffer from mode collapse or memorization issues, limiting their application to scientific data. The latter require restrictive assumptions such as log-concavity to escape the curse of dimensionality. We partially bridge this gap by introducing conditionally strongly log-concave (CSLC) models, which factorize the data distribution into a product of conditional probability distributions that are strongly log-concave. This factorization is obtained with orthogonal projectors adapted to the data distribution. It leads to efficient parameter estimation and sampling algorithms, with theoretical guarantees, although the data distribution is not globally log-concave. We show that several challenging multiscale processes are conditionally log-concave using wavelet packet orthogonal projectors. Numerical results are shown for physical fields such as the varphi^4 model and weak lensing convergence maps with higher resolution than in previous works.

Training large-scale neural networks in vision, and multimodal domains demands substantial memory resources, primarily due to the storage of optimizer states. While LoRA, a popular parameter-efficient method, reduces memory usage, it often suffers from suboptimal performance due to the constraints of low-rank updates. Low-rank gradient projection methods (e.g., GaLore, Flora) reduce optimizer memory by projecting gradients and moment estimates into low-rank spaces via singular value decomposition or random projection. However, they fail to account for inter-projection correlation, causing performance degradation, and their projection strategies often incur high computational costs. In this paper, we present COAP (Correlation-Aware Gradient Projection), a memory-efficient method that minimizes computational overhead while maintaining training performance. Evaluated across various vision, language, and multimodal tasks, COAP outperforms existing methods in both training speed and model performance. For LLaMA-1B, it reduces optimizer memory by 61% with only 2% additional time cost, achieving the same PPL as AdamW. With 8-bit quantization, COAP cuts optimizer memory by 81% and achieves 4x speedup over GaLore for LLaVA-v1.5-7B fine-tuning, while delivering higher accuracy.

Given a set of dissimilarity measurements amongst data points, determining what metric representation is most "consistent" with the input measurements or the metric that best captures the relevant geometric features of the data is a key step in many machine learning algorithms. Existing methods are restricted to specific kinds of metrics or small problem sizes because of the large number of metric constraints in such problems. In this paper, we provide an active set algorithm, Project and Forget, that uses Bregman projections, to solve metric constrained problems with many (possibly exponentially) inequality constraints. We provide a theoretical analysis of Project and Forget and prove that our algorithm converges to the global optimal solution and that the L_2 distance of the current iterate to the optimal solution decays asymptotically at an exponential rate. We demonstrate that using our method we can solve large problem instances of three types of metric constrained problems: general weight correlation clustering, metric nearness, and metric learning; in each case, out-performing the state of the art methods with respect to CPU times and problem sizes.

Transfer learning with a small amount of target data is an effective and common approach to adapting a pre-trained model to distribution shifts. In some situations, target data labels may be expensive to obtain, so we may only have access to a limited number of target data points. To make the most of a very small target dataset, we propose a lightweight, sample-efficient approach that learns a diverse set of features and adapts to a target distribution by interpolating these features. Our approach, Project and Probe (Pro^2), first learns a linear projection that maps a pre-trained embedding onto orthogonal directions while being predictive of labels in the source dataset. The goal of this step is to learn a variety of predictive features, so that at least some of them remain useful after distribution shift. Pro^2 then learns a linear classifier on top of these projected features using a small target dataset. Theoretically, we find that Pro^2 results in more sample-efficient generalization by inducing a favorable bias-variance tradeoff. Our experiments on four datasets, with multiple distribution shift settings for each, show that Pro^2 improves performance by 5-15% when given limited target data compared to prior methods such as standard linear probing.

We tackle the problem disentangling the latent space of an autoencoder in order to separate labelled attribute information from other characteristic information. This then allows us to change selected attributes while preserving other information. Our method, matrix subspace projection, is much simpler than previous approaches to latent space factorisation, for example not requiring multiple discriminators or a careful weighting among their loss functions. Furthermore our new model can be applied to autoencoders as a plugin, and works across diverse domains such as images or text. We demonstrate the utility of our method for attribute manipulation in autoencoders trained across varied domains, using both human evaluation and automated methods. The quality of generation of our new model (e.g. reconstruction, conditional generation) is highly competitive to a number of strong baselines.

In this paper, we revisit the problem of sparse linear regression in the local differential privacy (LDP) model. Existing research in the non-interactive and sequentially local models has focused on obtaining the lower bounds for the case where the underlying parameter is 1-sparse, and extending such bounds to the more general k-sparse case has proven to be challenging. Moreover, it is unclear whether efficient non-interactive LDP (NLDP) algorithms exist. To address these issues, we first consider the problem in the epsilon non-interactive LDP model and provide a lower bound of Omega(sqrt{dklog d}{nepsilon}) on the ell_2-norm estimation error for sub-Gaussian data, where n is the sample size and d is the dimension of the space. We propose an innovative NLDP algorithm, the very first of its kind for the problem. As a remarkable outcome, this algorithm also yields a novel and highly efficient estimator as a valuable by-product. Our algorithm achieves an upper bound of O({dsqrt{k}{nepsilon}}) for the estimation error when the data is sub-Gaussian, which can be further improved by a factor of O(d) if the server has additional public but unlabeled data. For the sequentially interactive LDP model, we show a similar lower bound of Omega({sqrt{dk}{nepsilon}}). As for the upper bound, we rectify a previous method and show that it is possible to achieve a bound of O(ksqrt{d}{nepsilon}). Our findings reveal fundamental differences between the non-private case, central DP model, and local DP model in the sparse linear regression problem.

The ability to control for the kinds of information encoded in neural representation has a variety of use cases, especially in light of the challenge of interpreting these models. We present Iterative Null-space Projection (INLP), a novel method for removing information from neural representations. Our method is based on repeated training of linear classifiers that predict a certain property we aim to remove, followed by projection of the representations on their null-space. By doing so, the classifiers become oblivious to that target property, making it hard to linearly separate the data according to it. While applicable for multiple uses, we evaluate our method on bias and fairness use-cases, and show that our method is able to mitigate bias in word embeddings, as well as to increase fairness in a setting of multi-class classification.

This paper introduces a new parameterization of deep neural networks (both fully-connected and convolutional) with guaranteed ell^2 Lipschitz bounds, i.e. limited sensitivity to input perturbations. The Lipschitz guarantees are equivalent to the tightest-known bounds based on certification via a semidefinite program (SDP). We provide a ``direct'' parameterization, i.e., a smooth mapping from mathbb R^N onto the set of weights satisfying the SDP-based bound. Moreover, our parameterization is complete, i.e. a neural network satisfies the SDP bound if and only if it can be represented via our parameterization. This enables training using standard gradient methods, without any inner approximation or computationally intensive tasks (e.g. projections or barrier terms) for the SDP constraint. The new parameterization can equivalently be thought of as either a new layer type (the sandwich layer), or a novel parameterization of standard feedforward networks with parameter sharing between neighbouring layers. A comprehensive set of experiments on image classification shows that sandwich layers outperform previous approaches on both empirical and certified robust accuracy. Code is available at https://github.com/acfr/LBDN.

We study the task of agnostically learning halfspaces under the Gaussian distribution. Specifically, given labeled examples (x,y) from an unknown distribution on R^n times { pm 1}, whose marginal distribution on x is the standard Gaussian and the labels y can be arbitrary, the goal is to output a hypothesis with 0-1 loss OPT+epsilon, where OPT is the 0-1 loss of the best-fitting halfspace. We prove a near-optimal computational hardness result for this task, under the widely believed sub-exponential time hardness of the Learning with Errors (LWE) problem. Prior hardness results are either qualitatively suboptimal or apply to restricted families of algorithms. Our techniques extend to yield near-optimal lower bounds for related problems, including ReLU regression.

Recently, a wide range of memory-efficient LLM training algorithms have gained substantial popularity. These methods leverage the low-rank structure of gradients to project optimizer states into a subspace using projection matrix found by singular value decomposition (SVD). However, convergence of these algorithms is highly dependent on the update rules of their projection matrix. In this work, we provide the first convergence guarantee for arbitrary update rules of projection matrix. This guarantee is generally applicable to optimizers that can be analyzed with Hamiltonian Descent, including most common ones, such as LION, Adam. Inspired by our theoretical understanding, we propose Online Subspace Descent, a new family of subspace descent optimizer without SVD. Instead of updating the projection matrix with eigenvectors, Online Subspace Descent updates the projection matrix with online PCA. Online Subspace Descent is flexible and introduces only minimum overhead to training. We show that for the task of pretraining LLaMA models ranging from 60M to 7B parameters on the C4 dataset, Online Subspace Descent achieves lower perplexity and better downstream tasks performance than state-of-the-art low-rank training methods across different settings and narrows the gap with full-rank baselines.

The irregularity and permutation invariance of point cloud data pose challenges for effective learning. Conventional methods for addressing this issue involve converting raw point clouds to intermediate representations such as 3D voxel grids or range images. While such intermediate representations solve the problem of permutation invariance, they can result in significant loss of information. Approaches that do learn on raw point clouds either have trouble in resolving neighborhood relationships between points or are too complicated in their formulation. In this paper, we propose a novel approach to representing point clouds as a locality preserving 1D ordering induced by the Hilbert space-filling curve. We also introduce Point2Point, a neural architecture that can effectively learn on Hilbert-sorted point clouds. We show that Point2Point shows competitive performance on point cloud segmentation and generation tasks. Finally, we show the performance of Point2Point on Spatio-temporal Occupancy prediction from Point clouds.

Optimal transport (OT) has gained popularity due to its various applications in fields such as machine learning, statistics, and signal processing. However, the balanced mass requirement limits its performance in practical problems. To address these limitations, variants of the OT problem, including unbalanced OT, Optimal partial transport (OPT), and Hellinger Kantorovich (HK), have been proposed. In this paper, we propose the Linear optimal partial transport (LOPT) embedding, which extends the (local) linearization technique on OT and HK to the OPT problem. The proposed embedding allows for faster computation of OPT distance between pairs of positive measures. Besides our theoretical contributions, we demonstrate the LOPT embedding technique in point-cloud interpolation and PCA analysis.

Representations learned via self-supervised learning (SSL) can be susceptible to dimensional collapse, where the learned representation subspace is of extremely low dimensionality and thus fails to represent the full data distribution and modalities. Dimensional collapse also known as the "underfilling" phenomenon is one of the major causes of degraded performance on downstream tasks. Previous work has investigated the dimensional collapse problem of SSL at a global level. In this paper, we demonstrate that representations can span over high dimensional space globally, but collapse locally. To address this, we propose a method called local dimensionality regularization (LDReg). Our formulation is based on the derivation of the Fisher-Rao metric to compare and optimize local distance distributions at an asymptotically small radius for each data point. By increasing the local intrinsic dimensionality, we demonstrate through a range of experiments that LDReg improves the representation quality of SSL. The results also show that LDReg can regularize dimensionality at both local and global levels.

Learning from Label Proportions (LLP) is a learning problem where only aggregate level labels are available for groups of instances, called bags, during training, and the aim is to get the best performance at the instance-level on the test data. This setting arises in domains like advertising and medicine due to privacy considerations. We propose a novel algorithmic framework for this problem that iteratively performs two main steps. For the first step (Pseudo Labeling) in every iteration, we define a Gibbs distribution over binary instance labels that incorporates a) covariate information through the constraint that instances with similar covariates should have similar labels and b) the bag level aggregated label. We then use Belief Propagation (BP) to marginalize the Gibbs distribution to obtain pseudo labels. In the second step (Embedding Refinement), we use the pseudo labels to provide supervision for a learner that yields a better embedding. Further, we iterate on the two steps again by using the second step's embeddings as new covariates for the next iteration. In the final iteration, a classifier is trained using the pseudo labels. Our algorithm displays strong gains against several SOTA baselines (up to 15%) for the LLP Binary Classification problem on various dataset types - tabular and Image. We achieve these improvements with minimal computational overhead above standard supervised learning due to Belief Propagation, for large bag sizes, even for a million samples.

Given a K-vertex simplex in a d-dimensional space, suppose we measure n points on the simplex with noise (hence, some of the observed points fall outside the simplex). Vertex hunting is the problem of estimating the K vertices of the simplex. A popular vertex hunting algorithm is successive projection algorithm (SPA). However, SPA is observed to perform unsatisfactorily under strong noise or outliers. We propose pseudo-point SPA (pp-SPA). It uses a projection step and a denoise step to generate pseudo-points and feed them into SPA for vertex hunting. We derive error bounds for pp-SPA, leveraging on extreme value theory of (possibly) high-dimensional random vectors. The results suggest that pp-SPA has faster rates and better numerical performances than SPA. Our analysis includes an improved non-asymptotic bound for the original SPA, which is of independent interest.

Large language model (LLM) training and finetuning are often bottlenecked by limited GPU memory. While existing projection-based optimization methods address this by projecting gradients into a lower-dimensional subspace to reduce optimizer state memory, they typically rely on dense projection matrices, which can introduce computational and memory overheads. In this work, we propose Grass (GRAdient Stuctured Sparsification), a novel approach that leverages sparse projections to transform gradients into structured sparse updates. This design not only significantly reduces memory usage for optimizer states but also minimizes gradient memory footprint, computation, and communication costs, leading to substantial throughput improvements. Extensive experiments on pretraining and finetuning tasks demonstrate that Grass achieves competitive performance to full-rank training and existing projection-based methods. Notably, Grass enables half-precision pretraining of a 13B parameter LLaMA model on a single 40GB A100 GPU--a feat infeasible for previous methods--and yields up to a 2times throughput improvement on an 8-GPU system. Code can be found at https://github.com/aashiqmuhamed/GRASS .

We show how perceptual embeddings of the visual system can be constructed at inference-time with no training data or deep neural network features. Our perceptual embeddings are solutions to a weighted least squares (WLS) problem, defined at the pixel-level, and solved at inference-time, that can capture global and local image characteristics. The distance in embedding space is used to define a perceptual similarity metric which we call LASI: Linear Autoregressive Similarity Index. Experiments on full-reference image quality assessment datasets show LASI performs competitively with learned deep feature based methods like LPIPS (Zhang et al., 2018) and PIM (Bhardwaj et al., 2020), at a similar computational cost to hand-crafted methods such as MS-SSIM (Wang et al., 2003). We found that increasing the dimensionality of the embedding space consistently reduces the WLS loss while increasing performance on perceptual tasks, at the cost of increasing the computational complexity. LASI is fully differentiable, scales cubically with the number of embedding dimensions, and can be parallelized at the pixel-level. A Maximum Differentiation (MAD) competition (Wang & Simoncelli, 2008) between LASI and LPIPS shows that both methods are capable of finding failure points for the other, suggesting these metrics can be combined.

We propose a new localized inference algorithm for answering marginalization queries in large graphical models with the correlation decay property. Given a query variable and a large graphical model, we define a much smaller model in a local region around the query variable in the target model so that the marginal distribution of the query variable can be accurately approximated. We introduce two approximation error bounds based on the Dobrushin's comparison theorem and apply our bounds to derive a greedy expansion algorithm that efficiently guides the selection of neighbor nodes for localized inference. We verify our theoretical bounds on various datasets and demonstrate that our localized inference algorithm can provide fast and accurate approximation for large graphical models.

Quantizing large language models has become a standard way to reduce their memory and computational costs. Typically, existing methods focus on breaking down the problem into individual layer-wise sub-problems, and minimizing per-layer error, measured via various metrics. Yet, this approach currently lacks theoretical justification and the metrics employed may be sub-optimal. In this paper, we present a "linearity theorem" establishing a direct relationship between the layer-wise ell_2 reconstruction error and the model perplexity increase due to quantization. This insight enables two novel applications: (1) a simple data-free LLM quantization method using Hadamard rotations and MSE-optimal grids, dubbed HIGGS, which outperforms all prior data-free approaches such as the extremely popular NF4 quantized format, and (2) an optimal solution to the problem of finding non-uniform per-layer quantization levels which match a given compression constraint in the medium-bitwidth regime, obtained by reduction to dynamic programming. On the practical side, we demonstrate improved accuracy-compression trade-offs on Llama-3.1 and 3.2-family models, as well as on Qwen-family models. Further, we show that our method can be efficiently supported in terms of GPU kernels at various batch sizes, advancing both data-free and non-uniform quantization for LLMs.

This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an algorithm with provable approximation guarantees for its reconstruction error via connections to higher-order singular values. Specifically, we introduce a novel Tucker packing problem, which we prove is NP-hard, and give a polynomial-time approximation scheme based on a reduction to the 2-dimensional knapsack problem with a matroid constraint. We also generalize our techniques to tree tensor network decompositions. We implement our algorithm using an integer programming solver, and show that its solution quality is competitive with (and sometimes better than) the greedy algorithm that uses the true Tucker decomposition loss at each step, while also running up to 1000x faster.

Projection maintenance is one of the core data structure tasks. Efficient data structures for projection maintenance have led to recent breakthroughs in many convex programming algorithms. In this work, we further extend this framework to the Kronecker product structure. Given a constraint matrix {sf A} and a positive semi-definite matrix Win R^{ntimes n} with a sparse eigenbasis, we consider the task of maintaining the projection in the form of {sf B}^top({sf B}{sf B}^top)^{-1}{sf B}, where {sf B}={sf A}(Wotimes I) or {sf B}={sf A}(W^{1/2}otimes W^{1/2}). At each iteration, the weight matrix W receives a low rank change and we receive a new vector h. The goal is to maintain the projection matrix and answer the query {sf B}^top({sf B}{sf B}^top)^{-1}{sf B}h with good approximation guarantees. We design a fast dynamic data structure for this task and it is robust against an adaptive adversary. Following the beautiful and pioneering work of [Beimel, Kaplan, Mansour, Nissim, Saranurak and Stemmer, STOC'22], we use tools from differential privacy to reduce the randomness required by the data structure and further improve the running time.

We introduce pixelSplat, a feed-forward model that learns to reconstruct 3D radiance fields parameterized by 3D Gaussian primitives from pairs of images. Our model features real-time and memory-efficient rendering for scalable training as well as fast 3D reconstruction at inference time. To overcome local minima inherent to sparse and locally supported representations, we predict a dense probability distribution over 3D and sample Gaussian means from that probability distribution. We make this sampling operation differentiable via a reparameterization trick, allowing us to back-propagate gradients through the Gaussian splatting representation. We benchmark our method on wide-baseline novel view synthesis on the real-world RealEstate10k and ACID datasets, where we outperform state-of-the-art light field transformers and accelerate rendering by 2.5 orders of magnitude while reconstructing an interpretable and editable 3D radiance field.

Integer Linear Programs (ILPs) are powerful tools for modeling and solving a large number of combinatorial optimization problems. Recently, it has been shown that Large Neighborhood Search (LNS), as a heuristic algorithm, can find high quality solutions to ILPs faster than Branch and Bound. However, how to find the right heuristics to maximize the performance of LNS remains an open problem. In this paper, we propose a novel approach, CL-LNS, that delivers state-of-the-art anytime performance on several ILP benchmarks measured by metrics including the primal gap, the primal integral, survival rates and the best performing rate. Specifically, CL-LNS collects positive and negative solution samples from an expert heuristic that is slow to compute and learns a new one with a contrastive loss. We use graph attention networks and a richer set of features to further improve its performance.

In this work, we present a variety of novel information-theoretic generalization bounds for learning algorithms, from the supersample setting of Steinke & Zakynthinou (2020)-the setting of the "conditional mutual information" framework. Our development exploits projecting the loss pair (obtained from a training instance and a testing instance) down to a single number and correlating loss values with a Rademacher sequence (and its shifted variants). The presented bounds include square-root bounds, fast-rate bounds, including those based on variance and sharpness, and bounds for interpolating algorithms etc. We show theoretically or empirically that these bounds are tighter than all information-theoretic bounds known to date on the same supersample setting.

We propose algorithms for approximate filtering and smoothing in high-dimensional Factorial hidden Markov models. The approximation involves discarding, in a principled way, likelihood factors according to a notion of locality in a factor graph associated with the emission distribution. This allows the exponential-in-dimension cost of exact filtering and smoothing to be avoided. We prove that the approximation accuracy, measured in a local total variation norm, is "dimension-free" in the sense that as the overall dimension of the model increases the error bounds we derive do not necessarily degrade. A key step in the analysis is to quantify the error introduced by localizing the likelihood function in a Bayes' rule update. The factorial structure of the likelihood function which we exploit arises naturally when data have known spatial or network structure. We demonstrate the new algorithms on synthetic examples and a London Underground passenger flow problem, where the factor graph is effectively given by the train network.

Dimensionality reduction methods are unsupervised approaches which learn low-dimensional spaces where some properties of the initial space, typically the notion of "neighborhood", are preserved. Such methods usually require propagation on large k-NN graphs or complicated optimization solvers. On the other hand, self-supervised learning approaches, typically used to learn representations from scratch, rely on simple and more scalable frameworks for learning. In this paper, we propose TLDR, a dimensionality reduction method for generic input spaces that is porting the recent self-supervised learning framework of Zbontar et al. (2021) to the specific task of dimensionality reduction, over arbitrary representations. We propose to use nearest neighbors to build pairs from a training set and a redundancy reduction loss to learn an encoder that produces representations invariant across such pairs. TLDR is a method that is simple, easy to train, and of broad applicability; it consists of an offline nearest neighbor computation step that can be highly approximated, and a straightforward learning process. Aiming for scalability, we focus on improving linear dimensionality reduction, and show consistent gains on image and document retrieval tasks, e.g. gaining +4% mAP over PCA on ROxford for GeM- AP, improving the performance of DINO on ImageNet or retaining it with a 10x compression.

Proximal operators are ubiquitous in inverse problems, commonly appearing as part of algorithmic strategies to regularize problems that are otherwise ill-posed. Modern deep learning models have been brought to bear for these tasks too, as in the framework of plug-and-play or deep unrolling, where they loosely resemble proximal operators. Yet, something essential is lost in employing these purely data-driven approaches: there is no guarantee that a general deep network represents the proximal operator of any function, nor is there any characterization of the function for which the network might provide some approximate proximal. This not only makes guaranteeing convergence of iterative schemes challenging but, more fundamentally, complicates the analysis of what has been learned by these networks about their training data. Herein we provide a framework to develop learned proximal networks (LPN), prove that they provide exact proximal operators for a data-driven nonconvex regularizer, and show how a new training strategy, dubbed proximal matching, provably promotes the recovery of the log-prior of the true data distribution. Such LPN provide general, unsupervised, expressive proximal operators that can be used for general inverse problems with convergence guarantees. We illustrate our results in a series of cases of increasing complexity, demonstrating that these models not only result in state-of-the-art performance, but provide a window into the resulting priors learned from data.

Recently, efficient fine-tuning of large-scale pre-trained models has attracted increasing research interests, where linear probing (LP) as a fundamental module is involved in exploiting the final representations for task-dependent classification. However, most of the existing methods focus on how to effectively introduce a few of learnable parameters, and little work pays attention to the commonly used LP module. In this paper, we propose a novel Moment Probing (MP) method to further explore the potential of LP. Distinguished from LP which builds a linear classification head based on the mean of final features (e.g., word tokens for ViT) or classification tokens, our MP performs a linear classifier on feature distribution, which provides the stronger representation ability by exploiting richer statistical information inherent in features. Specifically, we represent feature distribution by its characteristic function, which is efficiently approximated by using first- and second-order moments of features. Furthermore, we propose a multi-head convolutional cross-covariance (MHC^3) to compute second-order moments in an efficient and effective manner. By considering that MP could affect feature learning, we introduce a partially shared module to learn two recalibrating parameters (PSRP) for backbones based on MP, namely MP_{+}. Extensive experiments on ten benchmarks using various models show that our MP significantly outperforms LP and is competitive with counterparts at less training cost, while our MP_{+} achieves state-of-the-art performance.

Despite large neural networks demonstrating remarkable abilities to complete different tasks, they require excessive memory usage to store the optimization states for training. To alleviate this, the low-rank adaptation (LoRA) is proposed to reduce the optimization states by training fewer parameters. However, LoRA restricts overall weight update matrices to be low-rank, limiting the model performance. In this work, we investigate the dynamics of LoRA and identify that it can be approximated by a random projection. Based on this observation, we propose Flora, which is able to achieve high-rank updates by resampling the projection matrices while enjoying the sublinear space complexity of optimization states. We conduct experiments across different tasks and model architectures to verify the effectiveness of our approach.

We investigate a general formulation for clustering and transductive few-shot learning, which integrates prototype-based objectives, Laplacian regularization and supervision constraints from a few labeled data points. We propose a concave-convex relaxation of the problem, and derive a computationally efficient block-coordinate bound optimizer, with convergence guarantee. At each iteration,our optimizer computes independent (parallel) updates for each point-to-cluster assignment. Therefore, it could be trivially distributed for large-scale clustering and few-shot tasks. Furthermore, we provides a thorough convergence analysis based on point-to-set maps. Were port comprehensive clustering and few-shot learning experiments over various data sets, showing that our method yields competitive performances, in term of accuracy and optimization quality, while scaling up to large problems. Using standard training on the base classes, without resorting to complex meta-learning and episodic-training strategies, our approach outperforms state-of-the-art few-shot methods by significant margins, across various models, settings and data sets. Surprisingly, we found that even standard clustering procedures (e.g., K-means), which correspond to particular, non-regularized cases of our general model, already achieve competitive performances in comparison to the state-of-the-art in few-shot learning. These surprising results point to the limitations of the current few-shot benchmarks, and question the viability of a large body of convoluted few-shot learning techniques in the recent literature.

Point clouds are naturally sparse, while image pixels are dense. The inconsistency limits feature fusion from both modalities for point-wise scene flow estimation. Previous methods rarely predict scene flow from the entire point clouds of the scene with one-time inference due to the memory inefficiency and heavy overhead from distance calculation and sorting involved in commonly used farthest point sampling, KNN, and ball query algorithms for local feature aggregation. To mitigate these issues in scene flow learning, we regularize raw points to a dense format by storing 3D coordinates in 2D grids. Unlike the sampling operation commonly used in existing works, the dense 2D representation 1) preserves most points in the given scene, 2) brings in a significant boost of efficiency, and 3) eliminates the density gap between points and pixels, allowing us to perform effective feature fusion. We also present a novel warping projection technique to alleviate the information loss problem resulting from the fact that multiple points could be mapped into one grid during projection when computing cost volume. Sufficient experiments demonstrate the efficiency and effectiveness of our method, outperforming the prior-arts on the FlyingThings3D and KITTI dataset.

We propose a novel mixed-integer programming (MIP) formulation for generating precise sparse correspondences for highly non-rigid shapes. To this end, we introduce a projected Laplace-Beltrami operator (PLBO) which combines intrinsic and extrinsic geometric information to measure the deformation quality induced by predicted correspondences. We integrate the PLBO, together with an orientation-aware regulariser, into a novel MIP formulation that can be solved to global optimality for many practical problems. In contrast to previous methods, our approach is provably invariant to rigid transformations and global scaling, initialisation-free, has optimality guarantees, and scales to high resolution meshes with (empirically observed) linear time. We show state-of-the-art results for sparse non-rigid matching on several challenging 3D datasets, including data with inconsistent meshing, as well as applications in mesh-to-point-cloud matching.

While theoretically appealing, the application of the Wasserstein distance to large-scale machine learning problems has been hampered by its prohibitive computational cost. The sliced Wasserstein distance and its variants improve the computational efficiency through the random projection, yet they suffer from low accuracy if the number of projections is not sufficiently large, because the majority of projections result in trivially small values. In this work, we propose a new family of distance metrics, called augmented sliced Wasserstein distances (ASWDs), constructed by first mapping samples to higher-dimensional hypersurfaces parameterized by neural networks. It is derived from a key observation that (random) linear projections of samples residing on these hypersurfaces would translate to much more flexible nonlinear projections in the original sample space, so they can capture complex structures of the data distribution. We show that the hypersurfaces can be optimized by gradient ascent efficiently. We provide the condition under which the ASWD is a valid metric and show that this can be obtained by an injective neural network architecture. Numerical results demonstrate that the ASWD significantly outperforms other Wasserstein variants for both synthetic and real-world problems.

Catastrophic forgetting has been a major challenge in continual learning, where the model needs to learn new tasks with limited or no access to data from previously seen tasks. To tackle this challenge, methods based on knowledge distillation in feature space have been proposed and shown to reduce forgetting. However, most feature distillation methods directly constrain the new features to match the old ones, overlooking the need for plasticity. To achieve a better stability-plasticity trade-off, we propose Backward Feature Projection (BFP), a method for continual learning that allows the new features to change up to a learnable linear transformation of the old features. BFP preserves the linear separability of the old classes while allowing the emergence of new feature directions to accommodate new classes. BFP can be integrated with existing experience replay methods and boost performance by a significant margin. We also demonstrate that BFP helps learn a better representation space, in which linear separability is well preserved during continual learning and linear probing achieves high classification accuracy. The code can be found at https://github.com/rvl-lab-utoronto/BFP

Deep models have achieved impressive progress in solving partial differential equations (PDEs). A burgeoning paradigm is learning neural operators to approximate the input-output mappings of PDEs. While previous deep models have explored the multiscale architectures and various operator designs, they are limited to learning the operators as a whole in the coordinate space. In real physical science problems, PDEs are complex coupled equations with numerical solvers relying on discretization into high-dimensional coordinate space, which cannot be precisely approximated by a single operator nor efficiently learned due to the curse of dimensionality. We present Latent Spectral Models (LSM) toward an efficient and precise solver for high-dimensional PDEs. Going beyond the coordinate space, LSM enables an attention-based hierarchical projection network to reduce the high-dimensional data into a compact latent space in linear time. Inspired by classical spectral methods in numerical analysis, we design a neural spectral block to solve PDEs in the latent space that approximates complex input-output mappings via learning multiple basis operators, enjoying nice theoretical guarantees for convergence and approximation. Experimentally, LSM achieves consistent state-of-the-art and yields a relative gain of 11.5% averaged on seven benchmarks covering both solid and fluid physics. Code is available at https://github.com/thuml/Latent-Spectral-Models.

Dictionary learning is a classic representation learning method that has been widely applied in signal processing and data analytics. In this paper, we investigate a family of ell_p-norm (p>2,p in N) maximization approaches for the complete dictionary learning problem from theoretical and algorithmic aspects. Specifically, we prove that the global maximizers of these formulations are very close to the true dictionary with high probability, even when Gaussian noise is present. Based on the generalized power method (GPM), an efficient algorithm is then developed for the ell_p-based formulations. We further show the efficacy of the developed algorithm: for the population GPM algorithm over the sphere constraint, it first quickly enters the neighborhood of a global maximizer, and then converges linearly in this region. Extensive experiments will demonstrate that the ell_p-based approaches enjoy a higher computational efficiency and better robustness than conventional approaches and p=3 performs the best.

Point management is a critical component in optimizing 3D Gaussian Splatting (3DGS) models, as the point initiation (e.g., via structure from motion) is distributionally inappropriate. Typically, the Adaptive Density Control (ADC) algorithm is applied, leveraging view-averaged gradient magnitude thresholding for point densification, opacity thresholding for pruning, and regular all-points opacity reset. However, we reveal that this strategy is limited in tackling intricate/special image regions (e.g., transparent) as it is unable to identify all the 3D zones that require point densification, and lacking an appropriate mechanism to handle the ill-conditioned points with negative impacts (occlusion due to false high opacity). To address these limitations, we propose a Localized Point Management (LPM) strategy, capable of identifying those error-contributing zones in the highest demand for both point addition and geometry calibration. Zone identification is achieved by leveraging the underlying multiview geometry constraints, with the guidance of image rendering errors. We apply point densification in the identified zone, whilst resetting the opacity of those points residing in front of these regions so that a new opportunity is created to correct ill-conditioned points. Serving as a versatile plugin, LPM can be seamlessly integrated into existing 3D Gaussian Splatting models. Experimental evaluation across both static 3D and dynamic 4D scenes validate the efficacy of our LPM strategy in boosting a variety of existing 3DGS models both quantitatively and qualitatively. Notably, LPM improves both vanilla 3DGS and SpaceTimeGS to achieve state-of-the-art rendering quality while retaining real-time speeds, outperforming on challenging datasets such as Tanks & Temples and the Neural 3D Video Dataset.

We study the implications of the modeling choice to use a graph, instead of a hypergraph, to represent real-world interconnected systems whose constituent relationships are of higher order by nature. Such a modeling choice typically involves an underlying projection process that maps the original hypergraph onto a graph, and is common in graph-based analysis. While hypergraph projection can potentially lead to loss of higher-order relations, there exists very limited studies on the consequences of doing so, as well as its remediation. This work fills this gap by doing two things: (1) we develop analysis based on graph and set theory, showing two ubiquitous patterns of hyperedges that are root to structural information loss in all hypergraph projections; we also quantify the combinatorial impossibility of recovering the lost higher-order structures if no extra help is provided; (2) we still seek to recover the lost higher-order structures in hypergraph projection, and in light of (1)'s findings we propose to relax the problem into a learning-based setting. Under this setting, we develop a learning-based hypergraph reconstruction method based on an important statistic of hyperedge distributions that we find. Our reconstruction method is evaluated on 8 real-world datasets under different settings, and exhibits consistently good performance. We also demonstrate benefits of the reconstructed hypergraphs via use cases of protein rankings and link predictions.

Non-linear state-space models, also known as general hidden Markov models, are ubiquitous in statistical machine learning, being the most classical generative models for serial data and sequences in general. The particle-based, rapid incremental smoother PaRIS is a sequential Monte Carlo (SMC) technique allowing for efficient online approximation of expectations of additive functionals under the smoothing distribution in these models. Such expectations appear naturally in several learning contexts, such as likelihood estimation (MLE) and Markov score climbing (MSC). PARIS has linear computational complexity, limited memory requirements and comes with non-asymptotic bounds, convergence results and stability guarantees. Still, being based on self-normalised importance sampling, the PaRIS estimator is biased. Our first contribution is to design a novel additive smoothing algorithm, the Parisian particle Gibbs PPG sampler, which can be viewed as a PaRIS algorithm driven by conditional SMC moves, resulting in bias-reduced estimates of the targeted quantities. We substantiate the PPG algorithm with theoretical results, including new bounds on bias and variance as well as deviation inequalities. Our second contribution is to apply PPG in a learning framework, covering MLE and MSC as special examples. In this context, we establish, under standard assumptions, non-asymptotic bounds highlighting the value of bias reduction and the implicit Rao--Blackwellization of PPG. These are the first non-asymptotic results of this kind in this setting. We illustrate our theoretical results with numerical experiments supporting our claims.

We investigate a primal-dual (PD) method for the saddle point problem (SPP) that uses a linear approximation of the primal function instead of the standard proximal step, resulting in a linearized PD (LPD) method. For convex-strongly concave SPP, we observe that the LPD method has a suboptimal dependence on the Lipschitz constant of the primal function. To fix this issue, we combine features of Accelerated Gradient Descent with the LPD method resulting in a single-loop Accelerated Linearized Primal-Dual (ALPD) method. ALPD method achieves the optimal gradient complexity when the SPP has a semi-linear coupling function. We also present an inexact ALPD method for SPPs with a general nonlinear coupling function that maintains the optimal gradient evaluations of the primal parts and significantly improves the gradient evaluations of the coupling term compared to the ALPD method. We verify our findings with numerical experiments.

We study the approximability of an existing framework for clustering edge-colored hypergraphs, which is closely related to chromatic correlation clustering and is motivated by machine learning and data mining applications where the goal is to cluster a set of objects based on multiway interactions of different categories or types. We present improved approximation guarantees based on linear programming, and show they are tight by proving a matching integrality gap. Our results also include new approximation hardness results, a combinatorial 2-approximation whose runtime is linear in the hypergraph size, and several new connections to well-studied objectives such as vertex cover and hypergraph multiway cut.

Training Large Language Models (LLMs) presents significant memory challenges, predominantly due to the growing size of weights and optimizer states. Common memory-reduction approaches, such as low-rank adaptation (LoRA), add a trainable low-rank matrix to the frozen pre-trained weight in each layer, reducing trainable parameters and optimizer states. However, such approaches typically underperform training with full-rank weights in both pre-training and fine-tuning stages since they limit the parameter search to a low-rank subspace and alter the training dynamics, and further, may require full-rank warm start. In this work, we propose Gradient Low-Rank Projection (GaLore), a training strategy that allows full-parameter learning but is more memory-efficient than common low-rank adaptation methods such as LoRA. Our approach reduces memory usage by up to 65.5% in optimizer states while maintaining both efficiency and performance for pre-training on LLaMA 1B and 7B architectures with C4 dataset with up to 19.7B tokens, and on fine-tuning RoBERTa on GLUE tasks. Our 8-bit GaLore further reduces optimizer memory by up to 82.5% and total training memory by 63.3%, compared to a BF16 baseline. Notably, we demonstrate, for the first time, the feasibility of pre-training a 7B model on consumer GPUs with 24GB memory (e.g., NVIDIA RTX 4090) without model parallel, checkpointing, or offloading strategies.

In large scale machine learning, random sampling is a popular way to approximate datasets by a small representative subset of examples. In particular, sensitivity sampling is an intensely studied technique which provides provable guarantees on the quality of approximation, while reducing the number of examples to the product of the VC dimension d and the total sensitivity mathfrak S in remarkably general settings. However, guarantees going beyond this general bound of mathfrak S d are known in perhaps only one setting, for ell_2 subspace embeddings, despite intense study of sensitivity sampling in prior work. In this work, we show the first bounds for sensitivity sampling for ell_p subspace embeddings for pneq 2 that improve over the general mathfrak S d bound, achieving a bound of roughly mathfrak S^{2/p} for 1leq p<2 and mathfrak S^{2-2/p} for 2<p<infty. For 1leq p<2, we show that this bound is tight, in the sense that there exist matrices for which mathfrak S^{2/p} samples is necessary. Furthermore, our techniques yield further new results in the study of sampling algorithms, showing that the root leverage score sampling algorithm achieves a bound of roughly d for 1leq p<2, and that a combination of leverage score and sensitivity sampling achieves an improved bound of roughly d^{2/p}mathfrak S^{2-4/p} for 2<p<infty. Our sensitivity sampling results yield the best known sample complexity for a wide class of structured matrices that have small ell_p sensitivity.

Modern Large Language Models (LLMs) are composed of matrices with billions of elements, making their storage and processing quite demanding in terms of computational resources and memory usage. Being significantly large, such matrices can often be expressed in low-rank format with potential to relax resource requirements. Unlike prior works which focus on developing novel matrix decomposition algorithms, in this work we first study the emergence of low-rank structures across matrices within different layers of LLMs and establish a consequential relationship between the gradient dynamics and emerging low-rank expressiveness of matrices. Our findings reveal that different layers exhibit varying levels of converged low-rank structure, necessitating a non-uniform rank reduction across them to minimize performance drop due to compression. In view of that, we present Weight Low-Rank Projection (WeLore) that unifies weight compression and memory-efficient fine-tuning as ONE, in a data-agnostic and one-shot way. WeLore capitalizes the heavy-tail distribution of singular values to identify a suitable rank reduction ratio for matrices within LLMs. Going beyond only as a compression technique, WeLore categorizes weight matrices into Low-rank Components (LRCs) and Non-Low-rank Components (N-LRCs) based on their ability to express themselves as low-rank. Our gradient perspective and extensive experiments illustrate that LRCs tend to have better finetuning capabilities and can closely mimic (sometimes outperform) the training loss trajectory and performance of full-finetuning with notable memory and compute footprint reduction. For example, finetuning a 50\% compressed LLaMa-2 7B model using only a fraction of parameters in LRCs (WeLore) can outperform its full finetuning with ~3x better throughput and ~0.6x GPU requirement. Our codes are available at https://github.com/VITA-Group/welore

Approximate inference in Gaussian process (GP) models with non-conjugate likelihoods gets entangled with the learning of the model hyperparameters. We improve hyperparameter learning in GP models and focus on the interplay between variational inference (VI) and the learning target. While VI's lower bound to the marginal likelihood is a suitable objective for inferring the approximate posterior, we show that a direct approximation of the marginal likelihood as in Expectation Propagation (EP) is a better learning objective for hyperparameter optimization. We design a hybrid training procedure to bring the best of both worlds: it leverages conjugate-computation VI for inference and uses an EP-like marginal likelihood approximation for hyperparameter learning. We compare VI, EP, Laplace approximation, and our proposed training procedure and empirically demonstrate the effectiveness of our proposal across a wide range of data sets.

Recent low-rank training methods, such as GaLore, have significantly reduced the memory required to optimize large language models (LLMs). However, these methods often suffer from time-consuming low-rank projection estimations. In particular, the singular value decomposition (SVD) in GaLore can consume more than 80\% of the total training time. To address this issue, we propose GaLore+, which uses cross-head low-rank projection to reduce the substantial time consumption in estimating low-rank projections for multi-head attention. In addition, we employ randomized subspace iteration to achieve fast SVD. To further enhance performance, we propose sparsely coded residuals to reduce the errors caused by low-rank approximation on the first- and second-order moments of the optimizers and weight updates. We evaluate GaLore+ on arithmetic reasoning and natural language generation datasets. Our experiments demonstrate that GaLore+ delivers superior performance while achieving approximately 4times fine-tuning speed compared to vanilla GaLore.

We propose a Pose-Free Large Reconstruction Model (PF-LRM) for reconstructing a 3D object from a few unposed images even with little visual overlap, while simultaneously estimating the relative camera poses in ~1.3 seconds on a single A100 GPU. PF-LRM is a highly scalable method utilizing the self-attention blocks to exchange information between 3D object tokens and 2D image tokens; we predict a coarse point cloud for each view, and then use a differentiable Perspective-n-Point (PnP) solver to obtain camera poses. When trained on a huge amount of multi-view posed data of ~1M objects, PF-LRM shows strong cross-dataset generalization ability, and outperforms baseline methods by a large margin in terms of pose prediction accuracy and 3D reconstruction quality on various unseen evaluation datasets. We also demonstrate our model's applicability in downstream text/image-to-3D task with fast feed-forward inference. Our project website is at: https://totoro97.github.io/pf-lrm .

Instance segmentation on point clouds is crucially important for 3D scene understanding. Most SOTAs adopt distance clustering, which is typically effective but does not perform well in segmenting adjacent objects with the same semantic label (especially when they share neighboring points). Due to the uneven distribution of offset points, these existing methods can hardly cluster all instance points. To this end, we design a novel divide-and-conquer strategy named PBNet that binarizes each point and clusters them separately to segment instances. Our binary clustering divides offset instance points into two categories: high and low density points (HPs vs. LPs). Adjacent objects can be clearly separated by removing LPs, and then be completed and refined by assigning LPs via a neighbor voting method. To suppress potential over-segmentation, we propose to construct local scenes with the weight mask for each instance. As a plug-in, the proposed binary clustering can replace the traditional distance clustering and lead to consistent performance gains on many mainstream baselines. A series of experiments on ScanNetV2 and S3DIS datasets indicate the superiority of our model. In particular, PBNet ranks first on the ScanNetV2 official benchmark challenge, achieving the highest mAP.

We present latentSplat, a method to predict semantic Gaussians in a 3D latent space that can be splatted and decoded by a light-weight generative 2D architecture. Existing methods for generalizable 3D reconstruction either do not scale to large scenes and resolutions, or are limited to interpolation of close input views. latentSplat combines the strengths of regression-based and generative approaches while being trained purely on readily available real video data. The core of our method are variational 3D Gaussians, a representation that efficiently encodes varying uncertainty within a latent space consisting of 3D feature Gaussians. From these Gaussians, specific instances can be sampled and rendered via efficient splatting and a fast, generative decoder. We show that latentSplat outperforms previous works in reconstruction quality and generalization, while being fast and scalable to high-resolution data.

We present a novel stochastic variational Gaussian process (GP) inference method, based on a posterior over a learnable set of weighted pseudo input-output points (coresets). Instead of a free-form variational family, the proposed coreset-based, variational tempered family for GPs (CVTGP) is defined in terms of the GP prior and the data-likelihood; hence, accommodating the modeling inductive biases. We derive CVTGP's lower bound for the log-marginal likelihood via marginalization of the proposed posterior over latent GP coreset variables, and show it is amenable to stochastic optimization. CVTGP reduces the learnable parameter size to O(M), enjoys numerical stability, and maintains O(M^3) time- and O(M^2) space-complexity, by leveraging a coreset-based tempered posterior that, in turn, provides sparse and explainable representations of the data. Results on simulated and real-world regression problems with Gaussian observation noise validate that CVTGP provides better evidence lower-bound estimates and predictive root mean squared error than alternative stochastic GP inference methods.

Large pre-trained models (LPMs), such as LLaMA and GLM, have shown exceptional performance across various tasks through fine-tuning. Although low-rank adaption (LoRA) has emerged to cheaply fine-tune these LPMs on downstream tasks, their deployment is still hindered by the vast model scale and computational costs. Neural network pruning offers a way to compress LPMs. However, the current pruning methods designed for LPMs are not compatible with LoRA. This is due to their utilization of unstructured pruning on LPMs, impeding the merging of LoRA weights, or their dependence on the gradients of pre-trained weights to guide pruning, which can impose significant memory overhead. To this end, we propose LoRAPrune, a new framework that delivers an accurate, compact model for efficient inference in a highly memory-effective manner. Specifically, we first design a LoRA-guided pruning criterion, which uses the weights and gradients of LoRA, rather than the gradients of pre-trained weights for importance estimation. We then propose a structured iterative pruning procedure, to remove redundant channels and heads. Extensive experimental results demonstrate the superior performance of our LoRAPrune over existing approaches on the LLaMA series models. For instance, at a 50\% compression rate, LoRAPrune outperforms LLM-Pruner by a perplexity reduction of 8.0 on WikiText2 and 16.05 on PTB datasets, while concurrently reducing memory usage by 52.6\%. The code will be released after review

Conditional 3D generation is undergoing a significant advancement, enabling the free creation of 3D content from inputs such as text or 2D images. However, previous approaches have suffered from low inference efficiency, limited generation categories, and restricted downstream applications. In this work, we revisit the impact of different 3D representations on generation quality and efficiency. We propose a progressive generation method through Voxel-Point Progressive Representation (VPP). VPP leverages structured voxel representation in the proposed Voxel Semantic Generator and the sparsity of unstructured point representation in the Point Upsampler, enabling efficient generation of multi-category objects. VPP can generate high-quality 8K point clouds within 0.2 seconds. Additionally, the masked generation Transformer allows for various 3D downstream tasks, such as generation, editing, completion, and pre-training. Extensive experiments demonstrate that VPP efficiently generates high-fidelity and diverse 3D shapes across different categories, while also exhibiting excellent representation transfer performance. Codes will be released at https://github.com/qizekun/VPP.

Multiple types of inference are available for probabilistic graphical models, e.g., marginal, maximum-a-posteriori, and even marginal maximum-a-posteriori. Which one do researchers mean when they talk about ``planning as inference''? There is no consistency in the literature, different types are used, and their ability to do planning is further entangled with specific approximations or additional constraints. In this work we use the variational framework to show that, just like all commonly used types of inference correspond to different weightings of the entropy terms in the variational problem, planning corresponds exactly to a different set of weights. This means that all the tricks of variational inference are readily applicable to planning. We develop an analogue of loopy belief propagation that allows us to perform approximate planning in factored-state Markov decisions processes without incurring intractability due to the exponentially large state space. The variational perspective shows that the previous types of inference for planning are only adequate in environments with low stochasticity, and allows us to characterize each type by its own merits, disentangling the type of inference from the additional approximations that its practical use requires. We validate these results empirically on synthetic MDPs and tasks posed in the International Planning Competition.

Given a matrix Ain R^{ntimes d} and a vector bin R^n, we consider the regression problem with ell_infty guarantees: finding a vector x'in R^d such that |x'-x^*|_infty leq epsilon{d}cdot |Ax^*-b|_2cdot |A^dagger| where x^*=argmin_{xin R^d}|Ax-b|_2. One popular approach for solving such ell_2 regression problem is via sketching: picking a structured random matrix Sin R^{mtimes n} with mll n and SA can be quickly computed, solve the ``sketched'' regression problem argmin_{xin R^d} |SAx-Sb|_2. In this paper, we show that in order to obtain such ell_infty guarantee for ell_2 regression, one has to use sketching matrices that are dense. To the best of our knowledge, this is the first user case in which dense sketching matrices are necessary. On the algorithmic side, we prove that there exists a distribution of dense sketching matrices with m=epsilon^{-2}dlog^3(n/delta) such that solving the sketched regression problem gives the ell_infty guarantee, with probability at least 1-delta. Moreover, the matrix SA can be computed in time O(ndlog n). Our row count is nearly-optimal up to logarithmic factors, and significantly improves the result in [Price, Song and Woodruff, ICALP'17], in which a super-linear in d rows, m=Omega(epsilon^{-2}d^{1+gamma}) for gamma=Theta(frac{loglog n{log d}}) is required. We also develop a novel analytical framework for ell_infty guarantee regression that utilizes the Oblivious Coordinate-wise Embedding (OCE) property introduced in [Song and Yu, ICML'21]. Our analysis is arguably much simpler and more general than [Price, Song and Woodruff, ICALP'17], and it extends to dense sketches for tensor product of vectors.

We consider the block coordinate descent methods of Gauss-Seidel type with proximal regularization (BCD-PR), which is a classical method of minimizing general nonconvex objectives under constraints that has a wide range of practical applications. We theoretically establish the worst-case complexity bound for this algorithm. Namely, we show that for general nonconvex smooth objectives with block-wise constraints, the classical BCD-PR algorithm converges to an epsilon-stationary point within O(1/epsilon) iterations. Under a mild condition, this result still holds even if the algorithm is executed inexactly in each step. As an application, we propose a provable and efficient algorithm for `Wasserstein CP-dictionary learning', which seeks a set of elementary probability distributions that can well-approximate a given set of d-dimensional joint probability distributions. Our algorithm is a version of BCD-PR that operates in the dual space, where the primal problem is regularized both entropically and proximally.

In contrast to classical reinforcement learning, distributional reinforcement learning algorithms aim to learn the distribution of returns rather than their expected value. Since the nature of the return distribution is generally unknown a priori or arbitrarily complex, a common approach finds approximations within a set of representable, parametric distributions. Typically, this involves a projection of the unconstrained distribution onto the set of simplified distributions. We argue that this projection step entails a strong inductive bias when coupled with neural networks and gradient descent, thereby profoundly impacting the generalization behavior of learned models. In order to facilitate reliable uncertainty estimation through diversity, this work studies the combination of several different projections and representations in a distributional ensemble. We establish theoretical properties of such projection ensembles and derive an algorithm that uses ensemble disagreement, measured by the average 1-Wasserstein distance, as a bonus for deep exploration. We evaluate our algorithm on the behavior suite benchmark and find that diverse projection ensembles lead to significant performance improvements over existing methods on a wide variety of tasks with the most pronounced gains in directed exploration problems.

Generative Adversarial Networks (GANs), especially the recent style-based generators (StyleGANs), have versatile semantics in the structured latent space. Latent semantics discovery methods emerge to move around the latent code such that only one factor varies during the traversal. Recently, an unsupervised method proposed a promising direction to directly use the eigenvectors of the projection matrix that maps latent codes to features as the interpretable directions. However, one overlooked fact is that the projection matrix is non-orthogonal and the number of eigenvectors is too large. The non-orthogonality would entangle semantic attributes in the top few eigenvectors, and the large dimensionality might result in meaningless variations among the directions even if the matrix is orthogonal. To avoid these issues, we propose Householder Projector, a flexible and general low-rank orthogonal matrix representation based on Householder transformations, to parameterize the projection matrix. The orthogonality guarantees that the eigenvectors correspond to disentangled interpretable semantics, while the low-rank property encourages that each identified direction has meaningful variations. We integrate our projector into pre-trained StyleGAN2/StyleGAN3 and evaluate the models on several benchmarks. Within only 1% of the original training steps for fine-tuning, our projector helps StyleGANs to discover more disentangled and precise semantic attributes without sacrificing image fidelity.

Compared to the wide array of advanced Monte Carlo methods supported by modern probabilistic programming languages (PPLs), PPL support for variational inference (VI) is less developed: users are typically limited to a predefined selection of variational objectives and gradient estimators, which are implemented monolithically (and without formal correctness arguments) in PPL backends. In this paper, we propose a more modular approach to supporting variational inference in PPLs, based on compositional program transformation. In our approach, variational objectives are expressed as programs, that may employ first-class constructs for computing densities of and expected values under user-defined models and variational families. We then transform these programs systematically into unbiased gradient estimators for optimizing the objectives they define. Our design enables modular reasoning about many interacting concerns, including automatic differentiation, density accumulation, tracing, and the application of unbiased gradient estimation strategies. Additionally, relative to existing support for VI in PPLs, our design increases expressiveness along three axes: (1) it supports an open-ended set of user-defined variational objectives, rather than a fixed menu of options; (2) it supports a combinatorial space of gradient estimation strategies, many not automated by today's PPLs; and (3) it supports a broader class of models and variational families, because it supports constructs for approximate marginalization and normalization (previously introduced only for Monte Carlo inference). We implement our approach in an extension to the Gen probabilistic programming system (genjax.vi, implemented in JAX), and evaluate on several deep generative modeling tasks, showing minimal performance overhead vs. hand-coded implementations and performance competitive with well-established open-source PPLs.

In this paper, we present a pure-Python library called PyPop7 for black-box optimization (BBO). As population-based methods are becoming increasingly popular for BBO, our design goal is to provide a unified API and elegant implementations for them, particularly in high-dimensional cases. Since population-based methods suffer easily from the curse of dimensionality owing to their random sampling nature, various improvements have been proposed to alleviate this issue via exploiting possible problem structures: such as space decomposition, low-memory approximation, low-rank metric learning, variance reduction, ensemble of random subspaces, model self-adaptation, and smoothing. Now PyPop7 has covered these advances with >72 versions and variants of 13 BBO algorithm families from different research communities. Its open-source code and full-fledged documents are available at https://github.com/Evolutionary-Intelligence/pypop and https://pypop.readthedocs.io, respectively.

This paper investigates scaling laws for local SGD in LLM training, a distributed optimization algorithm that facilitates training on loosely connected devices. Through extensive experiments, we show that local SGD achieves competitive results compared to conventional methods, given equivalent model parameters, datasets, and computational resources. Furthermore, we explore the application of local SGD in various practical scenarios, including multi-cluster setups and edge computing environments. Our findings elucidate the necessary conditions for effective multi-cluster LLM training and examine the potential and limitations of leveraging edge computing resources in the LLM training process. This demonstrates its viability as an alternative to single large-cluster training.

To achieve scalable and accurate inference for latent Gaussian processes, we propose a variational approximation based on a family of Gaussian distributions whose covariance matrices have sparse inverse Cholesky (SIC) factors. We combine this variational approximation of the posterior with a similar and efficient SIC-restricted Kullback-Leibler-optimal approximation of the prior. We then focus on a particular SIC ordering and nearest-neighbor-based sparsity pattern resulting in highly accurate prior and posterior approximations. For this setting, our variational approximation can be computed via stochastic gradient descent in polylogarithmic time per iteration. We provide numerical comparisons showing that the proposed double-Kullback-Leibler-optimal Gaussian-process approximation (DKLGP) can sometimes be vastly more accurate for stationary kernels than alternative approaches such as inducing-point and mean-field approximations at similar computational complexity.

Since the pioneering work on the lottery ticket hypothesis for graph neural networks (GNNs) was proposed in Chen et al. (2021), the study on finding graph lottery tickets (GLT) has become one of the pivotal focus in the GNN community, inspiring researchers to discover sparser GLT while achieving comparable performance to original dense networks. In parallel, the graph structure has gained substantial attention as a crucial factor in GNN training dynamics, also elucidated by several recent studies. Despite this, contemporary studies on GLT, in general, have not fully exploited inherent pathways in the graph structure and identified tickets in an iterative manner, which is time-consuming and inefficient. To address these limitations, we introduce TEDDY, a one-shot edge sparsification framework that leverages structural information by incorporating edge-degree information. Following edge sparsification, we encourage the parameter sparsity during training via simple projected gradient descent on the ell_0 ball. Given the target sparsity levels for both the graph structure and the model parameters, our TEDDY facilitates efficient and rapid realization of GLT within a single training. Remarkably, our experimental results demonstrate that TEDDY significantly surpasses conventional iterative approaches in generalization, even when conducting one-shot sparsification that solely utilizes graph structures, without taking feature information into account.

We study the problem of learning optimal policy from a set of discrete treatment options using observational data. We propose a piecewise linear neural network model that can balance strong prescriptive performance and interpretability, which we refer to as the prescriptive ReLU network, or P-ReLU. We show analytically that this model (i) partitions the input space into disjoint polyhedra, where all instances that belong to the same partition receive the same treatment, and (ii) can be converted into an equivalent prescriptive tree with hyperplane splits for interpretability. We demonstrate the flexibility of the P-ReLU network as constraints can be easily incorporated with minor modifications to the architecture. Through experiments, we validate the superior prescriptive accuracy of P-ReLU against competing benchmarks. Lastly, we present examples of interpretable prescriptive trees extracted from trained P-ReLUs using a real-world dataset, for both the unconstrained and constrained scenarios.

Consistency models are a nascent family of generative models that can sample high quality data in one step without the need for adversarial training. Current consistency models achieve optimal sample quality by distilling from pre-trained diffusion models and employing learned metrics such as LPIPS. However, distillation limits the quality of consistency models to that of the pre-trained diffusion model, and LPIPS causes undesirable bias in evaluation. To tackle these challenges, we present improved techniques for consistency training, where consistency models learn directly from data without distillation. We delve into the theory behind consistency training and identify a previously overlooked flaw, which we address by eliminating Exponential Moving Average from the teacher consistency model. To replace learned metrics like LPIPS, we adopt Pseudo-Huber losses from robust statistics. Additionally, we introduce a lognormal noise schedule for the consistency training objective, and propose to double total discretization steps every set number of training iterations. Combined with better hyperparameter tuning, these modifications enable consistency models to achieve FID scores of 2.51 and 3.25 on CIFAR-10 and ImageNet 64times 64 respectively in a single sampling step. These scores mark a 3.5times and 4times improvement compared to prior consistency training approaches. Through two-step sampling, we further reduce FID scores to 2.24 and 2.77 on these two datasets, surpassing those obtained via distillation in both one-step and two-step settings, while narrowing the gap between consistency models and other state-of-the-art generative models.

Sequential learning with Gaussian processes (GPs) is challenging when access to past data is limited, for example, in continual and active learning. In such cases, errors can accumulate over time due to inaccuracies in the posterior, hyperparameters, and inducing points, making accurate learning challenging. Here, we present a method to keep all such errors in check using the recently proposed dual sparse variational GP. Our method enables accurate inference for generic likelihoods and improves learning by actively building and updating a memory of past data. We demonstrate its effectiveness in several applications involving Bayesian optimization, active learning, and continual learning.

Optimal transport aligns samples across distributions by minimizing the transportation cost between them, e.g., the geometric distances. Yet, it ignores coherence structure in the data such as clusters, does not handle outliers well, and cannot integrate new data points. To address these drawbacks, we propose InfoOT, an information-theoretic extension of optimal transport that maximizes the mutual information between domains while minimizing geometric distances. The resulting objective can still be formulated as a (generalized) optimal transport problem, and can be efficiently solved by projected gradient descent. This formulation yields a new projection method that is robust to outliers and generalizes to unseen samples. Empirically, InfoOT improves the quality of alignments across benchmarks in domain adaptation, cross-domain retrieval, and single-cell alignment.

Generating high-quality 3D content requires models capable of learning robust distributions of complex scenes and the real-world objects within them. Recent Gaussian-based 3D reconstruction techniques have achieved impressive results in recovering high-fidelity 3D assets from sparse input images by predicting 3D Gaussians in a feed-forward manner. However, these techniques often lack the extensive priors and expressiveness offered by Diffusion Models. On the other hand, 2D Diffusion Models, which have been successfully applied to denoise multiview images, show potential for generating a wide range of photorealistic 3D outputs but still fall short on explicit 3D priors and consistency. In this work, we aim to bridge these two approaches by introducing DSplats, a novel method that directly denoises multiview images using Gaussian Splat-based Reconstructors to produce a diverse array of realistic 3D assets. To harness the extensive priors of 2D Diffusion Models, we incorporate a pretrained Latent Diffusion Model into the reconstructor backbone to predict a set of 3D Gaussians. Additionally, the explicit 3D representation embedded in the denoising network provides a strong inductive bias, ensuring geometrically consistent novel view generation. Our qualitative and quantitative experiments demonstrate that DSplats not only produces high-quality, spatially consistent outputs, but also sets a new standard in single-image to 3D reconstruction. When evaluated on the Google Scanned Objects dataset, DSplats achieves a PSNR of 20.38, an SSIM of 0.842, and an LPIPS of 0.109.

In this paper, we study the problem of inference in high-order structured prediction tasks. In the context of Markov random fields, the goal of a high-order inference task is to maximize a score function on the space of labels, and the score function can be decomposed into sum of unary and high-order potentials. We apply a generative model approach to study the problem of high-order inference, and provide a two-stage convex optimization algorithm for exact label recovery. We also provide a new class of hypergraph structural properties related to hyperedge expansion that drives the success in general high-order inference problems. Finally, we connect the performance of our algorithm and the hyperedge expansion property using a novel hypergraph Cheeger-type inequality.

Continuous latent variables (LVs) are a key ingredient of many generative models, as they allow modelling expressive mixtures with an uncountable number of components. In contrast, probabilistic circuits (PCs) are hierarchical discrete mixtures represented as computational graphs composed of input, sum and product units. Unlike continuous LV models, PCs provide tractable inference but are limited to discrete LVs with categorical (i.e. unordered) states. We bridge these model classes by introducing probabilistic integral circuits (PICs), a new language of computational graphs that extends PCs with integral units representing continuous LVs. In the first place, PICs are symbolic computational graphs and are fully tractable in simple cases where analytical integration is possible. In practice, we parameterise PICs with light-weight neural nets delivering an intractable hierarchical continuous mixture that can be approximated arbitrarily well with large PCs using numerical quadrature. On several distribution estimation benchmarks, we show that such PIC-approximating PCs systematically outperform PCs commonly learned via expectation-maximization or SGD.

3D Gaussian Splatting has demonstrated notable success in large-scale scene reconstruction, but challenges persist due to high training memory consumption and storage overhead. Hybrid representations that integrate implicit and explicit features offer a way to mitigate these limitations. However, when applied in parallelized block-wise training, two critical issues arise since reconstruction accuracy deteriorates due to reduced data diversity when training each block independently, and parallel training restricts the number of divided blocks to the available number of GPUs. To address these issues, we propose Momentum-GS, a novel approach that leverages momentum-based self-distillation to promote consistency and accuracy across the blocks while decoupling the number of blocks from the physical GPU count. Our method maintains a teacher Gaussian decoder updated with momentum, ensuring a stable reference during training. This teacher provides each block with global guidance in a self-distillation manner, promoting spatial consistency in reconstruction. To further ensure consistency across the blocks, we incorporate block weighting, dynamically adjusting each block's weight according to its reconstruction accuracy. Extensive experiments on large-scale scenes show that our method consistently outperforms existing techniques, achieving a 12.8% improvement in LPIPS over CityGaussian with much fewer divided blocks and establishing a new state of the art. Project page: https://jixuan-fan.github.io/Momentum-GS_Page/

We propose a new approach for propagating stable probability distributions through neural networks. Our method is based on local linearization, which we show to be an optimal approximation in terms of total variation distance for the ReLU non-linearity. This allows propagating Gaussian and Cauchy input uncertainties through neural networks to quantify their output uncertainties. To demonstrate the utility of propagating distributions, we apply the proposed method to predicting calibrated confidence intervals and selective prediction on out-of-distribution data. The results demonstrate a broad applicability of propagating distributions and show the advantages of our method over other approaches such as moment matching.

Unsupervised learning of depth from indoor monocular videos is challenging as the artificial environment contains many textureless regions. Fortunately, the indoor scenes are full of specific structures, such as planes and lines, which should help guide unsupervised depth learning. This paper proposes PLNet that leverages the plane and line priors to enhance the depth estimation. We first represent the scene geometry using local planar coefficients and impose the smoothness constraint on the representation. Moreover, we enforce the planar and linear consistency by randomly selecting some sets of points that are probably coplanar or collinear to construct simple and effective consistency losses. To verify the proposed method's effectiveness, we further propose to evaluate the flatness and straightness of the predicted point cloud on the reliable planar and linear regions. The regularity of these regions indicates quality indoor reconstruction. Experiments on NYU Depth V2 and ScanNet show that PLNet outperforms existing methods. The code is available at https://github.com/HalleyJiang/PLNet.

We present FastRP, a scalable and performant algorithm for learning distributed node representations in a graph. FastRP is over 4,000 times faster than state-of-the-art methods such as DeepWalk and node2vec, while achieving comparable or even better performance as evaluated on several real-world networks on various downstream tasks. We observe that most network embedding methods consist of two components: construct a node similarity matrix and then apply dimension reduction techniques to this matrix. We show that the success of these methods should be attributed to the proper construction of this similarity matrix, rather than the dimension reduction method employed. FastRP is proposed as a scalable algorithm for network embeddings. Two key features of FastRP are: 1) it explicitly constructs a node similarity matrix that captures transitive relationships in a graph and normalizes matrix entries based on node degrees; 2) it utilizes very sparse random projection, which is a scalable optimization-free method for dimension reduction. An extra benefit from combining these two design choices is that it allows the iterative computation of node embeddings so that the similarity matrix need not be explicitly constructed, which further speeds up FastRP. FastRP is also advantageous for its ease of implementation, parallelization and hyperparameter tuning. The source code is available at https://github.com/GTmac/FastRP.

Updating a truncated Singular Value Decomposition (SVD) is crucial in representation learning, especially when dealing with large-scale data matrices that continuously evolve in practical scenarios. Aligning SVD-based models with fast-paced updates becomes increasingly important. Existing methods for updating truncated SVDs employ Rayleigh-Ritz projection procedures, where projection matrices are augmented based on original singular vectors. However, these methods suffer from inefficiency due to the densification of the update matrix and the application of the projection to all singular vectors. To address these limitations, we introduce a novel method for dynamically approximating the truncated SVD of a sparse and temporally evolving matrix. Our approach leverages sparsity in the orthogonalization process of augmented matrices and utilizes an extended decomposition to independently store projections in the column space of singular vectors. Numerical experiments demonstrate a remarkable efficiency improvement of an order of magnitude compared to previous methods. Remarkably, this improvement is achieved while maintaining a comparable precision to existing approaches.

We study the problem of visualizing large-scale and high-dimensional data in a low-dimensional (typically 2D or 3D) space. Much success has been reported recently by techniques that first compute a similarity structure of the data points and then project them into a low-dimensional space with the structure preserved. These two steps suffer from considerable computational costs, preventing the state-of-the-art methods such as the t-SNE from scaling to large-scale and high-dimensional data (e.g., millions of data points and hundreds of dimensions). We propose the LargeVis, a technique that first constructs an accurately approximated K-nearest neighbor graph from the data and then layouts the graph in the low-dimensional space. Comparing to t-SNE, LargeVis significantly reduces the computational cost of the graph construction step and employs a principled probabilistic model for the visualization step, the objective of which can be effectively optimized through asynchronous stochastic gradient descent with a linear time complexity. The whole procedure thus easily scales to millions of high-dimensional data points. Experimental results on real-world data sets demonstrate that the LargeVis outperforms the state-of-the-art methods in both efficiency and effectiveness. The hyper-parameters of LargeVis are also much more stable over different data sets.

Gaussian processes (GPs) are popular nonparametric statistical models for learning unknown functions and quantifying the spatiotemporal uncertainty in data. Recent works have extended GPs to model scalar and vector quantities distributed over non-Euclidean domains, including smooth manifolds appearing in numerous fields such as computer vision, dynamical systems, and neuroscience. However, these approaches assume that the manifold underlying the data is known, limiting their practical utility. We introduce RVGP, a generalisation of GPs for learning vector signals over latent Riemannian manifolds. Our method uses positional encoding with eigenfunctions of the connection Laplacian, associated with the tangent bundle, readily derived from common graph-based approximation of data. We demonstrate that RVGP possesses global regularity over the manifold, which allows it to super-resolve and inpaint vector fields while preserving singularities. Furthermore, we use RVGP to reconstruct high-density neural dynamics derived from low-density EEG recordings in healthy individuals and Alzheimer's patients. We show that vector field singularities are important disease markers and that their reconstruction leads to a comparable classification accuracy of disease states to high-density recordings. Thus, our method overcomes a significant practical limitation in experimental and clinical applications.

We present a novel Parameter-Efficient Fine-Tuning (PEFT) method, dubbed as Adaptive Freezing of Low Rank Adaptation (AFLoRA). Specifically, for each pre-trained frozen weight tensor, we add a parallel path of trainable low-rank matrices, namely a down-projection and an up-projection matrix, each of which is followed by a feature transformation vector. Based on a novel freezing score, we the incrementally freeze these projection matrices during fine-tuning to reduce the computation and alleviate over-fitting. Our experimental results demonstrate that we can achieve state-of-the-art performance with an average improvement of up to 0.85% as evaluated on GLUE benchmark while yeilding up to 9.5times fewer average trainable parameters. While compared in terms of runtime, AFLoRA can yield up to 1.86times improvement as opposed to similar PEFT alternatives. Besides the practical utility of our approach, we provide insights on the trainability requirements of LoRA paths at different modules and the freezing schedule for the different projection matrices. Code will be released.

We propose Long-LRM, a generalizable 3D Gaussian reconstruction model that is capable of reconstructing a large scene from a long sequence of input images. Specifically, our model can process 32 source images at 960x540 resolution within only 1.3 seconds on a single A100 80G GPU. Our architecture features a mixture of the recent Mamba2 blocks and the classical transformer blocks which allowed many more tokens to be processed than prior work, enhanced by efficient token merging and Gaussian pruning steps that balance between quality and efficiency. Unlike previous feed-forward models that are limited to processing 1~4 input images and can only reconstruct a small portion of a large scene, Long-LRM reconstructs the entire scene in a single feed-forward step. On large-scale scene datasets such as DL3DV-140 and Tanks and Temples, our method achieves performance comparable to optimization-based approaches while being two orders of magnitude more efficient. Project page: https://arthurhero.github.io/projects/llrm

Clustering is a widely deployed unsupervised learning tool. Model-based clustering is a flexible framework to tackle data heterogeneity when the clusters have different shapes. Likelihood-based inference for mixture distributions often involves non-convex and high-dimensional objective functions, imposing difficult computational and statistical challenges. The classic expectation-maximization (EM) algorithm is a computationally thrifty iterative method that maximizes a surrogate function minorizing the log-likelihood of observed data in each iteration, which however suffers from bad local maxima even in the special case of the standard Gaussian mixture model with common isotropic covariance matrices. On the other hand, recent studies reveal that the unique global solution of a semidefinite programming (SDP) relaxed K-means achieves the information-theoretically sharp threshold for perfectly recovering the cluster labels under the standard Gaussian mixture model. In this paper, we extend the SDP approach to a general setting by integrating cluster labels as model parameters and propose an iterative likelihood adjusted SDP (iLA-SDP) method that directly maximizes the exact observed likelihood in the presence of data heterogeneity. By lifting the cluster assignment to group-specific membership matrices, iLA-SDP avoids centroids estimation -- a key feature that allows exact recovery under well-separateness of centroids without being trapped by their adversarial configurations. Thus iLA-SDP is less sensitive than EM to initialization and more stable on high-dimensional data. Our numeric experiments demonstrate that iLA-SDP can achieve lower mis-clustering errors over several widely used clustering methods including K-means, SDP and EM algorithms.

We consider the problem of estimating (diagonally dominant) M-matrices as precision matrices in Gaussian graphical models. These models exhibit intriguing properties, such as the existence of the maximum likelihood estimator with merely two observations for M-matrices lauritzen2019maximum,slawski2015estimation and even one observation for diagonally dominant M-matrices truell2021maximum. We propose an adaptive multiple-stage estimation method that refines the estimate by solving a weighted ell_1-regularized problem at each stage. Furthermore, we develop a unified framework based on the gradient projection method to solve the regularized problem, incorporating distinct projections to handle the constraints of M-matrices and diagonally dominant M-matrices. A theoretical analysis of the estimation error is provided. Our method outperforms state-of-the-art methods in precision matrix estimation and graph edge identification, as evidenced by synthetic and financial time-series data sets.

This paper studies the online node classification problem under a transductive learning setting. Current methods either invert a graph kernel matrix with O(n^3) runtime and O(n^2) space complexity or sample a large volume of random spanning trees, thus are difficult to scale to large graphs. In this work, we propose an improvement based on the online relaxation technique introduced by a series of works (Rakhlin et al.,2012; Rakhlin and Sridharan, 2015; 2017). We first prove an effective regret O(n^{1+gamma}) when suitable parameterized graph kernels are chosen, then propose an approximate algorithm FastONL enjoying O(kn^{1+gamma}) regret based on this relaxation. The key of FastONL is a generalized local push method that effectively approximates inverse matrix columns and applies to a series of popular kernels. Furthermore, the per-prediction cost is O(vol({S})log 1/epsilon) locally dependent on the graph with linear memory cost. Experiments show that our scalable method enjoys a better tradeoff between local and global consistency.

The rapid growth of model scale has necessitated substantial computational resources for fine-tuning. Existing approach such as Low-Rank Adaptation (LoRA) has sought to address the problem of handling the large updated parameters in full fine-tuning. However, LoRA utilize random initialization and optimization of low-rank matrices to approximate updated weights, which can result in suboptimal convergence and an accuracy gap compared to full fine-tuning. To address these issues, we propose LoLDU, a Parameter-Efficient Fine-Tuning (PEFT) approach that significantly reduces trainable parameters by 2600 times compared to regular PEFT methods while maintaining comparable performance. LoLDU leverages Lower-Diag-Upper Decomposition (LDU) to initialize low-rank matrices for faster convergence and orthogonality. We focus on optimizing the diagonal matrix for scaling transformations. To the best of our knowledge, LoLDU has the fewest parameters among all PEFT approaches. We conducted extensive experiments across 4 instruction-following datasets, 6 natural language understanding (NLU) datasets, 8 image classification datasets, and image generation datasets with multiple model types (LLaMA2, RoBERTa, ViT, and Stable Diffusion), providing a comprehensive and detailed analysis. Our open-source code can be accessed at https://github.com/SKDDJ/LoLDU{https://github.com/SKDDJ/LoLDU}.

Modern ML applications increasingly rely on complex deep learning models and large datasets. There has been an exponential growth in the amount of computation needed to train the largest models. Therefore, to scale computation and data, these models are inevitably trained in a distributed manner in clusters of nodes, and their updates are aggregated before being applied to the model. However, a distributed setup is prone to Byzantine failures of individual nodes, components, and software. With data augmentation added to these settings, there is a critical need for robust and efficient aggregation systems. We define the quality of workers as reconstruction ratios in (0,1], and formulate aggregation as a Maximum Likelihood Estimation procedure using Beta densities. We show that the Regularized form of log-likelihood wrt subspace can be approximately solved using iterative least squares solver, and provide convergence guarantees using recent Convex Optimization landscape results. Our empirical findings demonstrate that our approach significantly enhances the robustness of state-of-the-art Byzantine resilient aggregators. We evaluate our method in a distributed setup with a parameter server, and show simultaneous improvements in communication efficiency and accuracy across various tasks. The code is publicly available at https://github.com/hamidralmasi/FlagAggregator

We address the problem of learning the dynamics of an unknown non-parametric system linking a target and a feature time series. The feature time series is measured on a sparse and irregular grid, while we have access to only a few points of the target time series. Once learned, we can use these dynamics to predict values of the target from the previous values of the feature time series. We frame this task as learning the solution map of a controlled differential equation (CDE). By leveraging the rich theory of signatures, we are able to cast this non-linear problem as a high-dimensional linear regression. We provide an oracle bound on the prediction error which exhibits explicit dependencies on the individual-specific sampling schemes. Our theoretical results are illustrated by simulations which show that our method outperforms existing algorithms for recovering the full time series while being computationally cheap. We conclude by demonstrating its potential on real-world epidemiological data.

Monocular depth estimation aims to infer a dense depth map from a single image, which is a fundamental and prevalent task in computer vision. Many previous works have shown impressive depth estimation results through carefully designed network structures, but they usually ignore the planar information and therefore perform poorly in low-texture areas of indoor scenes. In this paper, we propose Plane2Depth, which adaptively utilizes plane information to improve depth prediction within a hierarchical framework. Specifically, in the proposed plane guided depth generator (PGDG), we design a set of plane queries as prototypes to softly model planes in the scene and predict per-pixel plane coefficients. Then the predicted plane coefficients can be converted into metric depth values with the pinhole camera model. In the proposed adaptive plane query aggregation (APGA) module, we introduce a novel feature interaction approach to improve the aggregation of multi-scale plane features in a top-down manner. Extensive experiments show that our method can achieve outstanding performance, especially in low-texture or repetitive areas. Furthermore, under the same backbone network, our method outperforms the state-of-the-art methods on the NYU-Depth-v2 dataset, achieves competitive results with state-of-the-art methods KITTI dataset and can be generalized to unseen scenes effectively.

We study reinforcement learning with function approximation for large-scale Partially Observable Markov Decision Processes (POMDPs) where the state space and observation space are large or even continuous. Particularly, we consider Hilbert space embeddings of POMDP where the feature of latent states and the feature of observations admit a conditional Hilbert space embedding of the observation emission process, and the latent state transition is deterministic. Under the function approximation setup where the optimal latent state-action Q-function is linear in the state feature, and the optimal Q-function has a gap in actions, we provide a computationally and statistically efficient algorithm for finding the exact optimal policy. We show our algorithm's computational and statistical complexities scale polynomially with respect to the horizon and the intrinsic dimension of the feature on the observation space. Furthermore, we show both the deterministic latent transitions and gap assumptions are necessary to avoid statistical complexity exponential in horizon or dimension. Since our guarantee does not have an explicit dependence on the size of the state and observation spaces, our algorithm provably scales to large-scale POMDPs.

Recently, the impressive empirical success of policy gradient (PG) methods has catalyzed the development of their theoretical foundations. Despite the huge efforts directed at the design of efficient stochastic PG-type algorithms, the understanding of their convergence to a globally optimal policy is still limited. In this work, we develop improved global convergence guarantees for a general class of Fisher-non-degenerate parameterized policies which allows to address the case of continuous state action spaces. First, we propose a Normalized Policy Gradient method with Implicit Gradient Transport (N-PG-IGT) and derive a mathcal{O}(varepsilon^{-2.5}) sample complexity of this method for finding a global varepsilon-optimal policy. Improving over the previously known mathcal{O}(varepsilon^{-3}) complexity, this algorithm does not require the use of importance sampling or second-order information and samples only one trajectory per iteration. Second, we further improve this complexity to mathcal{mathcal{O} }(varepsilon^{-2}) by considering a Hessian-Aided Recursive Policy Gradient ((N)-HARPG) algorithm enhanced with a correction based on a Hessian-vector product. Interestingly, both algorithms are (i) simple and easy to implement: single-loop, do not require large batches of trajectories and sample at most two trajectories per iteration; (ii) computationally and memory efficient: they do not require expensive subroutines at each iteration and can be implemented with memory linear in the dimension of parameters.

We propose a simple approach for memory-efficient adaptation of pretrained language models. Our approach uses an iterative algorithm to decompose each pretrained matrix into a high-precision low-rank component and a memory-efficient quantized component. During finetuning, the quantized component remains fixed and only the low-rank component is updated. We present an integer linear programming formulation of the quantization component which enables dynamic configuration of quantization parameters (e.g., bit-width, block size) for each matrix given an overall target memory budget. We further explore a data-aware version of the algorithm which uses an approximation of the Fisher information matrix to weight the reconstruction objective during matrix decomposition. Experiments on adapting RoBERTa and LLaMA-2 (7B and 70B) demonstrate that our low-rank plus quantized matrix decomposition approach (LQ-LoRA) outperforms strong QLoRA and GPTQ-LoRA baselines and moreover enables more aggressive quantization. For example, on the OpenAssistant benchmark LQ-LoRA is able to learn a 2.5-bit LLaMA-2 model that is competitive with a model finetuned with 4-bit QLoRA. When finetuned on a language modeling calibration dataset, LQ-LoRA can also be used for model compression; in this setting our 2.75-bit LLaMA-2-70B model (which has 2.85 bits on average when including the low-rank components and requires 27GB of GPU memory) is competitive with the original model in full precision.

We study the computational limits of Low-Rank Adaptation (LoRA) update for finetuning transformer-based models using fine-grained complexity theory. Our key observation is that the existence of low-rank decompositions within the gradient computation of LoRA adaptation leads to possible algorithmic speedup. This allows us to (i) identify a phase transition behavior and (ii) prove the existence of nearly linear algorithms by controlling the LoRA update computation term by term, assuming the Strong Exponential Time Hypothesis (SETH). For the former, we identify a sharp transition in the efficiency of all possible rank-r LoRA update algorithms for transformers, based on specific norms resulting from the multiplications of the input sequence X, pretrained weights W^star, and adapter matrices alpha B A / r. Specifically, we derive a shared upper bound threshold for such norms and show that efficient (sub-quadratic) approximation algorithms of LoRA exist only below this threshold. For the latter, we prove the existence of nearly linear approximation algorithms for LoRA adaptation by utilizing the hierarchical low-rank structures of LoRA gradients and approximating the gradients with a series of chained low-rank approximations. To showcase our theory, we consider two practical scenarios: partial (e.g., only W_V and W_Q) and full adaptations (e.g., W_Q, W_V, and W_K) of weights in attention heads.

When considering a model architecture, there are several ways to reduce its memory footprint. Historically, popular approaches included selecting smaller architectures and creating sparse networks through pruning. More recently, randomized parameter-sharing (RPS) methods have gained traction for model compression at start of training. In this paper, we comprehensively assess the trade-off between memory and accuracy across RPS, pruning techniques, and building smaller models. Our findings demonstrate that RPS, which is both data and model-agnostic, consistently outperforms/matches smaller models and all moderately informed pruning strategies, such as MAG, SNIP, SYNFLOW, and GRASP, across the entire compression range. This advantage becomes particularly pronounced in higher compression scenarios. Notably, even when compared to highly informed pruning techniques like Lottery Ticket Rewinding (LTR), RPS exhibits superior performance in high compression settings. This points out inherent capacity advantage that RPS enjoys over sparse models. Theoretically, we establish RPS as a superior technique in terms of memory-efficient representation when compared to pruning for linear models. This paper argues in favor of paradigm shift towards RPS based models. During our rigorous evaluation of RPS, we identified issues in the state-of-the-art RPS technique ROAST, specifically regarding stability (ROAST's sensitivity to initialization hyperparameters, often leading to divergence) and Pareto-continuity (ROAST's inability to recover the accuracy of the original model at zero compression). We provably address both of these issues. We refer to the modified RPS, which incorporates our improvements, as STABLE-RPS.

We aim to address sparse-view reconstruction of a 3D scene by leveraging priors from large-scale vision models. While recent advancements such as 3D Gaussian Splatting (3DGS) have demonstrated remarkable successes in 3D reconstruction, these methods typically necessitate hundreds of input images that densely capture the underlying scene, making them time-consuming and impractical for real-world applications. However, sparse-view reconstruction is inherently ill-posed and under-constrained, often resulting in inferior and incomplete outcomes. This is due to issues such as failed initialization, overfitting on input images, and a lack of details. To mitigate these challenges, we introduce LM-Gaussian, a method capable of generating high-quality reconstructions from a limited number of images. Specifically, we propose a robust initialization module that leverages stereo priors to aid in the recovery of camera poses and the reliable point clouds. Additionally, a diffusion-based refinement is iteratively applied to incorporate image diffusion priors into the Gaussian optimization process to preserve intricate scene details. Finally, we utilize video diffusion priors to further enhance the rendered images for realistic visual effects. Overall, our approach significantly reduces the data acquisition requirements compared to previous 3DGS methods. We validate the effectiveness of our framework through experiments on various public datasets, demonstrating its potential for high-quality 360-degree scene reconstruction. Visual results are on our website.

Unsupervised learning of probabilistic models is a central yet challenging problem in machine learning. Specifically, designing models with tractable learning, sampling, inference and evaluation is crucial in solving this task. We extend the space of such models using real-valued non-volume preserving (real NVP) transformations, a set of powerful invertible and learnable transformations, resulting in an unsupervised learning algorithm with exact log-likelihood computation, exact sampling, exact inference of latent variables, and an interpretable latent space. We demonstrate its ability to model natural images on four datasets through sampling, log-likelihood evaluation and latent variable manipulations.

How can we perform efficient inference and learning in directed probabilistic models, in the presence of continuous latent variables with intractable posterior distributions, and large datasets? We introduce a stochastic variational inference and learning algorithm that scales to large datasets and, under some mild differentiability conditions, even works in the intractable case. Our contributions are two-fold. First, we show that a reparameterization of the variational lower bound yields a lower bound estimator that can be straightforwardly optimized using standard stochastic gradient methods. Second, we show that for i.i.d. datasets with continuous latent variables per datapoint, posterior inference can be made especially efficient by fitting an approximate inference model (also called a recognition model) to the intractable posterior using the proposed lower bound estimator. Theoretical advantages are reflected in experimental results.

Preference optimization for diffusion models aims to align them with human preferences for images. Previous methods typically leverage Vision-Language Models (VLMs) as pixel-level reward models to approximate human preferences. However, when used for step-level preference optimization, these models face challenges in handling noisy images of different timesteps and require complex transformations into pixel space. In this work, we demonstrate that diffusion models are inherently well-suited for step-level reward modeling in the latent space, as they can naturally extract features from noisy latent images. Accordingly, we propose the Latent Reward Model (LRM), which repurposes components of diffusion models to predict preferences of latent images at various timesteps. Building on LRM, we introduce Latent Preference Optimization (LPO), a method designed for step-level preference optimization directly in the latent space. Experimental results indicate that LPO not only significantly enhances performance in aligning diffusion models with general, aesthetic, and text-image alignment preferences, but also achieves 2.5-28times training speedup compared to existing preference optimization methods. Our code will be available at https://github.com/casiatao/LPO.

We develop a novel theoretical framework for understating OT schemes respecting a class structure. For this purpose, we propose a convex OT program with a sum-of-norms regularization term, which provably recovers the underlying class structure under geometric assumptions. Furthermore, we derive an accelerated proximal algorithm with a closed-form projection and proximal operator scheme, thereby affording a more scalable algorithm for computing optimal transport plans. We provide a novel argument for the uniqueness of the optimum even in the absence of strong convexity. Our experiments show that the new regularizer not only results in a better preservation of the class structure in the data but also yields additional robustness to the data geometry, compared to previous regularizers.

Rendering high-fidelity images from sparse point clouds is still challenging. Existing learning-based approaches suffer from either hole artifacts, missing details, or expensive computations. In this paper, we propose a novel framework to render high-quality images from sparse points. This method first attempts to bridge the 3D Gaussian Splatting and point cloud rendering, which includes several cascaded modules. We first use a regressor to estimate Gaussian properties in a point-wise manner, the estimated properties are used to rasterize neural feature descriptors into 2D planes which are extracted from a multiscale extractor. The projected feature volume is gradually decoded toward the final prediction via a multiscale and progressive decoder. The whole pipeline experiences a two-stage training and is driven by our well-designed progressive and multiscale reconstruction loss. Experiments on different benchmarks show the superiority of our method in terms of rendering qualities and the necessities of our main components.

Max sliced Wasserstein (Max-SW) distance has been widely known as a solution for less discriminative projections of sliced Wasserstein (SW) distance. In applications that have various independent pairs of probability measures, amortized projection optimization is utilized to predict the ``max" projecting directions given two input measures instead of using projected gradient ascent multiple times. Despite being efficient, Max-SW and its amortized version cannot guarantee metricity property due to the sub-optimality of the projected gradient ascent and the amortization gap. Therefore, we propose to replace Max-SW with distributional sliced Wasserstein distance with von Mises-Fisher (vMF) projecting distribution (v-DSW). Since v-DSW is a metric with any non-degenerate vMF distribution, its amortized version can guarantee the metricity when performing amortization. Furthermore, current amortized models are not permutation invariant and symmetric. To address the issue, we design amortized models based on self-attention architecture. In particular, we adopt efficient self-attention architectures to make the computation linear in the number of supports. With the two improvements, we derive self-attention amortized distributional projection optimization and show its appealing performance in point-cloud reconstruction and its downstream applications.

We introduce a highly performant 3D object detector for point clouds using the DETR framework. The prior attempts all end up with suboptimal results because they fail to learn accurate inductive biases from the limited scale of training data. In particular, the queries often attend to points that are far away from the target objects, violating the locality principle in object detection. To address the limitation, we introduce a novel 3D Vertex Relative Position Encoding (3DV-RPE) method which computes position encoding for each point based on its relative position to the 3D boxes predicted by the queries in each decoder layer, thus providing clear information to guide the model to focus on points near the objects, in accordance with the principle of locality. In addition, we systematically improve the pipeline from various aspects such as data normalization based on our understanding of the task. We show exceptional results on the challenging ScanNetV2 benchmark, achieving significant improvements over the previous 3DETR in AP_{25}/AP_{50} from 65.0\%/47.0\% to 77.8\%/66.0\%, respectively. In addition, our method sets a new record on ScanNetV2 and SUN RGB-D datasets.Code will be released at http://github.com/yichaoshen-MS/V-DETR.

Diffusion probabilistic models (DPMs) have demonstrated a very promising ability in high-resolution image synthesis. However, sampling from a pre-trained DPM usually requires hundreds of model evaluations, which is computationally expensive. Despite recent progress in designing high-order solvers for DPMs, there still exists room for further speedup, especially in extremely few steps (e.g., 5~10 steps). Inspired by the predictor-corrector for ODE solvers, we develop a unified corrector (UniC) that can be applied after any existing DPM sampler to increase the order of accuracy without extra model evaluations, and derive a unified predictor (UniP) that supports arbitrary order as a byproduct. Combining UniP and UniC, we propose a unified predictor-corrector framework called UniPC for the fast sampling of DPMs, which has a unified analytical form for any order and can significantly improve the sampling quality over previous methods. We evaluate our methods through extensive experiments including both unconditional and conditional sampling using pixel-space and latent-space DPMs. Our UniPC can achieve 3.87 FID on CIFAR10 (unconditional) and 7.51 FID on ImageNet 256times256 (conditional) with only 10 function evaluations. Code is available at https://github.com/wl-zhao/UniPC

It is well noted that coordinate based MLPs benefit -- in terms of preserving high-frequency information -- through the encoding of coordinate positions as an array of Fourier features. Hitherto, the rationale for the effectiveness of these positional encodings has been solely studied through a Fourier lens. In this paper, we strive to broaden this understanding by showing that alternative non-Fourier embedding functions can indeed be used for positional encoding. Moreover, we show that their performance is entirely determined by a trade-off between the stable rank of the embedded matrix and the distance preservation between embedded coordinates. We further establish that the now ubiquitous Fourier feature mapping of position is a special case that fulfills these conditions. Consequently, we present a more general theory to analyze positional encoding in terms of shifted basis functions. To this end, we develop the necessary theoretical formulae and empirically verify that our theoretical claims hold in practice. Codes available at https://github.com/osiriszjq/Rethinking-positional-encoding.

Enabling Large Language Models (LLMs) to understand the 3D physical world is an emerging yet challenging research direction. Current strategies for processing point clouds typically downsample the scene or divide it into smaller parts for separate analysis. However, both approaches risk losing key local details or global contextual information. In this paper, we introduce PerLA, a 3D language assistant designed to be more perceptive to both details and context, making visual representations more informative for the LLM. PerLA captures high-resolution (local) details in parallel from different point cloud areas and integrates them with (global) context obtained from a lower-resolution whole point cloud. We present a novel algorithm that preserves point cloud locality through the Hilbert curve and effectively aggregates local-to-global information via cross-attention and a graph neural network. Lastly, we introduce a novel loss for local representation consensus to promote training stability. PerLA outperforms state-of-the-art 3D language assistants, with gains of up to +1.34 CiDEr on ScanQA for question answering, and +4.22 on ScanRefer and +3.88 on Nr3D for dense captioning.https://gfmei.github.io/PerLA/

Diffusion models generating images conditionally on text, such as Dall-E 2 and Stable Diffusion, have recently made a splash far beyond the computer vision community. Here, we tackle the related problem of generating point clouds, both unconditionally, and conditionally with images. For the latter, we introduce a novel geometrically-motivated conditioning scheme based on projecting sparse image features into the point cloud and attaching them to each individual point, at every step in the denoising process. This approach improves geometric consistency and yields greater fidelity than current methods relying on unstructured, global latent codes. Additionally, we show how to apply recent continuous-time diffusion schemes. Our method performs on par or above the state of art on conditional and unconditional experiments on synthetic data, while being faster, lighter, and delivering tractable likelihoods. We show it can also scale to diverse indoors scenes.

Contrastive learning is a highly successful technique for learning representations of data from labeled tuples, specifying the distance relations within the tuple. We study the sample complexity of contrastive learning, i.e. the minimum number of labeled tuples sufficient for getting high generalization accuracy. We give tight bounds on the sample complexity in a variety of settings, focusing on arbitrary distance functions, both general ell_p-distances, and tree metrics. Our main result is an (almost) optimal bound on the sample complexity of learning ell_p-distances for integer p. For any p ge 1 we show that tilde Theta(min(nd,n^2)) labeled tuples are necessary and sufficient for learning d-dimensional representations of n-point datasets. Our results hold for an arbitrary distribution of the input samples and are based on giving the corresponding bounds on the Vapnik-Chervonenkis/Natarajan dimension of the associated problems. We further show that the theoretical bounds on sample complexity obtained via VC/Natarajan dimension can have strong predictive power for experimental results, in contrast with the folklore belief about a substantial gap between the statistical learning theory and the practice of deep learning.

A complex system with cluttered observations may be a coupled mixture of multiple simple sub-systems corresponding to latent entities. Such sub-systems may hold distinct dynamics in the continuous-time domain; therein, complicated interactions between sub-systems also evolve over time. This setting is fairly common in the real world but has been less considered. In this paper, we propose a sequential learning approach under this setting by decoupling a complex system for handling irregularly sampled and cluttered sequential observations. Such decoupling brings about not only subsystems describing the dynamics of each latent entity but also a meta-system capturing the interaction between entities over time. Specifically, we argue that the meta-system evolving within a simplex is governed by projected differential equations (ProjDEs). We further analyze and provide neural-friendly projection operators in the context of Bregman divergence. Experimental results on synthetic and real-world datasets show the advantages of our approach when facing complex and cluttered sequential data compared to the state-of-the-art.

In the era of foundation models with huge pre-training budgets, the downstream tasks have been shifted to the narrative of efficient and fast adaptation. For classification-based tasks in the domain of computer vision, the two most efficient approaches have been linear probing (LP) and visual prompting/reprogramming (VP); the former aims to learn a classifier in the form of a linear head on the features extracted by the pre-trained model, while the latter maps the input data to the domain of the source data on which the model was originally pre-trained on. Although extensive studies have demonstrated the differences between LP and VP in terms of downstream performance, we explore the capabilities of the two aforementioned methods via the sparsity axis: (a) Data sparsity: the impact of few-shot adaptation and (b) Model sparsity: the impact of lottery tickets (LT). We demonstrate that LT are not universal reprogrammers, i.e., for certain target datasets, reprogramming an LT yields significantly lower performance than the reprogrammed dense model although their corresponding upstream performance is similar. Further, we demonstrate that the calibration of dense models is always superior to that of their lottery ticket counterparts under both LP and VP regimes. Our empirical study opens a new avenue of research into VP for sparse models and encourages further understanding of the performance beyond the accuracy achieved by VP under constraints of sparsity. Code and logs can be accessed at https://github.com/landskape-ai/Reprogram_LT.

This work introduces the Efficient Transformed Gaussian Process (ETGP), a new way of creating C stochastic processes characterized by: 1) the C processes are non-stationary, 2) the C processes are dependent by construction without needing a mixing matrix, 3) training and making predictions is very efficient since the number of Gaussian Processes (GP) operations (e.g. inverting the inducing point's covariance matrix) do not depend on the number of processes. This makes the ETGP particularly suited for multi-class problems with a very large number of classes, which are the problems studied in this work. ETGPs exploit the recently proposed Transformed Gaussian Process (TGP), a stochastic process specified by transforming a Gaussian Process using an invertible transformation. However, unlike TGPs, ETGPs are constructed by transforming a single sample from a GP using C invertible transformations. We derive an efficient sparse variational inference algorithm for the proposed model and demonstrate its utility in 5 classification tasks which include low/medium/large datasets and a different number of classes, ranging from just a few to hundreds. Our results show that ETGPs, in general, outperform state-of-the-art methods for multi-class classification based on GPs, and have a lower computational cost (around one order of magnitude smaller).

Diffusion models have exhibited exciting capabilities in generating images and are also very promising for video creation. However, the inference speed of diffusion models is limited by the slow sampling process, restricting its use cases. The sequential denoising steps required for generating a single sample could take tens or hundreds of iterations and thus have become a significant bottleneck. This limitation is more salient for applications that are interactive in nature or require small latency. To address this challenge, we propose Partially Conditioned Patch Parallelism (PCPP) to accelerate the inference of high-resolution diffusion models. Using the fact that the difference between the images in adjacent diffusion steps is nearly zero, Patch Parallelism (PP) leverages multiple GPUs communicating asynchronously to compute patches of an image in multiple computing devices based on the entire image (all patches) in the previous diffusion step. PCPP develops PP to reduce computation in inference by conditioning only on parts of the neighboring patches in each diffusion step, which also decreases communication among computing devices. As a result, PCPP decreases the communication cost by around 70% compared to DistriFusion (the state of the art implementation of PP) and achieves 2.36sim 8.02times inference speed-up using 4sim 8 GPUs compared to 2.32sim 6.71times achieved by DistriFusion depending on the computing device configuration and resolution of generation at the cost of a possible decrease in image quality. PCPP demonstrates the potential to strike a favorable trade-off, enabling high-quality image generation with substantially reduced latency.

Hallucinations in LLMs pose a significant concern to their safe deployment in real-world applications. Recent approaches have leveraged the latent space of LLMs for hallucination detection, but their embeddings, optimized for linguistic coherence rather than factual accuracy, often fail to clearly separate truthful and hallucinated content. To this end, we propose the Truthfulness Separator Vector (TSV), a lightweight and flexible steering vector that reshapes the LLM's representation space during inference to enhance the separation between truthful and hallucinated outputs, without altering model parameters. Our two-stage framework first trains TSV on a small set of labeled exemplars to form compact and well-separated clusters. It then augments the exemplar set with unlabeled LLM generations, employing an optimal transport-based algorithm for pseudo-labeling combined with a confidence-based filtering process. Extensive experiments demonstrate that TSV achieves state-of-the-art performance with minimal labeled data, exhibiting strong generalization across datasets and providing a practical solution for real-world LLM applications.

We propose a class of greedy algorithms for weighted sparse recovery by considering new loss function-based generalizations of Orthogonal Matching Pursuit (OMP). Given a (regularized) loss function, the proposed algorithms alternate the iterative construction of the signal support via greedy index selection and a signal update based on solving a local data-fitting problem restricted to the current support. We show that greedy selection rules associated with popular weighted sparsity-promoting loss functions admit explicitly computable and simple formulas. Specifically, we consider ell^0 - and ell^1 -based versions of the weighted LASSO (Least Absolute Shrinkage and Selection Operator), the Square-Root LASSO (SR-LASSO) and the Least Absolute Deviations LASSO (LAD-LASSO). Through numerical experiments on Gaussian compressive sensing and high-dimensional function approximation, we demonstrate the effectiveness of the proposed algorithms and empirically show that they inherit desirable characteristics from the corresponding loss functions, such as SR-LASSO's noise-blind optimal parameter tuning and LAD-LASSO's fault tolerance. In doing so, our study sheds new light on the connection between greedy sparse recovery and convex relaxation.

We show how to obtain improved active learning methods in the agnostic (adversarial noise) setting by combining marginal leverage score sampling with non-independent sampling strategies that promote spatial coverage. In particular, we propose an easily implemented method based on the pivotal sampling algorithm, which we test on problems motivated by learning-based methods for parametric PDEs and uncertainty quantification. In comparison to independent sampling, our method reduces the number of samples needed to reach a given target accuracy by up to 50%. We support our findings with two theoretical results. First, we show that any non-independent leverage score sampling method that obeys a weak one-sided ell_{infty} independence condition (which includes pivotal sampling) can actively learn d dimensional linear functions with O(dlog d) samples, matching independent sampling. This result extends recent work on matrix Chernoff bounds under ell_{infty} independence, and may be of interest for analyzing other sampling strategies beyond pivotal sampling. Second, we show that, for the important case of polynomial regression, our pivotal method obtains an improved bound of O(d) samples.

Tucker decomposition is a powerful tensor model to handle multi-aspect data. It demonstrates the low-rank property by decomposing the grid-structured data as interactions between a core tensor and a set of object representations (factors). A fundamental assumption of such decomposition is that there are finite objects in each aspect or mode, corresponding to discrete indexes of data entries. However, real-world data is often not naturally posed in this setting. For example, geographic data is represented as continuous indexes of latitude and longitude coordinates, and cannot fit tensor models directly. To generalize Tucker decomposition to such scenarios, we propose Functional Bayesian Tucker Decomposition (FunBaT). We treat the continuous-indexed data as the interaction between the Tucker core and a group of latent functions. We use Gaussian processes (GP) as functional priors to model the latent functions. Then, we convert each GP into a state-space prior by constructing an equivalent stochastic differential equation (SDE) to reduce computational cost. An efficient inference algorithm is developed for scalable posterior approximation based on advanced message-passing techniques. The advantage of our method is shown in both synthetic data and several real-world applications. We release the code of FunBaT at https://github.com/xuangu-fang/Functional-Bayesian-Tucker-Decomposition.

Large Language Models (LLMs) have shown remarkable performance across various tasks, but the escalating demands on computational resources pose significant challenges, particularly in the extensive utilization of full fine-tuning for downstream tasks. To address this, parameter-efficient fine-tuning (PEFT) methods have been developed, but they often underperform compared to full fine-tuning and struggle with memory efficiency. In this work, we introduce Gradient Weight-Normalized Low-Rank Projection (GradNormLoRP), a novel approach that enhances both parameter and memory efficiency while maintaining comparable performance to full fine-tuning. GradNormLoRP normalizes the weight matrix to improve gradient conditioning, facilitating better convergence during optimization. Additionally, it applies low-rank approximations to the weight and gradient matrices, significantly reducing memory usage during training. Extensive experiments demonstrate that our 8-bit GradNormLoRP reduces optimizer memory usage by up to 89.5% and enables the pre-training of large LLMs, such as LLaMA 7B, on consumer-level GPUs like the NVIDIA RTX 4090, without additional inference costs. Moreover, GradNormLoRP outperforms existing low-rank methods in fine-tuning tasks. For instance, when fine-tuning the RoBERTa model on all GLUE tasks with a rank of 8, GradNormLoRP achieves an average score of 80.65, surpassing LoRA's score of 79.23. These results underscore GradNormLoRP as a promising alternative for efficient LLM pre-training and fine-tuning. Source code: https://github.com/Jhhuangkay/Gradient-Weight-normalized-Low-rank-Projection-for-Efficient-LLM-Training

Approximations to Gaussian processes based on inducing variables, combined with variational inference techniques, enable state-of-the-art sparse approaches to infer GPs at scale through mini batch-based learning. In this work, we address one limitation of sparse GPs, which is due to the challenge in dealing with a large number of inducing variables without imposing a special structure on the inducing inputs. In particular, we introduce a novel hierarchical prior, which imposes sparsity on the set of inducing variables. We treat our model variationally, and we experimentally show considerable computational gains compared to standard sparse GPs when sparsity on the inducing variables is realized considering the nearest inducing inputs of a random mini-batch of the data. We perform an extensive experimental validation that demonstrates the effectiveness of our approach compared to the state-of-the-art. Our approach enables the possibility to use sparse GPs using a large number of inducing points without incurring a prohibitive computational cost.

In this paper, we study the problem of principal component analysis with generative modeling assumptions, adopting a general model for the observed matrix that encompasses notable special cases, including spiked matrix recovery and phase retrieval. The key assumption is that the underlying signal lies near the range of an L-Lipschitz continuous generative model with bounded k-dimensional inputs. We propose a quadratic estimator, and show that it enjoys a statistical rate of order frac{klog L{m}}, where m is the number of samples. We also provide a near-matching algorithm-independent lower bound. Moreover, we provide a variant of the classic power method, which projects the calculated data onto the range of the generative model during each iteration. We show that under suitable conditions, this method converges exponentially fast to a point achieving the above-mentioned statistical rate. We perform experiments on various image datasets for spiked matrix and phase retrieval models, and illustrate performance gains of our method to the classic power method and the truncated power method devised for sparse principal component analysis.

Smoothness and low dimensional structures play central roles in improving generalization and stability in learning and statistics. This work combines techniques from semi-infinite constrained learning and manifold regularization to learn representations that are globally smooth on a manifold. To do so, it shows that under typical conditions the problem of learning a Lipschitz continuous function on a manifold is equivalent to a dynamically weighted manifold regularization problem. This observation leads to a practical algorithm based on a weighted Laplacian penalty whose weights are adapted using stochastic gradient techniques. It is shown that under mild conditions, this method estimates the Lipschitz constant of the solution, learning a globally smooth solution as a byproduct. Experiments on real world data illustrate the advantages of the proposed method relative to existing alternatives.

Supervised dictionary learning (SDL) is a classical machine learning method that simultaneously seeks feature extraction and classification tasks, which are not necessarily a priori aligned objectives. The goal of SDL is to learn a class-discriminative dictionary, which is a set of latent feature vectors that can well-explain both the features as well as labels of observed data. In this paper, we provide a systematic study of SDL, including the theory, algorithm, and applications of SDL. First, we provide a novel framework that `lifts' SDL as a convex problem in a combined factor space and propose a low-rank projected gradient descent algorithm that converges exponentially to the global minimizer of the objective. We also formulate generative models of SDL and provide global estimation guarantees of the true parameters depending on the hyperparameter regime. Second, viewed as a nonconvex constrained optimization problem, we provided an efficient block coordinate descent algorithm for SDL that is guaranteed to find an varepsilon-stationary point of the objective in O(varepsilon^{-1}(log varepsilon^{-1})^{2}) iterations. For the corresponding generative model, we establish a novel non-asymptotic local consistency result for constrained and regularized maximum likelihood estimation problems, which may be of independent interest. Third, we apply SDL for imbalanced document classification by supervised topic modeling and also for pneumonia detection from chest X-ray images. We also provide simulation studies to demonstrate that SDL becomes more effective when there is a discrepancy between the best reconstructive and the best discriminative dictionaries.

Recently, semidefinite programming (SDP) techniques have shown great promise in providing accurate Lipschitz bounds for neural networks. Specifically, the LipSDP approach (Fazlyab et al., 2019) has received much attention and provides the least conservative Lipschitz upper bounds that can be computed with polynomial time guarantees. However, one main restriction of LipSDP is that its formulation requires the activation functions to be slope-restricted on [0,1], preventing its further use for more general activation functions such as GroupSort, MaxMin, and Householder. One can rewrite MaxMin activations for example as residual ReLU networks. However, a direct application of LipSDP to the resultant residual ReLU networks is conservative and even fails in recovering the well-known fact that the MaxMin activation is 1-Lipschitz. Our paper bridges this gap and extends LipSDP beyond slope-restricted activation functions. To this end, we provide novel quadratic constraints for GroupSort, MaxMin, and Householder activations via leveraging their underlying properties such as sum preservation. Our proposed analysis is general and provides a unified approach for estimating ell_2 and ell_infty Lipschitz bounds for a rich class of neural network architectures, including non-residual and residual neural networks and implicit models, with GroupSort, MaxMin, and Householder activations. Finally, we illustrate the utility of our approach with a variety of experiments and show that our proposed SDPs generate less conservative Lipschitz bounds in comparison to existing approaches.

Partial label learning (PLL) aims to train multiclass classifiers from the examples each annotated with a set of candidate labels where a fixed but unknown candidate label is correct. In the last few years, the instance-independent generation process of candidate labels has been extensively studied, on the basis of which many theoretical advances have been made in PLL. Nevertheless, the candidate labels are always instance-dependent in practice and there is no theoretical guarantee that the model trained on the instance-dependent PLL examples can converge to an ideal one. In this paper, a theoretically grounded and practically effective approach named POP, i.e. PrOgressive Purification for instance-dependent partial label learning, is proposed. Specifically, POP updates the learning model and purifies each candidate label set progressively in every epoch. Theoretically, we prove that POP enlarges the region appropriately fast where the model is reliable, and eventually approximates the Bayes optimal classifier with mild assumptions. Technically, POP is flexible with arbitrary PLL losses and could improve the performance of the previous PLL losses in the instance-dependent case. Experiments on the benchmark datasets and the real-world datasets validate the effectiveness of the proposed method.

Many machine learning applications require operating on a spatially distributed dataset. Despite technological advances, privacy considerations and communication constraints may prevent gathering the entire dataset in a central unit. In this paper, we propose a distributed sampling scheme based on the alternating direction method of multipliers, which is commonly used in the optimization literature due to its fast convergence. In contrast to distributed optimization, distributed sampling allows for uncertainty quantification in Bayesian inference tasks. We provide both theoretical guarantees of our algorithm's convergence and experimental evidence of its superiority to the state-of-the-art. For our theoretical results, we use convex optimization tools to establish a fundamental inequality on the generated local sample iterates. This inequality enables us to show convergence of the distribution associated with these iterates to the underlying target distribution in Wasserstein distance. In simulation, we deploy our algorithm on linear and logistic regression tasks and illustrate its fast convergence compared to existing gradient-based methods.

We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. Previously proposed algorithms (such as DPS and DDRM) only apply to pixel-space diffusion models. We theoretically analyze our algorithm showing provable sample recovery in a linear model setting. The algorithmic insight obtained from our analysis extends to more general settings often considered in practice. Experimentally, we outperform previously proposed posterior sampling algorithms in a wide variety of problems including random inpainting, block inpainting, denoising, deblurring, destriping, and super-resolution.

We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to learning the transfer operator or the generator of the system, which in turn can be used for numerous tasks, such as forecasting and interpreting the system dynamics. We show that the search for a good representation can be cast as an optimization problem over neural networks. Our approach is supported by recent results in statistical learning theory, highlighting the role of approximation error and metric distortion in the learning problem. The objective function we propose is associated with projection operators from the representation space to the data space, overcomes metric distortion, and can be empirically estimated from data. In the discrete-time setting, we further derive a relaxed objective function that is differentiable and numerically well-conditioned. We compare our method against state-of-the-art approaches on different datasets, showing better performance across the board.

Posterior sampling has been shown to be a powerful Bayesian approach for solving imaging inverse problems. The recent plug-and-play unadjusted Langevin algorithm (PnP-ULA) has emerged as a promising method for Monte Carlo sampling and minimum mean squared error (MMSE) estimation by combining physical measurement models with deep-learning priors specified using image denoisers. However, the intricate relationship between the sampling distribution of PnP-ULA and the mismatched data-fidelity and denoiser has not been theoretically analyzed. We address this gap by proposing a posterior-L2 pseudometric and using it to quantify an explicit error bound for PnP-ULA under mismatched posterior distribution. We numerically validate our theory on several inverse problems such as sampling from Gaussian mixture models and image deblurring. Our results suggest that the sensitivity of the sampling distribution of PnP-ULA to a mismatch in the measurement model and the denoiser can be precisely characterized.

We introduce LDL, a fast and robust algorithm that localizes a panorama to a 3D map using line segments. LDL focuses on the sparse structural information of lines in the scene, which is robust to illumination changes and can potentially enable efficient computation. While previous line-based localization approaches tend to sacrifice accuracy or computation time, our method effectively observes the holistic distribution of lines within panoramic images and 3D maps. Specifically, LDL matches the distribution of lines with 2D and 3D line distance functions, which are further decomposed along principal directions of lines to increase the expressiveness. The distance functions provide coarse pose estimates by comparing the distributional information, where the poses are further optimized using conventional local feature matching. As our pipeline solely leverages line geometry and local features, it does not require costly additional training of line-specific features or correspondence matching. Nevertheless, our method demonstrates robust performance on challenging scenarios including object layout changes, illumination shifts, and large-scale scenes, while exhibiting fast pose search terminating within a matter of milliseconds. We thus expect our method to serve as a practical solution for line-based localization, and complement the well-established point-based paradigm. The code for LDL is available through the following link: https://github.com/82magnolia/panoramic-localization.

Latent variable generative models have emerged as powerful tools for generative tasks including image and video synthesis. These models are enabled by pretrained autoencoders that map high resolution data into a compressed lower dimensional latent space, where the generative models can subsequently be developed while requiring fewer computational resources. Despite their effectiveness, the direct application of latent variable models to higher dimensional domains such as videos continues to pose challenges for efficient training and inference. In this paper, we propose an autoencoder that projects volumetric data onto a four-plane factorized latent space that grows sublinearly with the input size, making it ideal for higher dimensional data like videos. The design of our factorized model supports straightforward adoption in a number of conditional generation tasks with latent diffusion models (LDMs), such as class-conditional generation, frame prediction, and video interpolation. Our results show that the proposed four-plane latent space retains a rich representation needed for high-fidelity reconstructions despite the heavy compression, while simultaneously enabling LDMs to operate with significant improvements in speed and memory.

Recent advances with large language models (LLM) illustrate their diverse capabilities. We propose a novel algorithm, staged speculative decoding, to accelerate LLM inference in small-batch, on-device scenarios. We address the low arithmetic intensity of small-batch inference by improving upon previous work in speculative decoding. First, we restructure the speculative batch as a tree, which reduces generation costs and increases the expected tokens per batch. Second, we add a second stage of speculative decoding. Taken together, we reduce single-batch decoding latency by 3.16x with a 762M parameter GPT-2-L model while perfectly preserving output quality.

The state space models, employing recursively propagated features, demonstrate strong representation capabilities comparable to Transformer models and superior efficiency. However, constrained by the inherent geometric constraints of sequences, it still falls short in modeling long-range dependencies. To address this issue, we propose the GrootVL network, which first dynamically generates a tree topology based on spatial relationships and input features. Then, feature propagation is performed based on this graph, thereby breaking the original sequence constraints to achieve stronger representation capabilities. Additionally, we introduce a linear complexity dynamic programming algorithm to enhance long-range interactions without increasing computational cost. GrootVL is a versatile multimodal framework that can be applied to both visual and textual tasks. Extensive experiments demonstrate that our method significantly outperforms existing structured state space models on image classification, object detection and segmentation. Besides, by fine-tuning large language models, our approach achieves consistent improvements in multiple textual tasks at minor training cost.

Most modern image-based 6D object pose estimation methods learn to predict 2D-3D correspondences, from which the pose can be obtained using a PnP solver. Because of the non-differentiable nature of common PnP solvers, these methods are supervised via the individual correspondences. To address this, several methods have designed differentiable PnP strategies, thus imposing supervision on the pose obtained after the PnP step. Here, we argue that this conflicts with the averaging nature of the PnP problem, leading to gradients that may encourage the network to degrade the accuracy of individual correspondences. To address this, we derive a loss function that exploits the ground truth pose before solving the PnP problem. Specifically, we linearize the PnP solver around the ground-truth pose and compute the covariance of the resulting pose distribution. We then define our loss based on the diagonal covariance elements, which entails considering the final pose estimate yet not suffering from the PnP averaging issue. Our experiments show that our loss consistently improves the pose estimation accuracy for both dense and sparse correspondence based methods, achieving state-of-the-art results on both Linemod-Occluded and YCB-Video.

In this paper, we present a novel method that reduces model inference latency during distributed deployment of Large Language Models (LLMs). Our contribution is an optimized inference deployment scheme that address the current limitations of state-of-the-art quantization kernels when used in conjunction with Tensor Parallel (TP). Our method preserves data locality in GPU memory access patterns and exploits a priori knowledge of TP to reduce global communication. We demonstrate an up to 1.81x speedup over existing methods for Llama-70B and up to 1.78x speedup for IBM WatsonX's Granite-20B MLP layer problem sizes on A100 and H100 NVIDIA DGX Systems for a variety of TP settings.

Partial differential equations (PDEs) are important tools to model physical systems, and including them into machine learning models is an important way of incorporating physical knowledge. Given any system of linear PDEs with constant coefficients, we propose a family of Gaussian process (GP) priors, which we call EPGP, such that all realizations are exact solutions of this system. We apply the Ehrenpreis-Palamodov fundamental principle, which works like a non-linear Fourier transform, to construct GP kernels mirroring standard spectral methods for GPs. Our approach can infer probable solutions of linear PDE systems from any data such as noisy measurements, or pointwise defined initial and boundary conditions. Constructing EPGP-priors is algorithmic, generally applicable, and comes with a sparse version (S-EPGP) that learns the relevant spectral frequencies and works better for big data sets. We demonstrate our approach on three families of systems of PDE, the heat equation, wave equation, and Maxwell's equations, where we improve upon the state of the art in computation time and precision, in some experiments by several orders of magnitude.

When training large flexible models, practitioners often rely on grid search to select hyperparameters that control over-fitting. This grid search has several disadvantages: the search is computationally expensive, requires carving out a validation set that reduces the available data for training, and requires users to specify candidate values. In this paper, we propose an alternative: directly learning regularization hyperparameters on the full training set via the evidence lower bound ("ELBo") objective from variational methods. For deep neural networks with millions of parameters, we recommend a modified ELBo that upweights the influence of the data likelihood relative to the prior. Our proposed technique overcomes all three disadvantages of grid search. In a case study on transfer learning of image classifiers, we show how our method reduces the 88+ hour grid search of past work to under 3 hours while delivering comparable accuracy. We further demonstrate how our approach enables efficient yet accurate approximations of Gaussian processes with learnable length-scale kernels.

When applying a pre-trained 2D-to-3D human pose lifting model to a target unseen dataset, large performance degradation is commonly encountered due to domain shift issues. We observe that the degradation is caused by two factors: 1) the large distribution gap over global positions of poses between the source and target datasets due to variant camera parameters and settings, and 2) the deficient diversity of local structures of poses in training. To this end, we combine global adaptation and local generalization in PoseDA, a simple yet effective framework of unsupervised domain adaptation for 3D human pose estimation. Specifically, global adaptation aims to align global positions of poses from the source domain to the target domain with a proposed global position alignment (GPA) module. And local generalization is designed to enhance the diversity of 2D-3D pose mapping with a local pose augmentation (LPA) module. These modules bring significant performance improvement without introducing additional learnable parameters. In addition, we propose local pose augmentation (LPA) to enhance the diversity of 3D poses following an adversarial training scheme consisting of 1) a augmentation generator that generates the parameters of pre-defined pose transformations and 2) an anchor discriminator to ensure the reality and quality of the augmented data. Our approach can be applicable to almost all 2D-3D lifting models. PoseDA achieves 61.3 mm of MPJPE on MPI-INF-3DHP under a cross-dataset evaluation setup, improving upon the previous state-of-the-art method by 10.2\%.

Lipschitz constants are connected to many properties of neural networks, such as robustness, fairness, and generalization. Existing methods for computing Lipschitz constants either produce relatively loose upper bounds or are limited to small networks. In this paper, we develop an efficient framework for computing the ell_infty local Lipschitz constant of a neural network by tightly upper bounding the norm of Clarke Jacobian via linear bound propagation. We formulate the computation of local Lipschitz constants with a linear bound propagation process on a high-order backward graph induced by the chain rule of Clarke Jacobian. To enable linear bound propagation, we derive tight linear relaxations for specific nonlinearities in Clarke Jacobian. This formulate unifies existing ad-hoc approaches such as RecurJac, which can be seen as a special case of ours with weaker relaxations. The bound propagation framework also allows us to easily borrow the popular Branch-and-Bound (BaB) approach from neural network verification to further tighten Lipschitz constants. Experiments show that on tiny models, our method produces comparable bounds compared to exact methods that cannot scale to slightly larger models; on larger models, our method efficiently produces tighter results than existing relaxed or naive methods, and our method scales to much larger practical models that previous works could not handle. We also demonstrate an application on provable monotonicity analysis. Code is available at https://github.com/shizhouxing/Local-Lipschitz-Constants.

We consider the problem of simultaneously clustering and learning a linear representation of data lying close to a union of low-dimensional manifolds, a fundamental task in machine learning and computer vision. When the manifolds are assumed to be linear subspaces, this reduces to the classical problem of subspace clustering, which has been studied extensively over the past two decades. Unfortunately, many real-world datasets such as natural images can not be well approximated by linear subspaces. On the other hand, numerous works have attempted to learn an appropriate transformation of the data, such that data is mapped from a union of general non-linear manifolds to a union of linear subspaces (with points from the same manifold being mapped to the same subspace). However, many existing works have limitations such as assuming knowledge of the membership of samples to clusters, requiring high sampling density, or being shown theoretically to learn trivial representations. In this paper, we propose to optimize the Maximal Coding Rate Reduction metric with respect to both the data representation and a novel doubly stochastic cluster membership, inspired by state-of-the-art subspace clustering results. We give a parameterization of such a representation and membership, allowing efficient mini-batching and one-shot initialization. Experiments on CIFAR-10, -20, -100, and TinyImageNet-200 datasets show that the proposed method is much more accurate and scalable than state-of-the-art deep clustering methods, and further learns a latent linear representation of the data.

State-space models (SSMs) have recently emerged as a framework for learning long-range sequence tasks. An example is the structured state-space sequence (S4) layer, which uses the diagonal-plus-low-rank structure of the HiPPO initialization framework. However, the complicated structure of the S4 layer poses challenges; and, in an effort to address these challenges, models such as S4D and S5 have considered a purely diagonal structure. This choice simplifies the implementation, improves computational efficiency, and allows channel communication. However, diagonalizing the HiPPO framework is itself an ill-posed problem. In this paper, we propose a general solution for this and related ill-posed diagonalization problems in machine learning. We introduce a generic, backward-stable "perturb-then-diagonalize" (PTD) methodology, which is based on the pseudospectral theory of non-normal operators, and which may be interpreted as the approximate diagonalization of the non-normal matrices defining SSMs. Based on this, we introduce the S4-PTD and S5-PTD models. Through theoretical analysis of the transfer functions of different initialization schemes, we demonstrate that the S4-PTD/S5-PTD initialization strongly converges to the HiPPO framework, while the S4D/S5 initialization only achieves weak convergences. As a result, our new models show resilience to Fourier-mode noise-perturbed inputs, a crucial property not achieved by the S4D/S5 models. In addition to improved robustness, our S5-PTD model averages 87.6% accuracy on the Long-Range Arena benchmark, demonstrating that the PTD methodology helps to improve the accuracy of deep learning models.

Vision-Language models (VLMs) pre-trained on large corpora have demonstrated notable success across a range of downstream tasks. In light of the rapidly increasing size of pre-trained VLMs, parameter-efficient transfer learning (PETL) has garnered attention as a viable alternative to full fine-tuning. One such approach is the adapter, which introduces a few trainable parameters into the pre-trained models while preserving the original parameters during adaptation. In this paper, we present a novel modeling framework that recasts adapter tuning after attention as a graph message passing process on attention graphs, where the projected query and value features and attention matrix constitute the node features and the graph adjacency matrix, respectively. Within this framework, tuning adapters in VLMs necessitates handling heterophilic graphs, owing to the disparity between the projected query and value space. To address this challenge, we propose a new adapter architecture, p-adapter, which employs p-Laplacian message passing in Graph Neural Networks (GNNs). Specifically, the attention weights are re-normalized based on the features, and the features are then aggregated using the calibrated attention matrix, enabling the dynamic exploitation of information with varying frequencies in the heterophilic attention graphs. We conduct extensive experiments on different pre-trained VLMs and multi-modal tasks, including visual question answering, visual entailment, and image captioning. The experimental results validate our method's significant superiority over other PETL methods.

This paper presents Dual Lagrangian Learning (DLL), a principled learning methodology for dual conic optimization proxies. DLL leverages conic duality and the representation power of ML models to provide high-duality, dual-feasible solutions, and therefore valid Lagrangian dual bounds, for linear and nonlinear conic optimization problems. The paper introduces a systematic dual completion procedure, differentiable conic projection layers, and a self-supervised learning framework based on Lagrangian duality. It also provides closed-form dual completion formulae for broad classes of conic problems, which eliminate the need for costly implicit layers. The effectiveness of DLL is demonstrated on linear and nonlinear conic optimization problems. The proposed methodology significantly outperforms a state-of-the-art learning-based method, and achieves 1000x speedups over commercial interior-point solvers with optimality gaps under 0.5\% on average.

We present a probabilistic model for point cloud generation, which is fundamental for various 3D vision tasks such as shape completion, upsampling, synthesis and data augmentation. Inspired by the diffusion process in non-equilibrium thermodynamics, we view points in point clouds as particles in a thermodynamic system in contact with a heat bath, which diffuse from the original distribution to a noise distribution. Point cloud generation thus amounts to learning the reverse diffusion process that transforms the noise distribution to the distribution of a desired shape. Specifically, we propose to model the reverse diffusion process for point clouds as a Markov chain conditioned on certain shape latent. We derive the variational bound in closed form for training and provide implementations of the model. Experimental results demonstrate that our model achieves competitive performance in point cloud generation and auto-encoding. The code is available at https://github.com/luost26/diffusion-point-cloud.

Large Language Models (LLMs) have recently gained popularity due to their impressive few-shot performance across various downstream tasks. However, fine-tuning all parameters and storing a unique model for each downstream task or domain becomes impractical because of the massive size of checkpoints (e.g., 350GB in GPT-3). Current literature, such as LoRA, showcases the potential of low-rank modifications to the original weights of an LLM, enabling efficient adaptation and storage for task-specific models. These methods can reduce the number of parameters needed to fine-tune an LLM by several orders of magnitude. Yet, these methods face two primary limitations: 1) the parameter reduction is lower-bounded by the rank one decomposition, and 2) the extent of reduction is heavily influenced by both the model architecture and the chosen rank. For instance, in larger models, even a rank one decomposition might exceed the number of parameters truly needed for adaptation. In this paper, we introduce NOLA, which overcomes the rank one lower bound present in LoRA. It achieves this by re-parameterizing the low-rank matrices in LoRA using linear combinations of randomly generated matrices (basis) and optimizing the linear mixture coefficients only. This approach allows us to decouple the number of trainable parameters from both the choice of rank and the network architecture. We present adaptation results using GPT-2 and ViT in natural language and computer vision tasks. NOLA performs as well as, or better than models with equivalent parameter counts. Furthermore, we demonstrate that we can halve the parameters in larger models compared to LoRA with rank one, without sacrificing performance.

The kernel thinning (KT) algorithm of Dwivedi and Mackey (2021) compresses a probability distribution more effectively than independent sampling by targeting a reproducing kernel Hilbert space (RKHS) and leveraging a less smooth square-root kernel. Here we provide four improvements. First, we show that KT applied directly to the target RKHS yields tighter, dimension-free guarantees for any kernel, any distribution, and any fixed function in the RKHS. Second, we show that, for analytic kernels like Gaussian, inverse multiquadric, and sinc, target KT admits maximum mean discrepancy (MMD) guarantees comparable to or better than those of square-root KT without making explicit use of a square-root kernel. Third, we prove that KT with a fractional power kernel yields better-than-Monte-Carlo MMD guarantees for non-smooth kernels, like Laplace and Mat\'ern, that do not have square-roots. Fourth, we establish that KT applied to a sum of the target and power kernels (a procedure we call KT+) simultaneously inherits the improved MMD guarantees of power KT and the tighter individual function guarantees of target KT. In our experiments with target KT and KT+, we witness significant improvements in integration error even in 100 dimensions and when compressing challenging differential equation posteriors.

We introduce ARPG, a novel visual autoregressive model that enables randomized parallel generation, addressing the inherent limitations of conventional raster-order approaches, which hinder inference efficiency and zero-shot generalization due to their sequential, predefined token generation order. Our key insight is that effective random-order modeling necessitates explicit guidance for determining the position of the next predicted token. To this end, we propose a novel guided decoding framework that decouples positional guidance from content representation, encoding them separately as queries and key-value pairs. By directly incorporating this guidance into the causal attention mechanism, our approach enables fully random-order training and generation, eliminating the need for bidirectional attention. Consequently, ARPG readily generalizes to zero-shot tasks such as image inpainting, outpainting, and resolution expansion. Furthermore, it supports parallel inference by concurrently processing multiple queries using a shared KV cache. On the ImageNet-1K 256 benchmark, our approach attains an FID of 1.94 with only 64 sampling steps, achieving over a 20-fold increase in throughput while reducing memory consumption by over 75% compared to representative recent autoregressive models at a similar scale.

Dealing with multi-task trade-offs during inference can be addressed via Pareto Front Learning (PFL) methods that parameterize the Pareto Front with a single model, contrary to traditional Multi-Task Learning (MTL) approaches that optimize for a single trade-off which has to be decided prior to training. However, recent PFL methodologies suffer from limited scalability, slow convergence and excessive memory requirements compared to MTL approaches while exhibiting inconsistent mappings from preference space to objective space. In this paper, we introduce PaLoRA, a novel parameter-efficient method that augments the original model with task-specific low-rank adapters and continuously parameterizes the Pareto Front in their convex hull. Our approach dedicates the original model and the adapters towards learning general and task-specific features, respectively. Additionally, we propose a deterministic sampling schedule of preference vectors that reinforces this division of labor, enabling faster convergence and scalability to real world networks. Our experimental results show that PaLoRA outperforms MTL and PFL baselines across various datasets, scales to large networks and provides a continuous parameterization of the Pareto Front, reducing the memory overhead 23.8-31.7 times compared with competing PFL baselines in scene understanding benchmarks.

Guided sampling is a vital approach for applying diffusion models in real-world tasks that embeds human-defined guidance during the sampling procedure. This paper considers a general setting where the guidance is defined by an (unnormalized) energy function. The main challenge for this setting is that the intermediate guidance during the diffusion sampling procedure, which is jointly defined by the sampling distribution and the energy function, is unknown and is hard to estimate. To address this challenge, we propose an exact formulation of the intermediate guidance as well as a novel training objective named contrastive energy prediction (CEP) to learn the exact guidance. Our method is guaranteed to converge to the exact guidance under unlimited model capacity and data samples, while previous methods can not. We demonstrate the effectiveness of our method by applying it to offline reinforcement learning (RL). Extensive experiments on D4RL benchmarks demonstrate that our method outperforms existing state-of-the-art algorithms. We also provide some examples of applying CEP for image synthesis to demonstrate the scalability of CEP on high-dimensional data.

The notion of omnipredictors (Gopalan, Kalai, Reingold, Sharan and Wieder ITCS 2021), suggested a new paradigm for loss minimization. Rather than learning a predictor based on a known loss function, omnipredictors can easily be post-processed to minimize any one of a rich family of loss functions compared with the loss of hypotheses in a class mathcal C. It has been shown that such omnipredictors exist and are implied (for all convex and Lipschitz loss functions) by the notion of multicalibration from the algorithmic fairness literature. In this paper, we introduce omnipredictors for constrained optimization and study their complexity and implications. The notion that we introduce allows the learner to be unaware of the loss function that will be later assigned as well as the constraints that will be later imposed, as long as the subpopulations that are used to define these constraints are known. We show how to obtain omnipredictors for constrained optimization problems, relying on appropriate variants of multicalibration. We also investigate the implications of this notion when the constraints used are so-called group fairness notions.

We analyze continual learning on a sequence of separable linear classification tasks with binary labels. We show theoretically that learning with weak regularization reduces to solving a sequential max-margin problem, corresponding to a special case of the Projection Onto Convex Sets (POCS) framework. We then develop upper bounds on the forgetting and other quantities of interest under various settings with recurring tasks, including cyclic and random orderings of tasks. We discuss several practical implications to popular training practices like regularization scheduling and weighting. We point out several theoretical differences between our continual classification setting and a recently studied continual regression setting.

Convex relaxations are a key component of training and certifying provably safe neural networks. However, despite substantial progress, a wide and poorly understood accuracy gap to standard networks remains, raising the question of whether this is due to fundamental limitations of convex relaxations. Initial work investigating this question focused on the simple and widely used IBP relaxation. It revealed that some univariate, convex, continuous piecewise linear (CPWL) functions cannot be encoded by any ReLU network such that its IBP-analysis is precise. To explore whether this limitation is shared by more advanced convex relaxations, we conduct the first in-depth study on the expressive power of ReLU networks across all commonly used convex relaxations. We show that: (i) more advanced relaxations allow a larger class of univariate functions to be expressed as precisely analyzable ReLU networks, (ii) more precise relaxations can allow exponentially larger solution spaces of ReLU networks encoding the same functions, and (iii) even using the most precise single-neuron relaxations, it is impossible to construct precisely analyzable ReLU networks that express multivariate, convex, monotone CPWL functions.

In location estimation, we are given n samples from a known distribution f shifted by an unknown translation lambda, and want to estimate lambda as precisely as possible. Asymptotically, the maximum likelihood estimate achieves the Cram\'er-Rao bound of error mathcal N(0, 1{nmathcal I}), where mathcal I is the Fisher information of f. However, the n required for convergence depends on f, and may be arbitrarily large. We build on the theory using smoothed estimators to bound the error for finite n in terms of mathcal I_r, the Fisher information of the r-smoothed distribution. As n to infty, r to 0 at an explicit rate and this converges to the Cram\'er-Rao bound. We (1) improve the prior work for 1-dimensional f to converge for constant failure probability in addition to high probability, and (2) extend the theory to high-dimensional distributions. In the process, we prove a new bound on the norm of a high-dimensional random variable whose 1-dimensional projections are subgamma, which may be of independent interest.

We present a differentiable approach to learn the probabilistic factors used for inference by a nonparametric belief propagation algorithm. Existing nonparametric belief propagation methods rely on domain-specific features encoded in the probabilistic factors of a graphical model. In this work, we replace each crafted factor with a differentiable neural network enabling the factors to be learned using an efficient optimization routine from labeled data. By combining differentiable neural networks with an efficient belief propagation algorithm, our method learns to maintain a set of marginal posterior samples using end-to-end training. We evaluate our differentiable nonparametric belief propagation (DNBP) method on a set of articulated pose tracking tasks and compare performance with learned baselines. Results from these experiments demonstrate the effectiveness of using learned factors for tracking and suggest the practical advantage over hand-crafted approaches. The project webpage is available at: https://progress.eecs.umich.edu/projects/dnbp/ .

We show for the first time that large-scale generative pretrained transformer (GPT) family models can be pruned to at least 50% sparsity in one-shot, without any retraining, at minimal loss of accuracy. This is achieved via a new pruning method called SparseGPT, specifically designed to work efficiently and accurately on massive GPT-family models. We can execute SparseGPT on the largest available open-source models, OPT-175B and BLOOM-176B, in under 4.5 hours, and can reach 60% unstructured sparsity with negligible increase in perplexity: remarkably, more than 100 billion weights from these models can be ignored at inference time. SparseGPT generalizes to semi-structured (2:4 and 4:8) patterns, and is compatible with weight quantization approaches. The code is available at: https://github.com/IST-DASLab/sparsegpt.

We consider solving equality-constrained nonlinear, nonconvex optimization problems. This class of problems appears widely in a variety of applications in machine learning and engineering, ranging from constrained deep neural networks, to optimal control, to PDE-constrained optimization. We develop an adaptive inexact Newton method for this problem class. In each iteration, we solve the Lagrangian Newton system inexactly via a randomized iterative sketching solver, and select a suitable stepsize by performing line search on an exact augmented Lagrangian merit function. The randomized solvers have advantages over deterministic linear system solvers by significantly reducing per-iteration flops complexity and storage cost, when equipped with suitable sketching matrices. Our method adaptively controls the accuracy of the randomized solver and the penalty parameters of the exact augmented Lagrangian, to ensure that the inexact Newton direction is a descent direction of the exact augmented Lagrangian. This allows us to establish a global almost sure convergence. We also show that a unit stepsize is admissible locally, so that our method exhibits a local linear convergence. Furthermore, we prove that the linear convergence can be strengthened to superlinear convergence if we gradually sharpen the adaptive accuracy condition on the randomized solver. We demonstrate the superior performance of our method on benchmark nonlinear problems in CUTEst test set, constrained logistic regression with data from LIBSVM, and a PDE-constrained problem.

Adversarial training is well-known to produce high-quality neural network models that are empirically robust against adversarial perturbations. Nevertheless, once a model has been adversarially trained, one often desires a certification that the model is truly robust against all future attacks. Unfortunately, when faced with adversarially trained models, all existing approaches have significant trouble making certifications that are strong enough to be practically useful. Linear programming (LP) techniques in particular face a "convex relaxation barrier" that prevent them from making high-quality certifications, even after refinement with mixed-integer linear programming (MILP) and branch-and-bound (BnB) techniques. In this paper, we propose a nonconvex certification technique, based on a low-rank restriction of a semidefinite programming (SDP) relaxation. The nonconvex relaxation makes strong certifications comparable to much more expensive SDP methods, while optimizing over dramatically fewer variables comparable to much weaker LP methods. Despite nonconvexity, we show how off-the-shelf local optimization algorithms can be used to achieve and to certify global optimality in polynomial time. Our experiments find that the nonconvex relaxation almost completely closes the gap towards exact certification of adversarially trained models.

Despite the recent advancements, conditional image generation still faces challenges of cost, generalizability, and the need for task-specific training. In this paper, we propose Manifold Preserving Guided Diffusion (MPGD), a training-free conditional generation framework that leverages pretrained diffusion models and off-the-shelf neural networks with minimal additional inference cost for a broad range of tasks. Specifically, we leverage the manifold hypothesis to refine the guided diffusion steps and introduce a shortcut algorithm in the process. We then propose two methods for on-manifold training-free guidance using pre-trained autoencoders and demonstrate that our shortcut inherently preserves the manifolds when applied to latent diffusion models. Our experiments show that MPGD is efficient and effective for solving a variety of conditional generation applications in low-compute settings, and can consistently offer up to 3.8x speed-ups with the same number of diffusion steps while maintaining high sample quality compared to the baselines.

Training state-of-the-art vision models has become prohibitively expensive for researchers and practitioners. For the sake of accessibility and resource reuse, it is important to focus on adapting these models to a variety of downstream scenarios. An interesting and practical paradigm is online test-time adaptation, according to which training data is inaccessible, no labelled data from the test distribution is available, and adaptation can only happen at test time and on a handful of samples. In this paper, we investigate how test-time adaptation methods fare for a number of pre-trained models on a variety of real-world scenarios, significantly extending the way they have been originally evaluated. We show that they perform well only in narrowly-defined experimental setups and sometimes fail catastrophically when their hyperparameters are not selected for the same scenario in which they are being tested. Motivated by the inherent uncertainty around the conditions that will ultimately be encountered at test time, we propose a particularly "conservative" approach, which addresses the problem with a Laplacian Adjusted Maximum-likelihood Estimation (LAME) objective. By adapting the model's output (not its parameters), and solving our objective with an efficient concave-convex procedure, our approach exhibits a much higher average accuracy across scenarios than existing methods, while being notably faster and have a much lower memory footprint. The code is available at https://github.com/fiveai/LAME.

With the increase in the number of parameters in large language models, the process of pre-training and fine-tuning increasingly demands larger volumes of GPU memory. A significant portion of this memory is typically consumed by the optimizer state. To overcome this challenge, recent approaches such as low-rank adaptation (LoRA (Hu et al., 2021)), low-rank gradient projection (GaLore (Zhao et al., 2024)), and blockwise optimization (BAdam (Luo et al., 2024)) have been proposed. However, in all these algorithms, the effective rank of the weight updates remains low-rank, which can lead to a substantial loss of information from the gradient. This loss can be critically important, especially during the pre-training stage. In this paper, we introduce FRUGAL (Full-Rank Updates with GrAdient spLitting), a new memory-efficient optimization framework. FRUGAL leverages gradient splitting to perform low-dimensional updates using advanced algorithms (such as Adam), while updates along the remaining directions are executed via state-free methods like SGD or signSGD (Bernstein et al., 2018). Our framework can be integrated with various low-rank update selection techniques, including GaLore and BAdam. We provide theoretical convergence guarantees for our framework when using SGDM for low-dimensional updates and SGD for state-free updates. Additionally, our method consistently outperforms concurrent approaches across various fixed memory budgets, achieving state-of-the-art results in pre-training and fine-tuning tasks while balancing memory efficiency and performance metrics.

We introduce a new neural architecture to learn the conditional probability of an output sequence with elements that are discrete tokens corresponding to positions in an input sequence. Such problems cannot be trivially addressed by existent approaches such as sequence-to-sequence and Neural Turing Machines, because the number of target classes in each step of the output depends on the length of the input, which is variable. Problems such as sorting variable sized sequences, and various combinatorial optimization problems belong to this class. Our model solves the problem of variable size output dictionaries using a recently proposed mechanism of neural attention. It differs from the previous attention attempts in that, instead of using attention to blend hidden units of an encoder to a context vector at each decoder step, it uses attention as a pointer to select a member of the input sequence as the output. We call this architecture a Pointer Net (Ptr-Net). We show Ptr-Nets can be used to learn approximate solutions to three challenging geometric problems -- finding planar convex hulls, computing Delaunay triangulations, and the planar Travelling Salesman Problem -- using training examples alone. Ptr-Nets not only improve over sequence-to-sequence with input attention, but also allow us to generalize to variable size output dictionaries. We show that the learnt models generalize beyond the maximum lengths they were trained on. We hope our results on these tasks will encourage a broader exploration of neural learning for discrete problems.

We adapt previous research on category theory and topological unsupervised learning to develop a functorial perspective on manifold learning, also known as nonlinear dimensionality reduction. We first characterize manifold learning algorithms as functors that map pseudometric spaces to optimization objectives and that factor through hierarchical clustering functors. We then use this characterization to prove refinement bounds on manifold learning loss functions and construct a hierarchy of manifold learning algorithms based on their equivariants. We express several popular manifold learning algorithms as functors at different levels of this hierarchy, including Metric Multidimensional Scaling, IsoMap, and UMAP. Next, we use interleaving distance to study the stability of a broad class of manifold learning algorithms. We present bounds on how closely the embeddings these algorithms produce from noisy data approximate the embeddings they would learn from noiseless data. Finally, we use our framework to derive a set of novel manifold learning algorithms, which we experimentally demonstrate are competitive with the state of the art.

This paper presents a new approach and algorithm for solving a class of constrained Bi-Level Optimization (BLO) problems in which the lower-level problem involves constraints coupling both upper-level and lower-level variables. Such problems have recently gained significant attention due to their broad applicability in machine learning. However, conventional gradient-based methods unavoidably rely on computationally intensive calculations related to the Hessian matrix. To address this challenge, we begin by devising a smooth proximal Lagrangian value function to handle the constrained lower-level problem. Utilizing this construct, we introduce a single-level reformulation for constrained BLOs that transforms the original BLO problem into an equivalent optimization problem with smooth constraints. Enabled by this reformulation, we develop a Hessian-free gradient-based algorithm-termed proximal Lagrangian Value function-based Hessian-free Bi-level Algorithm (LV-HBA)-that is straightforward to implement in a single loop manner. Consequently, LV-HBA is especially well-suited for machine learning applications. Furthermore, we offer non-asymptotic convergence analysis for LV-HBA, eliminating the need for traditional strong convexity assumptions for the lower-level problem while also being capable of accommodating non-singleton scenarios. Empirical results substantiate the algorithm's superior practical performance.

We introduce a unified framework for iterative reasoning that leverages non-Euclidean geometry via Bregman divergences, higher-order operator averaging, and adaptive feedback mechanisms. Our analysis establishes that, under mild smoothness and contractivity assumptions, a generalized update scheme not only unifies classical methods such as mirror descent and dynamic programming but also captures modern chain-of-thought reasoning processes in large language models. In particular, we prove that our accelerated iterative update achieves an O(1/t^2) convergence rate in the absence of persistent perturbations, and we further demonstrate that feedback (iterative) architectures are necessary to approximate certain fixed-point functions efficiently. These theoretical insights bridge classical acceleration techniques with contemporary applications in neural computation and optimization.

Parameter-efficient fine-tuning methods, such as LoRA, reduces the number of trainable parameters. However, they often suffer from scalability issues and differences between their learning pattern and full fine-tuning. To overcome these limitations, we propose Efficient Weight-Decomposed Low-Rank Adaptation (EDoRA): a novel PEFT method that decomposes pre-trained weights into magnitude and directional components. By freezing low-rank matrices, initializing them by singular value decomposition, and introducing a small trainable matrix between them, EDoRA achieves substantial reduction in trainable parameters while maintaining learning capacity. Experimental results on the GLUE benchmark demonstrate that EDoRA achieves competitive or superior performance compared to state-of-the-art methods, such as LoRA and DoRA, with up to 30x fewer trainable parameters. This makes EDoRA a highly efficient solution for adapting LLMs to diverse tasks under memory-constrained settings. Code is available at https://github.com/Hamid-Nasiri/EDoRA .

Despite Flow Matching and diffusion models having emerged as powerful generative paradigms for continuous variables such as images and videos, their application to high-dimensional discrete data, such as language, is still limited. In this work, we present Discrete Flow Matching, a novel discrete flow paradigm designed specifically for generating discrete data. Discrete Flow Matching offers several key contributions: (i) it works with a general family of probability paths interpolating between source and target distributions; (ii) it allows for a generic formula for sampling from these probability paths using learned posteriors such as the probability denoiser (x-prediction) and noise-prediction (epsilon-prediction); (iii) practically, focusing on specific probability paths defined with different schedulers considerably improves generative perplexity compared to previous discrete diffusion and flow models; and (iv) by scaling Discrete Flow Matching models up to 1.7B parameters, we reach 6.7% Pass@1 and 13.4% Pass@10 on HumanEval and 6.7% Pass@1 and 20.6% Pass@10 on 1-shot MBPP coding benchmarks. Our approach is capable of generating high-quality discrete data in a non-autoregressive fashion, significantly closing the gap between autoregressive models and discrete flow models.

Practitioners frequently aim to infer an unobserved population trajectory using sample snapshots at multiple time points. For instance, in single-cell sequencing, scientists would like to learn how gene expression evolves over time. But sequencing any cell destroys that cell. So we cannot access any cell's full trajectory, but we can access snapshot samples from many cells. Stochastic differential equations are commonly used to analyze systems with full individual-trajectory access; since here we have only sample snapshots, these methods are inapplicable. The deep learning community has recently explored using Schr\"odinger bridges (SBs) and their extensions to estimate these dynamics. However, these methods either (1) interpolate between just two time points or (2) require a single fixed reference dynamic within the SB, which is often just set to be Brownian motion. But learning piecewise from adjacent time points can fail to capture long-term dependencies. And practitioners are typically able to specify a model class for the reference dynamic but not the exact values of the parameters within it. So we propose a new method that (1) learns the unobserved trajectories from sample snapshots across multiple time points and (2) requires specification only of a class of reference dynamics, not a single fixed one. In particular, we suggest an iterative projection method inspired by Schr\"odinger bridges; we alternate between learning a piecewise SB on the unobserved trajectories and using the learned SB to refine our best guess for the dynamics within the reference class. We demonstrate the advantages of our method via a well-known simulated parametric model from ecology, simulated and real data from systems biology, and real motion-capture data.

We extend PAC-Bayesian theory to generative models and develop generalization bounds for models based on the Wasserstein distance and the total variation distance. Our first result on the Wasserstein distance assumes the instance space is bounded, while our second result takes advantage of dimensionality reduction. Our results naturally apply to Wasserstein GANs and Energy-Based GANs, and our bounds provide new training objectives for these two. Although our work is mainly theoretical, we perform numerical experiments showing non-vacuous generalization bounds for Wasserstein GANs on synthetic datasets.

Generative Large Language Models (LLMs) have demonstrated remarkable results for a wide range of tasks. However, deploying these models for inference has been a significant challenge due to their unprecedented resource requirements. This has forced existing deployment frameworks to use multi-GPU inference pipelines, which are often complex and costly, or to use smaller and less performant models. In this work, we demonstrate that the main bottleneck for generative inference with LLMs is memory bandwidth, rather than compute, specifically for single batch inference. While quantization has emerged as a promising solution by representing model weights with reduced precision, previous efforts have often resulted in notable performance degradation. To address this, we introduce SqueezeLLM, a post-training quantization framework that not only enables lossless compression to ultra-low precisions of up to 3-bit, but also achieves higher quantization performance under the same memory constraint. Our framework incorporates two novel ideas: (i) sensitivity-based non-uniform quantization, which searches for the optimal bit precision assignment based on second-order information; and (ii) the Dense-and-Sparse decomposition that stores outliers and sensitive weight values in an efficient sparse format. When applied to the LLaMA models, our 3-bit quantization significantly reduces the perplexity gap from the FP16 baseline by up to 2.1x as compared to the state-of-the-art methods with the same memory requirement. Furthermore, when deployed on an A6000 GPU, our quantized models achieve up to 2.3x speedup compared to the baseline. Our code is open-sourced and available online.

In this study, we introduce an innovative deep learning framework that employs a transformer model to address the challenges of mixed-integer programs, specifically focusing on the Capacitated Lot Sizing Problem (CLSP). Our approach, to our knowledge, is the first to utilize transformers to predict the binary variables of a mixed-integer programming (MIP) problem. Specifically, our approach harnesses the encoder decoder transformer's ability to process sequential data, making it well-suited for predicting binary variables indicating production setup decisions in each period of the CLSP. This problem is inherently dynamic, and we need to handle sequential decision making under constraints. We present an efficient algorithm in which CLSP solutions are learned through a transformer neural network. The proposed post-processed transformer algorithm surpasses the state-of-the-art solver, CPLEX and Long Short-Term Memory (LSTM) in solution time, optimal gap, and percent infeasibility over 240K benchmark CLSP instances tested. After the ML model is trained, conducting inference on the model, reduces the MIP into a linear program (LP). This transforms the ML-based algorithm, combined with an LP solver, into a polynomial-time approximation algorithm to solve a well-known NP-Hard problem, with almost perfect solution quality.

Finetuned LLMs often exhibit poor uncertainty quantification, manifesting as overconfidence, poor calibration, and unreliable prediction results on test data or out-of-distribution samples. One approach commonly used in vision for alleviating this issue is a deep ensemble, which constructs an ensemble by training the same model multiple times using different random initializations. However, there is a huge challenge to ensembling LLMs: the most effective LLMs are very, very large. Keeping a single LLM in memory is already challenging enough: keeping an ensemble of e.g. 5 LLMs in memory is impossible in many settings. To address these issues, we propose an ensemble approach using Low-Rank Adapters (LoRA), a parameter-efficient fine-tuning technique. Critically, these low-rank adapters represent a very small number of parameters, orders of magnitude less than the underlying pre-trained model. Thus, it is possible to construct large ensembles of LoRA adapters with almost the same computational overhead as using the original model. We find that LoRA ensembles, applied on its own or on top of pre-existing regularization techniques, gives consistent improvements in predictive accuracy and uncertainty quantification.

While score-based generative models (SGMs) have achieved remarkable success in enormous image generation tasks, their mathematical foundations are still limited. In this paper, we analyze the approximation and generalization of SGMs in learning a family of sub-Gaussian probability distributions. We introduce a notion of complexity for probability distributions in terms of their relative density with respect to the standard Gaussian measure. We prove that if the log-relative density can be locally approximated by a neural network whose parameters can be suitably bounded, then the distribution generated by empirical score matching approximates the target distribution in total variation with a dimension-independent rate. We illustrate our theory through examples, which include certain mixtures of Gaussians. An essential ingredient of our proof is to derive a dimension-free deep neural network approximation rate for the true score function associated with the forward process, which is interesting in its own right.

We introduce new differentially private (DP) mechanisms for gradient-based machine learning (ML) with multiple passes (epochs) over a dataset, substantially improving the achievable privacy-utility-computation tradeoffs. We formalize the problem of DP mechanisms for adaptive streams with multiple participations and introduce a non-trivial extension of online matrix factorization DP mechanisms to our setting. This includes establishing the necessary theory for sensitivity calculations and efficient computation of optimal matrices. For some applications like >!! 10,000 SGD steps, applying these optimal techniques becomes computationally expensive. We thus design an efficient Fourier-transform-based mechanism with only a minor utility loss. Extensive empirical evaluation on both example-level DP for image classification and user-level DP for language modeling demonstrate substantial improvements over all previous methods, including the widely-used DP-SGD . Though our primary application is to ML, our main DP results are applicable to arbitrary linear queries and hence may have much broader applicability.

Large language models (LLMs) have been widely applied but face challenges in efficient inference. While quantization methods reduce computational demands, ultra-low bit quantization with arbitrary precision is hindered by limited GPU Tensor Core support and inefficient memory management, leading to suboptimal acceleration. To address these challenges, we propose a comprehensive acceleration scheme for arbitrary precision LLMs. At its core, we introduce a novel bipolar-INT data format that facilitates parallel computing and supports symmetric quantization, effectively reducing data redundancy. Building on this, we implement an arbitrary precision matrix multiplication scheme that decomposes and recovers matrices at the bit level, enabling flexible precision while maximizing GPU Tensor Core utilization. Furthermore, we develop an efficient matrix preprocessing method that optimizes data layout for subsequent computations. Finally, we design a data recovery-oriented memory management system that strategically utilizes fast shared memory, significantly enhancing kernel execution speed and minimizing memory access latency. Experimental results demonstrate our approach's effectiveness, with up to 2.4\times speedup in matrix multiplication compared to NVIDIA's CUTLASS. When integrated into LLMs, we achieve up to 6.7\times inference acceleration. These improvements significantly enhance LLM inference efficiency, enabling broader and more responsive applications of LLMs.

The autoencoder is an unsupervised learning paradigm that aims to create a compact latent representation of data by minimizing the reconstruction loss. However, it tends to overlook the fact that most data (images) are embedded in a lower-dimensional space, which is crucial for effective data representation. To address this limitation, we propose a novel approach called Low-Rank Autoencoder (LoRAE). In LoRAE, we incorporated a low-rank regularizer to adaptively reconstruct a low-dimensional latent space while preserving the basic objective of an autoencoder. This helps embed the data in a lower-dimensional space while preserving important information. It is a simple autoencoder extension that learns low-rank latent space. Theoretically, we establish a tighter error bound for our model. Empirically, our model's superiority shines through various tasks such as image generation and downstream classification. Both theoretical and practical outcomes highlight the importance of acquiring low-dimensional embeddings.

Recent advances in radiance field reconstruction, such as 3D Gaussian Splatting (3DGS), have achieved high-quality novel view synthesis and fast rendering by representing scenes with compositions of Gaussian primitives. However, 3D Gaussians present several limitations for scene reconstruction. Accurately capturing hard edges is challenging without significantly increasing the number of Gaussians, creating a large memory footprint. Moreover, they struggle to represent flat surfaces, as they are diffused in space. Without hand-crafted regularizers, they tend to disperse irregularly around the actual surface. To circumvent these issues, we introduce a novel method, named 3D Convex Splatting (3DCS), which leverages 3D smooth convexes as primitives for modeling geometrically-meaningful radiance fields from multi-view images. Smooth convex shapes offer greater flexibility than Gaussians, allowing for a better representation of 3D scenes with hard edges and dense volumes using fewer primitives. Powered by our efficient CUDA-based rasterizer, 3DCS achieves superior performance over 3DGS on benchmarks such as Mip-NeRF360, Tanks and Temples, and Deep Blending. Specifically, our method attains an improvement of up to 0.81 in PSNR and 0.026 in LPIPS compared to 3DGS while maintaining high rendering speeds and reducing the number of required primitives. Our results highlight the potential of 3D Convex Splatting to become the new standard for high-quality scene reconstruction and novel view synthesis. Project page: convexsplatting.github.io.

Relational pooling is a framework for building more expressive and permutation-invariant graph neural networks. However, there is limited understanding of the exact enhancement in the expressivity of RP and its connection with the Weisfeiler Lehman hierarchy. Starting from RP, we propose to explicitly assign labels to nodes as additional features to improve expressive power of message passing neural networks. The method is then extended to higher dimensional WL, leading to a novel k,l-WL algorithm, a more general framework than k-WL. Theoretically, we analyze the expressivity of k,l-WL with respect to k and l and unifies it with a great number of subgraph GNNs. Complexity reduction methods are also systematically discussed to build powerful and practical k,l-GNN instances. We theoretically and experimentally prove that our method is universally compatible and capable of improving the expressivity of any base GNN model. Our k,l-GNNs achieve superior performance on many synthetic and real-world datasets, which verifies the effectiveness of our framework.

Structural and Positional Encodings can significantly improve the performance of Graph Neural Networks in downstream tasks. Recent literature has begun to systematically investigate differences in the structural properties that these approaches encode, as well as performance trade-offs between them. However, the question of which structural properties yield the most effective encoding remains open. In this paper, we investigate this question from a geometric perspective. We propose a novel structural encoding based on discrete Ricci curvature (Local Curvature Profiles, short LCP) and show that it significantly outperforms existing encoding approaches. We further show that combining local structural encodings, such as LCP, with global positional encodings improves downstream performance, suggesting that they capture complementary geometric information. Finally, we compare different encoding types with (curvature-based) rewiring techniques. Rewiring has recently received a surge of interest due to its ability to improve the performance of Graph Neural Networks by mitigating over-smoothing and over-squashing effects. Our results suggest that utilizing curvature information for structural encodings delivers significantly larger performance increases than rewiring.

Program synthesis methods aim to automatically generate programs restricted to a language that can explain a given specification of input-output pairs. While purely symbolic approaches suffer from a combinatorial search space, recent methods leverage neural networks to learn distributions over program structures to narrow this search space significantly, enabling more efficient search. However, for challenging problems, it remains difficult to train models to perform program synthesis in one shot, making test-time search essential. Most neural methods lack structured search mechanisms during inference, relying instead on stochastic sampling or gradient updates, which can be inefficient. In this work, we propose the Latent Program Network (LPN), a general algorithm for program induction that learns a distribution over latent programs in a continuous space, enabling efficient search and test-time adaptation. We explore how to train these networks to optimize for test-time computation and demonstrate the use of gradient-based search both during training and at test time. We evaluate LPN on ARC-AGI, a program synthesis benchmark that evaluates performance by generalizing programs to new inputs rather than explaining the underlying specification. We show that LPN can generalize beyond its training distribution and adapt to unseen tasks by utilizing test-time computation, outperforming algorithms without test-time adaptation mechanisms.

Designing effective positional encodings for graphs is key to building powerful graph transformers and enhancing message-passing graph neural networks. Although widespread, using Laplacian eigenvectors as positional encodings faces two fundamental challenges: (1) Non-uniqueness: there are many different eigendecompositions of the same Laplacian, and (2) Instability: small perturbations to the Laplacian could result in completely different eigenspaces, leading to unpredictable changes in positional encoding. Despite many attempts to address non-uniqueness, most methods overlook stability, leading to poor generalization on unseen graph structures. We identify the cause of instability to be a "hard partition" of eigenspaces. Hence, we introduce Stable and Expressive Positional Encodings (SPE), an architecture for processing eigenvectors that uses eigenvalues to "softly partition" eigenspaces. SPE is the first architecture that is (1) provably stable, and (2) universally expressive for basis invariant functions whilst respecting all symmetries of eigenvectors. Besides guaranteed stability, we prove that SPE is at least as expressive as existing methods, and highly capable of counting graph structures. Finally, we evaluate the effectiveness of our method on molecular property prediction, and out-of-distribution generalization tasks, finding improved generalization compared to existing positional encoding methods.

Existing monocular depth estimation methods have achieved excellent robustness in diverse scenes, but they can only retrieve affine-invariant depth, up to an unknown scale and shift. However, in some video-based scenarios such as video depth estimation and 3D scene reconstruction from a video, the unknown scale and shift residing in per-frame prediction may cause the depth inconsistency. To solve this problem, we propose a locally weighted linear regression method to recover the scale and shift with very sparse anchor points, which ensures the scale consistency along consecutive frames. Extensive experiments show that our method can boost the performance of existing state-of-the-art approaches by 50% at most over several zero-shot benchmarks. Besides, we merge over 6.3 million RGBD images to train strong and robust depth models. Our produced ResNet50-backbone model even outperforms the state-of-the-art DPT ViT-Large model. Combining with geometry-based reconstruction methods, we formulate a new dense 3D scene reconstruction pipeline, which benefits from both the scale consistency of sparse points and the robustness of monocular methods. By performing the simple per-frame prediction over a video, the accurate 3D scene shape can be recovered.

As the adoption of large language models increases and the need for per-user or per-task model customization grows, the parameter-efficient fine-tuning (PEFT) methods, such as low-rank adaptation (LoRA) and its variants, incur substantial storage and transmission costs. To further reduce stored parameters, we introduce a "divide-and-share" paradigm that breaks the barriers of low-rank decomposition across matrix dimensions, modules and layers by sharing parameters globally via a vector bank. As an instantiation of the paradigm to LoRA, our proposed VB-LoRA composites all the low-rank matrices of LoRA from a shared vector bank with a differentiable top-k admixture module. VB-LoRA achieves extreme parameter efficiency while maintaining comparable or better performance compared to state-of-the-art PEFT methods. Extensive experiments demonstrate the effectiveness of VB-LoRA on natural language understanding, natural language generation, and instruction tuning tasks. When fine-tuning the Llama2-13B model, VB-LoRA only uses 0.4% of LoRA's stored parameters, yet achieves superior results. Our source code is available at https://github.com/leo-yangli/VB-LoRA.

Loss functions serve as the foundation of supervised learning and are often chosen prior to model development. To avoid potentially ad hoc choices of losses, statistical decision theory describes a desirable property for losses known as properness, which asserts that Bayes' rule is optimal. Recent works have sought to learn losses and models jointly. Existing methods do this by fitting an inverse canonical link function which monotonically maps R to [0,1] to estimate probabilities for binary problems. In this paper, we extend monotonicity to maps between R^{C-1} and the projected probability simplex Delta^{C-1} by using monotonicity of gradients of convex functions. We present {\sc LegendreTron} as a novel and practical method that jointly learns proper canonical losses and probabilities for multiclass problems. Tested on a benchmark of domains with up to 1,000 classes, our experimental results show that our method consistently outperforms the natural multiclass baseline under a t-test at 99% significance on all datasets with greater than 10 classes.

This paper explores network binarization, a radical form of quantization, compressing model weights to a single bit, specifically for Large Language Models (LLMs) compression. Due to previous binarization methods collapsing LLMs, we propose a novel approach, Partially-Binarized LLM (PB-LLM), which can achieve extreme low-bit quantization while maintaining the linguistic reasoning capacity of quantized LLMs. Specifically, our exploration first uncovers the ineffectiveness of naive applications of existing binarization algorithms and highlights the imperative role of salient weights in achieving low-bit quantization. Thus, PB-LLM filters a small ratio of salient weights during binarization, allocating them to higher-bit storage, i.e., partially-binarization. PB-LLM is extended to recover the capacities of quantized LMMs, by analyzing from the perspective of post-training quantization (PTQ) and quantization-aware training (QAT). Under PTQ, combining the concepts from GPTQ, we reconstruct the binarized weight matrix guided by the Hessian matrix and successfully recover the reasoning capacity of PB-LLM in low-bit. Under QAT, we freeze the salient weights during training, explore the derivation of optimal scaling factors crucial for minimizing the quantization error, and propose a scaling mechanism based on this derived scaling strategy for residual binarized weights. Those explorations and the developed methodologies significantly contribute to rejuvenating the performance of low-bit quantized LLMs and present substantial advancements in the field of network binarization for LLMs.The code is available at https://github.com/hahnyuan/BinaryLLM.

This paper studies the fundamental limits of reinforcement learning (RL) in the challenging partially observable setting. While it is well-established that learning in Partially Observable Markov Decision Processes (POMDPs) requires exponentially many samples in the worst case, a surge of recent work shows that polynomial sample complexities are achievable under the revealing condition -- A natural condition that requires the observables to reveal some information about the unobserved latent states. However, the fundamental limits for learning in revealing POMDPs are much less understood, with existing lower bounds being rather preliminary and having substantial gaps from the current best upper bounds. We establish strong PAC and regret lower bounds for learning in revealing POMDPs. Our lower bounds scale polynomially in all relevant problem parameters in a multiplicative fashion, and achieve significantly smaller gaps against the current best upper bounds, providing a solid starting point for future studies. In particular, for multi-step revealing POMDPs, we show that (1) the latent state-space dependence is at least Omega(S^{1.5}) in the PAC sample complexity, which is notably harder than the Theta(S) scaling for fully-observable MDPs; (2) Any polynomial sublinear regret is at least Omega(T^{2/3}), suggesting its fundamental difference from the single-step case where O(T) regret is achievable. Technically, our hard instance construction adapts techniques in distribution testing, which is new to the RL literature and may be of independent interest.

The growing computational demands posed by increasingly number of neural network's parameters necessitate low-memory-consumption training approaches. Previous memory reduction techniques, such as Low-Rank Adaptation (LoRA) and ReLoRA, suffer from the limitation of low rank and saddle point issues, particularly during intensive tasks like pre-training. In this paper, we propose Sparse Spectral Training (SST), an advanced training methodology that updates all singular values and selectively updates singular vectors of network weights, thereby optimizing resource usage while closely approximating full-rank training. SST refines the training process by employing a targeted updating strategy for singular vectors, which is determined by a multinomial sampling method weighted by the significance of the singular values, ensuring both high performance and memory reduction. Through comprehensive testing on both Euclidean and hyperbolic neural networks across various tasks, including natural language generation, machine translation, node classification and link prediction, SST demonstrates its capability to outperform existing memory reduction training methods and is comparable with full-rank training in some cases. On OPT-125M, with rank equating to 8.3% of embedding dimension, SST reduces the perplexity gap to full-rank training by 67.6%, demonstrating a significant reduction of the performance loss with prevalent low-rank methods. This approach offers a strong alternative to traditional training techniques, paving the way for more efficient and scalable neural network training solutions.

In the field of algorithmic fairness, significant attention has been put on group fairness criteria, such as Demographic Parity and Equalized Odds. Nevertheless, these objectives, measured as global averages, have raised concerns about persistent local disparities between sensitive groups. In this work, we address the problem of local fairness, which ensures that the predictor is unbiased not only in terms of expectations over the whole population, but also within any subregion of the feature space, unknown at training time. To enforce this objective, we introduce ROAD, a novel approach that leverages the Distributionally Robust Optimization (DRO) framework within a fair adversarial learning objective, where an adversary tries to infer the sensitive attribute from the predictions. Using an instance-level re-weighting strategy, ROAD is designed to prioritize inputs that are likely to be locally unfair, i.e. where the adversary faces the least difficulty in reconstructing the sensitive attribute. Numerical experiments demonstrate the effectiveness of our method: it achieves Pareto dominance with respect to local fairness and accuracy for a given global fairness level across three standard datasets, and also enhances fairness generalization under distribution shift.

One method for obtaining generalizable solutions to machine learning tasks when presented with diverse training environments is to find invariant representations of the data. These are representations of the covariates such that the best model on top of the representation is invariant across training environments. In the context of linear Structural Equation Models (SEMs), invariant representations might allow us to learn models with out-of-distribution guarantees, i.e., models that are robust to interventions in the SEM. To address the invariant representation problem in a {\em finite sample} setting, we consider the notion of epsilon-approximate invariance. We study the following question: If a representation is approximately invariant with respect to a given number of training interventions, will it continue to be approximately invariant on a larger collection of unseen SEMs? This larger collection of SEMs is generated through a parameterized family of interventions. Inspired by PAC learning, we obtain finite-sample out-of-distribution generalization guarantees for approximate invariance that holds probabilistically over a family of linear SEMs without faithfulness assumptions. Our results show bounds that do not scale in ambient dimension when intervention sites are restricted to lie in a constant size subset of in-degree bounded nodes. We also show how to extend our results to a linear indirect observation model that incorporates latent variables.

Generative Adversarial Networks (GANs) produce high-quality images but are challenging to train. They need careful regularization, vast amounts of compute, and expensive hyper-parameter sweeps. We make significant headway on these issues by projecting generated and real samples into a fixed, pretrained feature space. Motivated by the finding that the discriminator cannot fully exploit features from deeper layers of the pretrained model, we propose a more effective strategy that mixes features across channels and resolutions. Our Projected GAN improves image quality, sample efficiency, and convergence speed. It is further compatible with resolutions of up to one Megapixel and advances the state-of-the-art Fr\'echet Inception Distance (FID) on twenty-two benchmark datasets. Importantly, Projected GANs match the previously lowest FIDs up to 40 times faster, cutting the wall-clock time from 5 days to less than 3 hours given the same computational resources.

The lottery ticket hypothesis (LTH) has increased attention to pruning neural networks at initialization. We study this problem in the linear setting. We show that finding a sparse mask at initialization is equivalent to the sketching problem introduced for efficient matrix multiplication. This gives us tools to analyze the LTH problem and gain insights into it. Specifically, using the mask found at initialization, we bound the approximation error of the pruned linear model at the end of training. We theoretically justify previous empirical evidence that the search for sparse networks may be data independent. By using the sketching perspective, we suggest a generic improvement to existing algorithms for pruning at initialization, which we show to be beneficial in the data-independent case.

Stochastic dual dynamic programming (SDDP) is a state-of-the-art method for solving multi-stage stochastic optimization, widely used for modeling real-world process optimization tasks. Unfortunately, SDDP has a worst-case complexity that scales exponentially in the number of decision variables, which severely limits applicability to only low dimensional problems. To overcome this limitation, we extend SDDP by introducing a trainable neural model that learns to map problem instances to a piece-wise linear value function within intrinsic low-dimension space, which is architected specifically to interact with a base SDDP solver, so that can accelerate optimization performance on new instances. The proposed Neural Stochastic Dual Dynamic Programming (nu-SDDP) continually self-improves by solving successive problems. An empirical investigation demonstrates that nu-SDDP can significantly reduce problem solving cost without sacrificing solution quality over competitors such as SDDP and reinforcement learning algorithms, across a range of synthetic and real-world process optimization problems.

Faithful visualizations of data residing on manifolds must take the underlying geometry into account when producing a flat planar view of the data. In this paper, we extend the classic stochastic neighbor embedding (SNE) algorithm to data on general Riemannian manifolds. We replace standard Gaussian assumptions with Riemannian diffusion counterparts and propose an efficient approximation that only requires access to calculations of Riemannian distances and volumes. We demonstrate that the approach also allows for mapping data from one manifold to another, e.g. from a high-dimensional sphere to a low-dimensional one.

We incorporate discrete and continuous time Markov processes as building blocks into probabilistic graphical models with latent and observed variables. We introduce the automatic Backward Filtering Forward Guiding (BFFG) paradigm (Mider et al., 2021) for programmable inference on latent states and model parameters. Our starting point is a generative model, a forward description of the probabilistic process dynamics. We backpropagate the information provided by observations through the model to transform the generative (forward) model into a pre-conditional model guided by the data. It approximates the actual conditional model with known likelihood-ratio between the two. The backward filter and the forward change of measure are suitable to be incorporated into a probabilistic programming context because they can be formulated as a set of transformation rules. The guided generative model can be incorporated in different approaches to efficiently sample latent states and parameters conditional on observations. We show applicability in a variety of settings, including Markov chains with discrete state space, interacting particle systems, state space models, branching diffusions and Gamma processes.

In this work, we introduce Brain Latent Progression (BrLP), a novel spatiotemporal disease progression model based on latent diffusion. BrLP is designed to predict the evolution of diseases at the individual level on 3D brain MRIs. Existing deep generative models developed for this task are primarily data-driven and face challenges in learning disease progressions. BrLP addresses these challenges by incorporating prior knowledge from disease models to enhance the accuracy of predictions. To implement this, we propose to integrate an auxiliary model that infers volumetric changes in various brain regions. Additionally, we introduce Latent Average Stabilization (LAS), a novel technique to improve spatiotemporal consistency of the predicted progression. BrLP is trained and evaluated on a large dataset comprising 11,730 T1-weighted brain MRIs from 2,805 subjects, collected from three publicly available, longitudinal Alzheimer's Disease (AD) studies. In our experiments, we compare the MRI scans generated by BrLP with the actual follow-up MRIs available from the subjects, in both cross-sectional and longitudinal settings. BrLP demonstrates significant improvements over existing methods, with an increase of 22% in volumetric accuracy across AD-related brain regions and 43% in image similarity to the ground-truth scans. The ability of BrLP to generate conditioned 3D scans at the subject level, along with the novelty of integrating prior knowledge to enhance accuracy, represents a significant advancement in disease progression modeling, opening new avenues for precision medicine. The code of BrLP is available at the following link: https://github.com/LemuelPuglisi/BrLP.

We present VoxelKP, a novel fully sparse network architecture tailored for human keypoint estimation in LiDAR data. The key challenge is that objects are distributed sparsely in 3D space, while human keypoint detection requires detailed local information wherever humans are present. We propose four novel ideas in this paper. First, we propose sparse selective kernels to capture multi-scale context. Second, we introduce sparse box-attention to focus on learning spatial correlations between keypoints within each human instance. Third, we incorporate a spatial encoding to leverage absolute 3D coordinates when projecting 3D voxels to a 2D grid encoding a bird's eye view. Finally, we propose hybrid feature learning to combine the processing of per-voxel features with sparse convolution. We evaluate our method on the Waymo dataset and achieve an improvement of 27% on the MPJPE metric compared to the state-of-the-art, HUM3DIL, trained on the same data, and 12% against the state-of-the-art, GC-KPL, pretrained on a 25times larger dataset. To the best of our knowledge, VoxelKP is the first single-staged, fully sparse network that is specifically designed for addressing the challenging task of 3D keypoint estimation from LiDAR data, achieving state-of-the-art performances. Our code is available at https://github.com/shijianjian/VoxelKP.

Given a set of K probability densities, we consider the multimarginal generative modeling problem of learning a joint distribution that recovers these densities as marginals. The structure of this joint distribution should identify multi-way correspondences among the prescribed marginals. We formalize an approach to this task within a generalization of the stochastic interpolant framework, leading to efficient learning algorithms built upon dynamical transport of measure. Our generative models are defined by velocity and score fields that can be characterized as the minimizers of simple quadratic objectives, and they are defined on a simplex that generalizes the time variable in the usual dynamical transport framework. The resulting transport on the simplex is influenced by all marginals, and we show that multi-way correspondences can be extracted. The identification of such correspondences has applications to style transfer, algorithmic fairness, and data decorruption. In addition, the multimarginal perspective enables an efficient algorithm for reducing the dynamical transport cost in the ordinary two-marginal setting. We demonstrate these capacities with several numerical examples.

Learned optimizers (LOs) can significantly reduce the wall-clock training time of neural networks, substantially reducing training costs. However, they often suffer from poor meta-generalization, especially when training networks larger than those seen during meta-training. To address this, we use the recently proposed Maximal Update Parametrization (muP), which allows zero-shot generalization of optimizer hyperparameters from smaller to larger models. We extend muP theory to learned optimizers, treating the meta-training problem as finding the learned optimizer under muP. Our evaluation shows that LOs meta-trained with muP substantially improve meta-generalization as compared to LOs trained under standard parametrization (SP). Notably, when applied to large-width models, our best muLO, trained for 103 GPU-hours, matches or exceeds the performance of VeLO, the largest publicly available learned optimizer, meta-trained with 4000 TPU-months of compute. Moreover, muLOs demonstrate better generalization than their SP counterparts to deeper networks and to much longer training horizons (25 times longer) than those seen during meta-training.

Many methods in differentially private model training rely on computing the similarity between a query point (such as public or synthetic data) and private data. We abstract out this common subroutine and study the following fundamental algorithmic problem: Given a similarity function f and a large high-dimensional private dataset X subset R^d, output a differentially private (DP) data structure which approximates sum_{x in X} f(x,y) for any query y. We consider the cases where f is a kernel function, such as f(x,y) = e^{-|x-y|_2^2/sigma^2} (also known as DP kernel density estimation), or a distance function such as f(x,y) = |x-y|_2, among others. Our theoretical results improve upon prior work and give better privacy-utility trade-offs as well as faster query times for a wide range of kernels and distance functions. The unifying approach behind our results is leveraging `low-dimensional structures' present in the specific functions f that we study, using tools such as provable dimensionality reduction, approximation theory, and one-dimensional decomposition of the functions. Our algorithms empirically exhibit improved query times and accuracy over prior state of the art. We also present an application to DP classification. Our experiments demonstrate that the simple methodology of classifying based on average similarity is orders of magnitude faster than prior DP-SGD based approaches for comparable accuracy.

We study the connection between multicalibration and boosting for squared error regression. First we prove a useful characterization of multicalibration in terms of a ``swap regret'' like condition on squared error. Using this characterization, we give an exceedingly simple algorithm that can be analyzed both as a boosting algorithm for regression and as a multicalibration algorithm for a class H that makes use only of a standard squared error regression oracle for H. We give a weak learning assumption on H that ensures convergence to Bayes optimality without the need to make any realizability assumptions -- giving us an agnostic boosting algorithm for regression. We then show that our weak learning assumption on H is both necessary and sufficient for multicalibration with respect to H to imply Bayes optimality. We also show that if H satisfies our weak learning condition relative to another class C then multicalibration with respect to H implies multicalibration with respect to C. Finally we investigate the empirical performance of our algorithm experimentally using an open source implementation that we make available. Our code repository can be found at https://github.com/Declancharrison/Level-Set-Boosting.

In this paper, we propose the first framework that enables solving graph learning tasks of all levels (node, edge and graph) and all types (generation, regression and classification) with one model. We first propose Latent Graph Diffusion (LGD), a generative model that can generate node, edge, and graph-level features of all categories simultaneously. We achieve this goal by embedding the graph structures and features into a latent space leveraging a powerful encoder which can also be decoded, then training a diffusion model in the latent space. LGD is also capable of conditional generation through a specifically designed cross-attention mechanism. Then we formulate prediction tasks including regression and classification as (conditional) generation, which enables our LGD to solve tasks of all levels and all types with provable guarantees. We verify the effectiveness of our framework with extensive experiments, where our models achieve state-of-the-art or highly competitive results across generation and regression tasks.

Low-rank adaptation (LoRA) has emerged as a new paradigm for cost-efficient fine-tuning of large language models (LLMs). However, fine-tuned LLMs often become overconfident especially when fine-tuned on small datasets. Bayesian methods, with their inherent ability to estimate uncertainty, serve as potent tools to mitigate overconfidence and enhance calibration. In this work, we introduce Laplace-LoRA, which applies a Bayesian approach to the LoRA parameters. Specifically, Laplace-LoRA applies a Laplace approximation to the posterior over the LoRA parameters, considerably improving the calibration of fine-tuned LLMs.

Recovering dense and long-range pixel motion in videos is a challenging problem. Part of the difficulty arises from the 3D-to-2D projection process, leading to occlusions and discontinuities in the 2D motion domain. While 2D motion can be intricate, we posit that the underlying 3D motion can often be simple and low-dimensional. In this work, we propose to estimate point trajectories in 3D space to mitigate the issues caused by image projection. Our method, named SpatialTracker, lifts 2D pixels to 3D using monocular depth estimators, represents the 3D content of each frame efficiently using a triplane representation, and performs iterative updates using a transformer to estimate 3D trajectories. Tracking in 3D allows us to leverage as-rigid-as-possible (ARAP) constraints while simultaneously learning a rigidity embedding that clusters pixels into different rigid parts. Extensive evaluation shows that our approach achieves state-of-the-art tracking performance both qualitatively and quantitatively, particularly in challenging scenarios such as out-of-plane rotation.

We present a generalization of the proximal operator defined through a convex combination of convex objectives, where the coefficients are updated in a minimax fashion. We prove that this new operator is Bregman firmly nonexpansive with respect to a Bregman divergence that combines Euclidean and information geometries.

Polygonal meshes are ubiquitous, but have only played a relatively minor role in the deep learning revolution. State-of-the-art neural generative models for 3D shapes learn implicit functions and generate meshes via expensive iso-surfacing. We overcome these challenges by employing a classical spatial data structure from computer graphics, Binary Space Partitioning (BSP), to facilitate 3D learning. The core operation of BSP involves recursive subdivision of 3D space to obtain convex sets. By exploiting this property, we devise BSP-Net, a network that learns to represent a 3D shape via convex decomposition without supervision. The network is trained to reconstruct a shape using a set of convexes obtained from a BSP-tree built over a set of planes, where the planes and convexes are both defined by learned network weights. BSP-Net directly outputs polygonal meshes from the inferred convexes. The generated meshes are watertight, compact (i.e., low-poly), and well suited to represent sharp geometry. We show that the reconstruction quality by BSP-Net is competitive with those from state-of-the-art methods while using much fewer primitives. We also explore variations to BSP-Net including using a more generic decoder for reconstruction, more general primitives than planes, as well as training a generative model with variational auto-encoders. Code is available at https://github.com/czq142857/BSP-NET-original.

We introduce a new family of physics-inspired generative models termed PFGM++ that unifies diffusion models and Poisson Flow Generative Models (PFGM). These models realize generative trajectories for N dimensional data by embedding paths in N{+}D dimensional space while still controlling the progression with a simple scalar norm of the D additional variables. The new models reduce to PFGM when D{=}1 and to diffusion models when D{to}infty. The flexibility of choosing D allows us to trade off robustness against rigidity as increasing D results in more concentrated coupling between the data and the additional variable norms. We dispense with the biased large batch field targets used in PFGM and instead provide an unbiased perturbation-based objective similar to diffusion models. To explore different choices of D, we provide a direct alignment method for transferring well-tuned hyperparameters from diffusion models (D{to} infty) to any finite D values. Our experiments show that models with finite D can be superior to previous state-of-the-art diffusion models on CIFAR-10/FFHQ 64{times}64 datasets, with FID scores of 1.91/2.43 when D{=}2048/128. In class-conditional setting, D{=}2048 yields current state-of-the-art FID of 1.74 on CIFAR-10. In addition, we demonstrate that models with smaller D exhibit improved robustness against modeling errors. Code is available at https://github.com/Newbeeer/pfgmpp

Most existing zero-shot learning approaches exploit transfer learning via an intermediate-level semantic representation shared between an annotated auxiliary dataset and a target dataset with different classes and no annotation. A projection from a low-level feature space to the semantic representation space is learned from the auxiliary dataset and is applied without adaptation to the target dataset. In this paper we identify two inherent limitations with these approaches. First, due to having disjoint and potentially unrelated classes, the projection functions learned from the auxiliary dataset/domain are biased when applied directly to the target dataset/domain. We call this problem the projection domain shift problem and propose a novel framework, transductive multi-view embedding, to solve it. The second limitation is the prototype sparsity problem which refers to the fact that for each target class, only a single prototype is available for zero-shot learning given a semantic representation. To overcome this problem, a novel heterogeneous multi-view hypergraph label propagation method is formulated for zero-shot learning in the transductive embedding space. It effectively exploits the complementary information offered by different semantic representations and takes advantage of the manifold structures of multiple representation spaces in a coherent manner. We demonstrate through extensive experiments that the proposed approach (1) rectifies the projection shift between the auxiliary and target domains, (2) exploits the complementarity of multiple semantic representations, (3) significantly outperforms existing methods for both zero-shot and N-shot recognition on three image and video benchmark datasets, and (4) enables novel cross-view annotation tasks.

Generating functions, which are widely used in combinatorics and probability theory, encode function values into the coefficients of a polynomial. In this paper, we explore their use as a tractable probabilistic model, and propose probabilistic generating circuits (PGCs) for their efficient representation. PGCs are strictly more expressive efficient than many existing tractable probabilistic models, including determinantal point processes (DPPs), probabilistic circuits (PCs) such as sum-product networks, and tractable graphical models. We contend that PGCs are not just a theoretical framework that unifies vastly different existing models, but also show great potential in modeling realistic data. We exhibit a simple class of PGCs that are not trivially subsumed by simple combinations of PCs and DPPs, and obtain competitive performance on a suite of density estimation benchmarks. We also highlight PGCs' connection to the theory of strongly Rayleigh distributions.

Distributed and federated learning algorithms and techniques associated primarily with minimization problems. However, with the increase of minimax optimization and variational inequality problems in machine learning, the necessity of designing efficient distributed/federated learning approaches for these problems is becoming more apparent. In this paper, we provide a unified convergence analysis of communication-efficient local training methods for distributed variational inequality problems (VIPs). Our approach is based on a general key assumption on the stochastic estimates that allows us to propose and analyze several novel local training algorithms under a single framework for solving a class of structured non-monotone VIPs. We present the first local gradient descent-accent algorithms with provable improved communication complexity for solving distributed variational inequalities on heterogeneous data. The general algorithmic framework recovers state-of-the-art algorithms and their sharp convergence guarantees when the setting is specialized to minimization or minimax optimization problems. Finally, we demonstrate the strong performance of the proposed algorithms compared to state-of-the-art methods when solving federated minimax optimization problems.

We present high quality image synthesis results using diffusion probabilistic models, a class of latent variable models inspired by considerations from nonequilibrium thermodynamics. Our best results are obtained by training on a weighted variational bound designed according to a novel connection between diffusion probabilistic models and denoising score matching with Langevin dynamics, and our models naturally admit a progressive lossy decompression scheme that can be interpreted as a generalization of autoregressive decoding. On the unconditional CIFAR10 dataset, we obtain an Inception score of 9.46 and a state-of-the-art FID score of 3.17. On 256x256 LSUN, we obtain sample quality similar to ProgressiveGAN. Our implementation is available at https://github.com/hojonathanho/diffusion

Establishing dense correspondence between two images is a fundamental computer vision problem, which is typically tackled by matching local feature descriptors. However, without global awareness, such local features are often insufficient for disambiguating similar regions. And computing the pairwise feature correlation across images is both computation-expensive and memory-intensive. To make the local features aware of the global context and improve their matching accuracy, we introduce DenseGAP, a new solution for efficient Dense correspondence learning with a Graph-structured neural network conditioned on Anchor Points. Specifically, we first propose a graph structure that utilizes anchor points to provide sparse but reliable prior on inter- and intra-image context and propagates them to all image points via directed edges. We also design a graph-structured network to broadcast multi-level contexts via light-weighted message-passing layers and generate high-resolution feature maps at low memory cost. Finally, based on the predicted feature maps, we introduce a coarse-to-fine framework for accurate correspondence prediction using cycle consistency. Our feature descriptors capture both local and global information, thus enabling a continuous feature field for querying arbitrary points at high resolution. Through comprehensive ablative experiments and evaluations on large-scale indoor and outdoor datasets, we demonstrate that our method advances the state-of-the-art of correspondence learning on most benchmarks.

Learning decompositions of expensive-to-evaluate black-box functions promises to scale Bayesian optimisation (BO) to high-dimensional problems. However, the success of these techniques depends on finding proper decompositions that accurately represent the black-box. While previous works learn those decompositions based on data, we investigate data-independent decomposition sampling rules in this paper. We find that data-driven learners of decompositions can be easily misled towards local decompositions that do not hold globally across the search space. Then, we formally show that a random tree-based decomposition sampler exhibits favourable theoretical guarantees that effectively trade off maximal information gain and functional mismatch between the actual black-box and its surrogate as provided by the decomposition. Those results motivate the development of the random decomposition upper-confidence bound algorithm (RDUCB) that is straightforward to implement - (almost) plug-and-play - and, surprisingly, yields significant empirical gains compared to the previous state-of-the-art on a comprehensive set of benchmarks. We also confirm the plug-and-play nature of our modelling component by integrating our method with HEBO, showing improved practical gains in the highest dimensional tasks from Bayesmark.

We introduce marginalization models (MaMs), a new family of generative models for high-dimensional discrete data. They offer scalable and flexible generative modeling with tractable likelihoods by explicitly modeling all induced marginal distributions. Marginalization models enable fast evaluation of arbitrary marginal probabilities with a single forward pass of the neural network, which overcomes a major limitation of methods with exact marginal inference, such as autoregressive models (ARMs). We propose scalable methods for learning the marginals, grounded in the concept of "marginalization self-consistency". Unlike previous methods, MaMs support scalable training of any-order generative models for high-dimensional problems under the setting of energy-based training, where the goal is to match the learned distribution to a given desired probability (specified by an unnormalized (log) probability function such as energy function or reward function). We demonstrate the effectiveness of the proposed model on a variety of discrete data distributions, including binary images, language, physical systems, and molecules, for maximum likelihood and energy-based training settings. MaMs achieve orders of magnitude speedup in evaluating the marginal probabilities on both settings. For energy-based training tasks, MaMs enable any-order generative modeling of high-dimensional problems beyond the capability of previous methods. Code is at https://github.com/PrincetonLIPS/MaM.

With the widespread adoption of machine learning systems, the need to curtail their behavior has become increasingly apparent. This is evidenced by recent advancements towards developing models that satisfy robustness, safety, and fairness requirements. These requirements can be imposed (with generalization guarantees) by formulating constrained learning problems that can then be tackled by dual ascent algorithms. Yet, though these algorithms converge in objective value, even in non-convex settings, they cannot guarantee that their outcome is feasible. Doing so requires randomizing over all iterates, which is impractical in virtually any modern applications. Still, final iterates have been observed to perform well in practice. In this work, we address this gap between theory and practice by characterizing the constraint violation of Lagrangian minimizers associated with optimal dual variables, despite lack of convexity. To do this, we leverage the fact that non-convex, finite-dimensional constrained learning problems can be seen as parametrizations of convex, functional problems. Our results show that rich parametrizations effectively mitigate the issue of feasibility in dual methods, shedding light on prior empirical successes of dual learning. We illustrate our findings in fair learning tasks.

We show that Large Language Model from Power Law Decoder Representations (PLDR-LLM) is a foundational model whose deductive outputs are invariant tensors up to a small perturbation. PLDR-LLM learns a singularity condition for the deductive outputs that enable the once-inferred energy-curvature tensor G_{LM} to replace the deep neural network of power law graph attention (PLGA) generating the deductive outputs at inference. We demonstrate that a cache for G_{LM} (G-cache) and KV-cache can be implemented in a straightforward manner to improve the inference time. The invariance and generalizable nature of deductive outputs is at a very high fidelity where deductive outputs have same RMSE and determinant values up to 15 decimal places after caching, and zero-shot benchmark scores remain unchanged. Ablation studies show that learned deductive outputs have distinct loss and accuracy characteristics from models pretrained with transferred, randomly initialized or identity tensors as a constant tensor operator and an LLM with scaled-dot product attention (SDPA) is a special case of PLDR-LLM where G_{LM} is predefined as identity. The observed invariance characteristic introduces a novel asymmetry between training and inference phases with caching. We outline observed common characteristics of the deductive outputs for the learned singularity condition. We provide an implementation of a training and inference framework for PLDR-LLM with KV-cache and G-cache.

Many state-of-the-art hyperparameter optimization (HPO) algorithms rely on model-based optimizers that learn surrogate models of the target function to guide the search. Gaussian processes are the de facto surrogate model due to their ability to capture uncertainty but they make strong assumptions about the observation noise, which might not be warranted in practice. In this work, we propose to leverage conformalized quantile regression which makes minimal assumptions about the observation noise and, as a result, models the target function in a more realistic and robust fashion which translates to quicker HPO convergence on empirical benchmarks. To apply our method in a multi-fidelity setting, we propose a simple, yet effective, technique that aggregates observed results across different resource levels and outperforms conventional methods across many empirical tasks.

Hyperbolic embeddings offer excellent quality with few dimensions when embedding hierarchical data structures like synonym or type hierarchies. Given a tree, we give a combinatorial construction that embeds the tree in hyperbolic space with arbitrarily low distortion without using optimization. On WordNet, our combinatorial embedding obtains a mean-average-precision of 0.989 with only two dimensions, while Nickel et al.'s recent construction obtains 0.87 using 200 dimensions. We provide upper and lower bounds that allow us to characterize the precision-dimensionality tradeoff inherent in any hyperbolic embedding. To embed general metric spaces, we propose a hyperbolic generalization of multidimensional scaling (h-MDS). We show how to perform exact recovery of hyperbolic points from distances, provide a perturbation analysis, and give a recovery result that allows us to reduce dimensionality. The h-MDS approach offers consistently low distortion even with few dimensions across several datasets. Finally, we extract lessons from the algorithms and theory above to design a PyTorch-based implementation that can handle incomplete information and is scalable.

The rapid growth of large models has raised concerns about their environmental impact and equity in accessibility due to significant computational costs. Low-Rank Adapters (LoRA) offer a lightweight solution for finetuning large models, resulting in an abundance of publicly available adapters tailored to diverse domains. We ask: Can these pretrained adapters be leveraged to further streamline adaptation to new tasks while addressing these challenges? We introduce EigenLoRAx, a parameter-efficient finetuning method that recycles existing adapters to create a principal subspace aligned with their shared domain knowledge which can be further augmented with orthogonal basis vectors in low-resource scenarios. This enables rapid adaptation to new tasks by learning only lightweight coefficients on the principal components of the subspace - eliminating the need to finetune entire adapters. EigenLoRAx requires significantly fewer parameters and memory, improving efficiency for both training and inference. Our method demonstrates strong performance across diverse domains and tasks, offering a scalable for edge-based applications, personalization, and equitable deployment of large models in resource-constrained environments.

The Evidence Lower Bound (ELBO) is a quantity that plays a key role in variational inference. It can also be used as a criterion in model selection. However, though extremely popular in practice in the variational Bayes community, there has never been a general theoretic justification for selecting based on the ELBO. In this paper, we show that the ELBO maximization strategy has strong theoretical guarantees, and is robust to model misspecification while most works rely on the assumption that one model is correctly specified. We illustrate our theoretical results by an application to the selection of the number of principal components in probabilistic PCA.

The trade-off between regret and computational cost is a fundamental problem for online kernel regression, and previous algorithms worked on the trade-off can not keep optimal regret bounds at a sublinear computational complexity. In this paper, we propose two new algorithms, AOGD-ALD and NONS-ALD, which can keep nearly optimal regret bounds at a sublinear computational complexity, and give sufficient conditions under which our algorithms work. Both algorithms dynamically maintain a group of nearly orthogonal basis used to approximate the kernel mapping, and keep nearly optimal regret bounds by controlling the approximate error. The number of basis depends on the approximate error and the decay rate of eigenvalues of the kernel matrix. If the eigenvalues decay exponentially, then AOGD-ALD and NONS-ALD separately achieves a regret of O(L(f)) and O(d_{eff}(mu)T) at a computational complexity in O(ln^2{T}). If the eigenvalues decay polynomially with degree pgeq 1, then our algorithms keep the same regret bounds at a computational complexity in o(T) in the case of p>4 and pgeq 10, respectively. L(f) is the cumulative losses of f and d_{eff}(mu) is the effective dimension of the problem. The two regret bounds are nearly optimal and are not comparable.

Due to the substantial scale of Large Language Models (LLMs), the direct application of conventional compression methodologies proves impractical. The computational demands associated with even minimal gradient updates present challenges, particularly on consumer-grade hardware. This paper introduces an innovative approach for the parametric and practical compression of LLMs based on reduced order modelling, which entails low-rank decomposition within the feature space and re-parameterization in the weight space. Notably, this compression technique operates in a layer-wise manner, obviating the need for a GPU device and enabling the compression of billion-scale models within stringent constraints of both memory and time. Our method represents a significant advancement in model compression by leveraging matrix decomposition, demonstrating superior efficacy compared to the prevailing state-of-the-art structured pruning method.

We propose a new method for optimistic planning in infinite-horizon discounted Markov decision processes based on the idea of adding regularization to the updates of an otherwise standard approximate value iteration procedure. This technique allows us to avoid contraction and monotonicity arguments typically required by existing analyses of approximate dynamic programming methods, and in particular to use approximate transition functions estimated via least-squares procedures in MDPs with linear function approximation. We use our method to recover known guarantees in tabular MDPs and to provide a computationally efficient algorithm for learning near-optimal policies in discounted linear mixture MDPs from a single stream of experience, and show it achieves near-optimal statistical guarantees.

Visual localization is the task of estimating a 6-DoF camera pose of a query image within a provided 3D reference map. Thanks to recent advances in various 3D sensors, 3D point clouds are becoming a more accurate and affordable option for building the reference map, but research to match the points of 3D point clouds with pixels in 2D images for visual localization remains challenging. Existing approaches that jointly learn 2D-3D feature matching suffer from low inliers due to representational differences between the two modalities, and the methods that bypass this problem into classification have an issue of poor refinement. In this work, we propose EP2P-Loc, a novel large-scale visual localization method that mitigates such appearance discrepancy and enables end-to-end training for pose estimation. To increase the number of inliers, we propose a simple algorithm to remove invisible 3D points in the image, and find all 2D-3D correspondences without keypoint detection. To reduce memory usage and search complexity, we take a coarse-to-fine approach where we extract patch-level features from 2D images, then perform 2D patch classification on each 3D point, and obtain the exact corresponding 2D pixel coordinates through positional encoding. Finally, for the first time in this task, we employ a differentiable PnP for end-to-end training. In the experiments on newly curated large-scale indoor and outdoor benchmarks based on 2D-3D-S and KITTI, we show that our method achieves the state-of-the-art performance compared to existing visual localization and image-to-point cloud registration methods.

Large Language Models (LLMs) have demonstrated remarkable performance across various tasks but remain prone to hallucinations. Detecting hallucinations is essential for safety-critical applications, and recent methods leverage attention map properties to this end, though their effectiveness remains limited. In this work, we investigate the spectral features of attention maps by interpreting them as adjacency matrices of graph structures. We propose the LapEigvals method, which utilises the top-k eigenvalues of the Laplacian matrix derived from the attention maps as an input to hallucination detection probes. Empirical evaluations demonstrate that our approach achieves state-of-the-art hallucination detection performance among attention-based methods. Extensive ablation studies further highlight the robustness and generalisation of LapEigvals, paving the way for future advancements in the hallucination detection domain.

In this article, we introduce a new parameterized family of topological invariants, taking the form of candidate decompositions, for multi-parameter persistence modules. We prove that our candidate decompositions are controllable approximations: when restricting to modules that can be decomposed into interval summands, we establish theoretical results about the approximation error between our candidate decompositions and the true underlying module in terms of the standard interleaving and bottleneck distances. Moreover, even when the underlying module does not admit such a decomposition, our candidate decompositions are nonetheless stable invariants; small perturbations in the underlying module lead to small perturbations in the candidate decomposition. Then, we introduce MMA (Multipersistence Module Approximation): an algorithm for computing stable instances of such invariants, which is based on fibered barcodes and exact matchings, two constructions that stem from the theory of single-parameter persistence. By design, MMA can handle an arbitrary number of filtrations, and has bounded complexity and running time. Finally, we present empirical evidence validating the generalization capabilities and running time speed-ups of MMA on several data sets.

Large pre-trained models (LPMs), such as large language models, have become ubiquitous and are employed in many applications. These models are often adapted to a desired domain or downstream task through a fine-tuning stage. This paper proposes SQFT, an end-to-end solution for low-precision sparse parameter-efficient fine-tuning of LPMs, allowing for effective model manipulation in resource-constrained environments. Additionally, an innovative strategy enables the merging of sparse weights with low-rank adapters without losing sparsity and accuracy, overcoming the limitations of previous approaches. SQFT also addresses the challenge of having quantized weights and adapters with different numerical precisions, enabling merging in the desired numerical format without sacrificing accuracy. Multiple adaptation scenarios, models, and comprehensive sparsity levels demonstrate the effectiveness of SQFT. Models and code are available at https://github.com/IntelLabs/Hardware-Aware-Automated-Machine-Learning.

We present a simple yet powerful neural network that implicitly represents and renders 3D objects and scenes only from 2D observations. The network models 3D geometries as a general radiance field, which takes a set of 2D images with camera poses and intrinsics as input, constructs an internal representation for each point of the 3D space, and then renders the corresponding appearance and geometry of that point viewed from an arbitrary position. The key to our approach is to learn local features for each pixel in 2D images and to then project these features to 3D points, thus yielding general and rich point representations. We additionally integrate an attention mechanism to aggregate pixel features from multiple 2D views, such that visual occlusions are implicitly taken into account. Extensive experiments demonstrate that our method can generate high-quality and realistic novel views for novel objects, unseen categories and challenging real-world scenes.

Recent works have revealed that infinitely-wide feed-forward or recurrent neural networks of any architecture correspond to Gaussian processes referred to as Neural Network Gaussian Processes (NNGPs). While these works have extended the class of neural networks converging to Gaussian processes significantly, however, there has been little focus on broadening the class of stochastic processes that such neural networks converge to. In this work, inspired by the scale mixture of Gaussian random variables, we propose the scale mixture of NNGPs for which we introduce a prior distribution on the scale of the last-layer parameters. We show that simply introducing a scale prior on the last-layer parameters can turn infinitely-wide neural networks of any architecture into a richer class of stochastic processes. With certain scale priors, we obtain heavy-tailed stochastic processes, and in the case of inverse gamma priors, we recover Student's t processes. We further analyze the distributions of the neural networks initialized with our prior setting and trained with gradient descents and obtain similar results as for NNGPs. We present a practical posterior-inference algorithm for the scale mixture of NNGPs and empirically demonstrate its usefulness on regression and classification tasks. In particular, we show that in both tasks, the heavy-tailed stochastic processes obtained from our framework are robust to out-of-distribution data.

We propose GS-LRM, a scalable large reconstruction model that can predict high-quality 3D Gaussian primitives from 2-4 posed sparse images in 0.23 seconds on single A100 GPU. Our model features a very simple transformer-based architecture; we patchify input posed images, pass the concatenated multi-view image tokens through a sequence of transformer blocks, and decode final per-pixel Gaussian parameters directly from these tokens for differentiable rendering. In contrast to previous LRMs that can only reconstruct objects, by predicting per-pixel Gaussians, GS-LRM naturally handles scenes with large variations in scale and complexity. We show that our model can work on both object and scene captures by training it on Objaverse and RealEstate10K respectively. In both scenarios, the models outperform state-of-the-art baselines by a wide margin. We also demonstrate applications of our model in downstream 3D generation tasks. Our project webpage is available at: https://sai-bi.github.io/project/gs-lrm/ .