Daily Papers

Persistent homology (PH) provides topological descriptors for geometric data, such as weighted graphs, which are interpretable, stable to perturbations, and invariant under, e.g., relabeling. Most applications of PH focus on the one-parameter case -- where the descriptors summarize the changes in topology of data as it is filtered by a single quantity of interest -- and there is now a wide array of methods enabling the use of one-parameter PH descriptors in data science, which rely on the stable vectorization of these descriptors as elements of a Hilbert space. Although the multiparameter PH (MPH) of data that is filtered by several quantities of interest encodes much richer information than its one-parameter counterpart, the scarceness of stability results for MPH descriptors has so far limited the available options for the stable vectorization of MPH. In this paper, we aim to bring together the best of both worlds by showing how the interpretation of signed barcodes -- a recent family of MPH descriptors -- as signed measures leads to natural extensions of vectorization strategies from one parameter to multiple parameters. The resulting feature vectors are easy to define and to compute, and provably stable. While, as a proof of concept, we focus on simple choices of signed barcodes and vectorizations, we already see notable performance improvements when comparing our feature vectors to state-of-the-art topology-based methods on various types of data.

Image segmentation is a largely researched field where neural networks find vast applications in many facets of technology. Some of the most popular approaches to train segmentation networks employ loss functions optimizing pixel-overlap, an objective that is insufficient for many segmentation tasks. In recent years, their limitations fueled a growing interest in topology-aware methods, which aim to recover the correct topology of the segmented structures. However, so far, none of the existing approaches achieve a spatially correct matching between the topological features of ground truth and prediction. In this work, we propose the first topologically and feature-wise accurate metric and loss function for supervised image segmentation, which we term Betti matching. We show how induced matchings guarantee the spatially correct matching between barcodes in a segmentation setting. Furthermore, we propose an efficient algorithm to compute the Betti matching of images. We show that the Betti matching error is an interpretable metric to evaluate the topological correctness of segmentations, which is more sensitive than the well-established Betti number error. Moreover, the differentiability of the Betti matching loss enables its use as a loss function. It improves the topological performance of segmentation networks across six diverse datasets while preserving the volumetric performance. Our code is available in https://github.com/nstucki/Betti-matching.

Understanding biodiversity is a global challenge, in which DNA barcodes - short snippets of DNA that cluster by species - play a pivotal role. In particular, invertebrates, a highly diverse and under-explored group, pose unique taxonomic complexities. We explore machine learning approaches, comparing supervised CNNs, fine-tuned foundation models, and a DNA barcode-specific masking strategy across datasets of varying complexity. While simpler datasets and tasks favor supervised CNNs or fine-tuned transformers, challenging species-level identification demands a paradigm shift towards self-supervised pretraining. We propose BarcodeBERT, the first self-supervised method for general biodiversity analysis, leveraging a 1.5 M invertebrate DNA barcode reference library. This work highlights how dataset specifics and coverage impact model selection, and underscores the role of self-supervised pretraining in achieving high-accuracy DNA barcode-based identification at the species and genus level. Indeed, without the fine-tuning step, BarcodeBERT pretrained on a large DNA barcode dataset outperforms DNABERT and DNABERT-2 on multiple downstream classification tasks. The code repository is available at https://github.com/Kari-Genomics-Lab/BarcodeBERT