new

Get trending papers in your email inbox!

Subscribe

byAK and the research community

Mar 14

Contrastive Learning with Logic-driven Data Augmentation for Logical Reasoning over Text

Pre-trained large language model (LLM) is under exploration to perform NLP tasks that may require logical reasoning. Logic-driven data augmentation for representation learning has been shown to improve the performance of tasks requiring logical reasoning, but most of these data rely on designed templates and therefore lack generalization. In this regard, we propose an AMR-based logical equivalence-driven data augmentation method (AMR-LE) for generating logically equivalent data. Specifically, we first parse a text into the form of an AMR graph, next apply four logical equivalence laws (contraposition, double negation, commutative and implication laws) on the AMR graph to construct a logically equivalent/inequivalent AMR graph, and then convert it into a logically equivalent/inequivalent sentence. To help the model to better learn these logical equivalence laws, we propose a logical equivalence-driven contrastive learning training paradigm, which aims to distinguish the difference between logical equivalence and inequivalence. Our AMR-LE (Ensemble) achieves #2 on the ReClor leaderboard https://eval.ai/web/challenges/challenge-page/503/leaderboard/1347 . Our model shows better performance on seven downstream tasks, including ReClor, LogiQA, MNLI, MRPC, RTE, QNLI, and QQP. The source code and dataset are public at https://github.com/Strong-AI-Lab/Logical-Equivalence-driven-AMR-Data-Augmentation-for-Representation-Learning .

Thought-Path Contrastive Learning via Premise-Oriented Data Augmentation for Logical Reading Comprehension

Logical reading comprehension is a challenging task that entails grasping the underlying semantics of text and applying reasoning to deduce the correct answer. Prior researches have primarily focused on enhancing logical reasoning capabilities through Chain-of-Thought (CoT) or data augmentation. However, previous work constructing chain-of-thought rationales concentrates solely on analyzing correct options, neglecting the incorrect alternatives. Addtionally, earlier efforts on data augmentation by altering contexts rely on rule-based methods, which result in generated contexts that lack diversity and coherence. To address these issues, we propose a Premise-Oriented Data Augmentation (PODA) framework. This framework can generate CoT rationales including analyses for both correct and incorrect options, while constructing diverse and high-quality counterfactual contexts from incorrect candidate options. We integrate summarizing premises and identifying premises for each option into rationales. Subsequently, we employ multi-step prompts with identified premises to construct counterfactual context. To facilitate the model's capabilities to better differentiate the reasoning process associated with each option, we introduce a novel thought-path contrastive learning method that compares reasoning paths between the original and counterfactual samples. Experimental results on three representative LLMs demonstrate that our method can improve the baselines substantially across two challenging logical reasoning benchmarks (ReClor and LogiQA 2.0). The data and code are released at https://github.com/lalalamdbf/TPReasoner.

Masked Thought: Simply Masking Partial Reasoning Steps Can Improve Mathematical Reasoning Learning of Language Models

In reasoning tasks, even a minor error can cascade into inaccurate results, leading to suboptimal performance of large language models in such domains. Earlier fine-tuning approaches sought to mitigate this by leveraging more precise supervisory signals from human labeling, larger models, or self-sampling, although at a high cost. Conversely, we develop a method that avoids external resources, relying instead on introducing perturbations to the input. Our training approach randomly masks certain tokens within the chain of thought, a technique we found to be particularly effective for reasoning tasks. When applied to fine-tuning with GSM8K, this method achieved a 5% improvement in accuracy over standard supervised fine-tuning with a few codes modified and no additional labeling effort. Furthermore, it is complementary to existing methods. When integrated with related data augmentation methods, it leads to an average improvement of 3% improvement in GSM8K accuracy and 1% improvement in MATH accuracy across five datasets of various quality and size, as well as two base models. We further investigate the mechanisms behind this improvement through case studies and quantitative analysis, suggesting that our approach may provide superior support for the model in capturing long-distance dependencies, especially those related to questions. This enhancement could deepen understanding of premises in questions and prior steps. Our code is available at Github.

Imitate, Explore, and Self-Improve: A Reproduction Report on Slow-thinking Reasoning Systems

Recently, slow-thinking reasoning systems, such as o1, have demonstrated remarkable capabilities in solving complex reasoning tasks. These systems typically engage in an extended thinking process before responding to a query, allowing them to generate more thorough, accurate, and well-reasoned solutions. These systems are primarily developed and maintained by industry, with their core techniques not publicly disclosed. In response, an increasing number of studies from the research community aim to explore the technical foundations underlying these powerful reasoning systems. Building on these prior efforts, this paper presents a reproduction report on implementing o1-like reasoning systems. We introduce an "imitate, explore, and self-improve" framework as our primary technical approach to train the reasoning model. In the initial phase, we use distilled long-form thought data to fine-tune the reasoning model, enabling it to invoke a slow-thinking mode. The model is then encouraged to explore challenging problems by generating multiple rollouts, which can result in increasingly more high-quality trajectories that lead to correct answers. Furthermore, the model undergoes self-improvement by iteratively refining its training dataset. To verify the effectiveness of this approach, we conduct extensive experiments on three challenging benchmarks. The experimental results demonstrate that our approach achieves competitive performance compared to industry-level reasoning systems on these benchmarks.

Towards LogiGLUE: A Brief Survey and A Benchmark for Analyzing Logical Reasoning Capabilities of Language Models

Logical reasoning is fundamental for humans yet presents a substantial challenge in the domain of Artificial Intelligence. Initially, researchers used Knowledge Representation and Reasoning (KR) systems that did not scale and required non trivial manual effort. Recently, the emergence of large language models (LLMs) has demonstrated the ability to overcome various limitations of formal Knowledge Representation (KR) systems. Consequently, there is a growing interest in using LLMs for logical reasoning via natural language. This work strives to understand the proficiency of LLMs in logical reasoning by offering a brief review of the latest progress in this area; with a focus on the logical reasoning datasets, tasks, and the methods adopted to utilize LLMs for reasoning. To offer a thorough analysis, we have compiled a benchmark titled LogiGLUE. This includes 24 varied datasets encompassing deductive, abductive, and inductive reasoning. We have standardized these datasets into Seq2Seq tasks to facilitate straightforward training and evaluation for future research. Utilizing LogiGLUE as a foundation, we have trained an instruction fine tuned language model, resulting in LogiT5. We study single task training, multi task training, and a chain of thought knowledge distillation fine tuning technique to assess the performance of model across the different logical reasoning categories. By this comprehensive process, we aim to shed light on the capabilities and potential pathways for enhancing logical reasoning proficiency in LLMs, paving the way for more advanced and nuanced developments in this critical field.

ReGenesis: LLMs can Grow into Reasoning Generalists via Self-Improvement

Post-training Large Language Models (LLMs) with explicit reasoning trajectories can enhance their reasoning abilities. However, acquiring such high-quality trajectory data typically demands meticulous supervision from humans or superior models, which can be either expensive or license-constrained. In this paper, we explore how far an LLM can improve its reasoning by self-synthesizing reasoning paths as training data without any additional supervision. Existing self-synthesizing methods, such as STaR, suffer from poor generalization to out-of-domain (OOD) reasoning tasks. We hypothesize it is due to that their self-synthesized reasoning paths are too task-specific, lacking general task-agnostic reasoning guidance. To address this, we propose Reasoning Generalist via Self-Improvement (ReGenesis), a method to self-synthesize reasoning paths as post-training data by progressing from abstract to concrete. More specifically, ReGenesis self-synthesizes reasoning paths by converting general reasoning guidelines into task-specific ones, generating reasoning structures, and subsequently transforming these structures into reasoning paths, without the need for human-designed task-specific examples used in existing methods. We show that ReGenesis achieves superior performance on all in-domain and OOD settings tested compared to existing methods. For six OOD tasks specifically, while previous methods exhibited an average performance decrease of approximately 4.6% after post training, ReGenesis delivers around 6.1% performance improvement. We also conduct in-depth analysis of our framework and show ReGenesis is effective across various LLMs and design choices.

Logic-of-Thought: Injecting Logic into Contexts for Full Reasoning in Large Language Models

Large Language Models (LLMs) have demonstrated remarkable capabilities across various tasks but their performance in complex logical reasoning tasks remains unsatisfactory. Although some prompting methods, such as Chain-of-Thought, can improve the reasoning ability of LLMs to some extent, they suffer from an unfaithful issue where derived conclusions may not align with the generated reasoning chain. To address this issue, some studies employ the approach of propositional logic to further enhance logical reasoning abilities of LLMs. However, the potential omissions in the extraction of logical expressions in these methods can cause information loss in the logical reasoning process, thereby generating incorrect results. To this end, we propose Logic-of-Thought (LoT) prompting which employs propositional logic to generate expanded logical information from input context, and utilizes the generated logical information as an additional augmentation to the input prompts, thereby enhancing the capability of logical reasoning. The LoT is orthogonal to existing prompting methods and can be seamlessly integrated with them. Extensive experiments demonstrate that LoT boosts the performance of various prompting methods with a striking margin across five logical reasoning tasks. In particular, the LoT enhances Chain-of-Thought's performance on the ReClor dataset by +4.35%; moreover, it improves Chain-of-Thought with Self-Consistency's performance on LogiQA by +5%; additionally, it boosts performance of Tree-of-Thoughts on ProofWriter dataset by +8%.

A & B == B & A: Triggering Logical Reasoning Failures in Large Language Models

Recent advancements in large language models (LLMs) have propelled Artificial Intelligence (AI) to new heights, enabling breakthroughs in various tasks such as writing assistance, code generation, and machine translation. A significant distinction of advanced LLMs, such as ChatGPT, is their demonstrated ability to "reason." However, evaluating the reasoning ability of LLMs remains a challenge as most existing evaluations focus on their accuracy on the downstream tasks rather than directly assessing their reasoning processes. Efforts have been made to develop benchmarks and metrics to assess reasoning in LLMs, but they suffer from data leakage or limited scope. In this paper, we introduce LogicAsker, an automatic approach that comprehensively evaluates and improves the logical reasoning abilities of LLMs under a set of atomic reasoning skills based on propositional and predicate logic. The results provide insights into LLMs' reasoning abilities and reveal the logical rules the LLMs did not learn well. We evaluate LogicAsker on six widely deployed LLMs, including GPT-3, ChatGPT, GPT-4, Bard, Vicuna, and Guanaco. The results show that test cases from LogicAsker can find logical reasoning failures in different LLMs with a rate of 25\% - 94\%. In addition, the test cases of LogicAsker can be further used to design demonstration examples for in-context learning, which effectively improves the logical reasoning ability of LLMs, e.g., 10\% for GPT-4. As far as we know, our work is the first to create prompts based on testing results to improve LLMs' formal reasoning ability effectively. All the code, data, and results will be released for reproduction and future research.

Query and Response Augmentation Cannot Help Out-of-domain Math Reasoning Generalization

In math reasoning with large language models (LLMs), fine-tuning data augmentation by query evolution and diverse reasoning paths is empirically verified effective, profoundly narrowing the gap between open-sourced LLMs and cutting-edge proprietary LLMs. In this paper, we conduct an investigation for such data augmentation in math reasoning and are intended to answer: (1) What strategies of data augmentation are more effective; (2) What is the scaling relationship between the amount of augmented data and model performance; and (3) Can data augmentation incentivize generalization to out-of-domain mathematical reasoning tasks? To this end, we create a new dataset, AugGSM8K, by complicating and diversifying the queries from GSM8K and sampling multiple reasoning paths. We obtained a series of LLMs called MuggleMath by fine-tuning on subsets of AugGSM8K. MuggleMath substantially achieves new state-of-the-art on GSM8K (from 54% to 68.4% at the scale of 7B, and from 63.9% to 74.0% at the scale of 13B). A log-linear relationship is presented between MuggleMath's performance and the amount of augmented data. We also find that MuggleMath is weak in out-of-domain math reasoning generalization to MATH. This is attributed to the differences in query distribution between AugGSM8K and MATH which suggest that augmentation on a single benchmark could not help with overall math reasoning performance. Codes and AugGSM8K will be uploaded to https://github.com/OFA-Sys/gsm8k-ScRel.

General Reasoning Requires Learning to Reason from the Get-go

Large Language Models (LLMs) have demonstrated impressive real-world utility, exemplifying artificial useful intelligence (AUI). However, their ability to reason adaptively and robustly -- the hallmarks of artificial general intelligence (AGI) -- remains fragile. While LLMs seemingly succeed in commonsense reasoning, programming, and mathematics, they struggle to generalize algorithmic understanding across novel contexts. Our experiments with algorithmic tasks in esoteric programming languages reveal that LLM's reasoning overfits to the training data and is limited in its transferability. We hypothesize that the core issue underlying such limited transferability is the coupling of reasoning and knowledge in LLMs. To transition from AUI to AGI, we propose disentangling knowledge and reasoning through three key directions: (1) pretaining to reason using RL from scratch as an alternative to the widely used next-token prediction pretraining, (2) using a curriculum of synthetic tasks to ease the learning of a reasoning prior for RL that can then be transferred to natural language tasks, and (3) learning more generalizable reasoning functions using a small context window to reduce exploiting spurious correlations between tokens. Such a reasoning system coupled with a trained retrieval system and a large external memory bank as a knowledge store can overcome several limitations of existing architectures at learning to reason in novel scenarios.

Don't Ignore Dual Logic Ability of LLMs while Privatizing: A Data-Intensive Analysis in Medical Domain

Extensive studies have been devoted to privatizing general-domain Large Language Models (LLMs) as Domain-Specific LLMs via feeding specific-domain data. However, these privatization efforts often ignored a critical aspect: Dual Logic Ability, which is a core reasoning ability for LLMs. The dual logic ability of LLMs ensures that they can maintain a consistent stance when confronted with both positive and negative statements about the same fact. Our study focuses on how the dual logic ability of LLMs is affected during the privatization process in the medical domain. We conduct several experiments to analyze the dual logic ability of LLMs by examining the consistency of the stance in responses to paired questions about the same fact. In our experiments, interestingly, we observed a significant decrease in the dual logic ability of existing LLMs after privatization. Besides, our results indicate that incorporating general domain dual logic data into LLMs not only enhances LLMs' dual logic ability but also further improves their accuracy. These findings underscore the importance of prioritizing LLMs' dual logic ability during the privatization process. Our study establishes a benchmark for future research aimed at exploring LLMs' dual logic ability during the privatization process and offers valuable guidance for privatization efforts in real-world applications.

Eliminating Reasoning via Inferring with Planning: A New Framework to Guide LLMs' Non-linear Thinking

Chain-of-Thought(CoT) prompting and its variants explore equipping large language models (LLMs) with high-level reasoning abilities by emulating human-like linear cognition and logic. However, the human mind is complicated and mixed with both linear and nonlinear thinking. In this work, we propose Inferential Exclusion Prompting (IEP), a novel prompting that combines the principles of elimination and inference in order to guide LLMs to think non-linearly. IEP guides LLMs to plan and then utilize Natural Language Inference (NLI) to deduce each possible solution's entailment relation with context, commonsense, or facts, therefore yielding a broader perspective by thinking back for inferring. This forward planning and backward eliminating process allows IEP to better simulate the complex human thinking processes compared to other CoT-based methods, which only reflect linear cognitive processes. We conducted a series of empirical studies and have corroborated that IEP consistently outperforms CoT across various tasks. Additionally, we observe that integrating IEP and CoT further improves the LLMs' performance on certain tasks, highlighting the necessity of equipping LLMs with mixed logic processes. Moreover, to better evaluate comprehensive features inherent in human logic, we introduce Mental-Ability Reasoning Benchmark (MARB). The benchmark comprises six novel subtasks with a total of 9,115 questions, among which 1,685 are developed with hand-crafted rationale references. We believe both IEP and MARB can serve as a promising direction for unveiling LLMs' logic and verbal reasoning abilities and drive further advancements. MARB will be available at ~anonymity link soon.

SRA-MCTS: Self-driven Reasoning Augmentation with Monte Carlo Tree Search for Code Generation

Large language models demonstrate exceptional performance in simple code generation tasks but still face challenges in tackling complex problems. These challenges may stem from insufficient reasoning and problem decomposition capabilities. To address this issue, we propose a reasoning-augmented data generation process, SRA-MCTS, which guides the model to autonomously generate high-quality intermediate reasoning paths. This creates a positive feedback loop, enabling continuous improvement. Our method operates entirely through the model itself without requiring additional supervision. By synthesizing natural language reasoning paths and translating them into executable code, the approach ensures analytical accuracy and enhances the success rate in solving complex tasks. Experimental results show that, even without additional supervisory signals, our method achieves performance improvements across different model scales, demonstrating the significant potential of self-improvement in small models. Furthermore, the method remains robust when traditional Chain-of-Thought (CoT) approaches exhibit performance degradation, with notable improvements observed in diversity metrics such as pass@10. We encourage further exploration of reasoning processes within training data to enhance the ability of language models to address complex problems. Our code and data are public at https://github.com/DIRECT-BIT/SRA-MCTS.

Unveiling the Mechanisms of Explicit CoT Training: How Chain-of-Thought Enhances Reasoning Generalization

Training large language models (LLMs) with high-quality Chain-of-Thought (CoT) annotations has become a widely adopted strategy due to its significant enhancement of reasoning capabilities. To fully comprehend this approach, two questions naturally arise: (Q1) What advantages does training with CoT offer compared to training without CoT? (Q2) If there are advantages, what are the underlying mechanisms of explicit CoT training? Analyzing the advantages and mechanisms of CoT training is challenging due to the many factors involved. To address this, we conduct a detailed analysis using clear and controllable data distributions and, for the first time, reveal that CoT training offers the following advantages: (1) Training with CoT markedly improves reasoning generalization, extending it from in-distribution (ID) to both ID and out-of-distribution (OOD) scenarios, while also speeding up convergence; (2) Even when training with CoT includes a certain range of erroneous reasoning steps, it still enables the model to learn reasoning patterns, leading to systematic generalization. We further explore the underlying mechanisms from a circuit perspective: (1) The data distribution (e.g., ratio lambda and pattern) plays a crucial role in influencing the model's systematic generalization; (2) CoT training (with two-hop facts) internalizes reasoning into a two-stage generalizing circuit, where the number of stages corresponds to the explicit reasoning steps during training. Our findings elucidate the mechanisms underlying explicit CoT training and offer critical insights into tuning strategies for LLMs to achieve robust generalization.

Reverse Thinking Makes LLMs Stronger Reasoners

Reverse thinking plays a crucial role in human reasoning. Humans can reason not only from a problem to a solution but also in reverse, i.e., start from the solution and reason towards the problem. This often enhances overall reasoning performance as it enables consistency checks between their forward and backward thinking. To enable Large Language Models (LLMs) to perform reverse thinking, we introduce Reverse-Enhanced Thinking (RevThink), a framework composed of data augmentation and learning objectives. In RevThink, we augment the dataset by collecting structured forward-backward reasoning from a teacher model, consisting of: (1) the original question, (2) forward reasoning, (3) backward question, and (4) backward reasoning. We then employ three objectives to train a smaller student model in a multi-task learning fashion: (a) generate forward reasoning from a question, (b) generate a backward question from a question, and (c) generate backward reasoning from the backward question. Experiments across 12 datasets covering commonsense, math, and logical reasoning show an average 13.53% improvement over the student model's zero-shot performance and a 6.84% improvement over the strongest knowledge distillation baselines. Moreover, our method demonstrates sample efficiency -- using only 10% of the correct forward reasoning from the training data, it outperforms a standard fine-tuning method trained on 10x more forward reasoning. RevThink also exhibits strong generalization to out-of-distribution held-out datasets.

ReFT: Reasoning with Reinforced Fine-Tuning

One way to enhance the reasoning capability of Large Language Models (LLMs) is to conduct Supervised Fine-Tuning (SFT) using Chain-of-Thought (CoT) annotations. This approach does not show sufficiently strong generalization ability, however, because the training only relies on the given CoT data. In math problem-solving, for example, there is usually only one annotated reasoning path for each question in the training data. Intuitively, it would be better for the algorithm to learn from multiple annotated reasoning paths given a question. To address this issue, we propose a simple yet effective approach called Reinforced Fine-Tuning (ReFT) to enhance the generalizability of learning LLMs for reasoning, with math problem-solving as an example. ReFT first warmups the model with SFT, and then employs on-line reinforcement learning, specifically the PPO algorithm in this paper, to further fine-tune the model, where an abundance of reasoning paths are automatically sampled given the question and the rewards are naturally derived from the ground-truth answers. Extensive experiments on GSM8K, MathQA, and SVAMP datasets show that ReFT significantly outperforms SFT, and the performance can be potentially further boosted by combining inference-time strategies such as majority voting and re-ranking. Note that ReFT obtains the improvement by learning from the same training questions as SFT, without relying on extra or augmented training questions. This indicates a superior generalization ability for ReFT.

Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debate

Modern large language models (LLMs) like ChatGPT have shown remarkable performance on general language tasks but still struggle on complex reasoning tasks, which drives the research on cognitive behaviors of LLMs to explore human-like problem-solving strategies. Along this direction, one representative strategy is self-reflection, which asks an LLM to refine the solution with the feedback generated by itself iteratively. However, our study shows that such reflection-style methods suffer from the Degeneration-of-Thought (DoT) problem: once the LLM has established confidence in its solutions, it is unable to generate novel thoughts later through reflection even if its initial stance is incorrect. To address the DoT problem, we propose a Multi-Agent Debate (MAD) framework, in which multiple agents express their arguments in the state of "tit for tat" and a judge manages the debate process to obtain a final solution. Clearly, our MAD framework encourages divergent thinking in LLMs which would be helpful for tasks that require deep levels of contemplation. Experiment results on two challenging datasets, commonsense machine translation and counter-intuitive arithmetic reasoning, demonstrate the effectiveness of our MAD framework. Extensive analyses suggest that the adaptive break of debate and the modest level of "tit for tat" state are required for MAD to obtain good performance. Moreover, we find that LLMs might not be a fair judge if different LLMs are used for agents. Codes: https://github.com/Skytliang/Multi-Agents-Debate

Learning Math Reasoning from Self-Sampled Correct and Partially-Correct Solutions

Pretrained language models have shown superior performance on many natural language processing tasks, yet they still struggle at multi-step formal reasoning tasks like grade school math problems. One key challenge of finetuning them to solve such math reasoning problems is that many existing datasets only contain one reference solution for each problem, despite the fact that there are often alternative solutions resembling different reasoning paths to the final answer. This way, the finetuned models are biased towards the limited reference solutions, which limits their generalization to unseen examples. To mitigate this issue, we propose to let the model perform sampling during training and learn from both self-sampled fully-correct solutions, which yield the correct answer upon execution, and partially-correct solutions, whose intermediate state matches an intermediate state of a known correct solution. We show that our use of self-sampled correct and partially-correct solutions can benefit learning and help guide the sampling process, leading to more efficient exploration of the solution space. Additionally, we explore various training objectives to support learning from multiple solutions per example and find they greatly affect the performance. Experiments on two math reasoning datasets show the effectiveness of our method compared to learning from a single reference solution with MLE, where we improve PASS@100 from 35.5% to 44.5% for GSM8K, and 27.6% to 36.2% PASS@80 for MathQA. Such improvements are also consistent across different model sizes. Our code is available at https://github.com/microsoft/TraceCodegen.

Critical-Questions-of-Thought: Steering LLM reasoning with Argumentative Querying

Studies have underscored how, regardless of the recent breakthrough and swift advances in AI research, even state-of-the-art Large Language models (LLMs) continue to struggle when performing logical and mathematical reasoning. The results seem to suggest that LLMs still work as (highly advanced) data pattern identifiers, scoring poorly when attempting to generalise and solve reasoning problems the models have never previously seen or that are not close to samples presented in their training data. To address this compelling concern, this paper makes use of the notion of critical questions from the literature on argumentation theory, focusing in particular on Toulmin's model of argumentation. We show that employing these critical questions can improve the reasoning capabilities of LLMs. By probing the rationale behind the models' reasoning process, the LLM can assess whether some logical mistake is occurring and correct it before providing the final reply to the user prompt. The underlying idea is drawn from the gold standard of any valid argumentative procedure: the conclusion is valid if it is entailed by accepted premises. Or, to paraphrase such Aristotelian principle in a real-world approximation, characterised by incomplete information and presumptive logic, the conclusion is valid if not proved otherwise. This approach successfully steers the models' output through a reasoning pipeline, resulting in better performance against the baseline and its Chain-of-Thought (CoT) implementation. To this end, an extensive evaluation of the proposed approach on the MT-Bench Reasoning and Math tasks across a range of LLMs is provided.

Satori: Reinforcement Learning with Chain-of-Action-Thought Enhances LLM Reasoning via Autoregressive Search

Large language models (LLMs) have demonstrated remarkable reasoning capabilities across diverse domains. Recent studies have shown that increasing test-time computation enhances LLMs' reasoning capabilities. This typically involves extensive sampling at inference time guided by an external LLM verifier, resulting in a two-player system. Despite external guidance, the effectiveness of this system demonstrates the potential of a single LLM to tackle complex tasks. Thus, we pose a new research problem: Can we internalize the searching capabilities to fundamentally enhance the reasoning abilities of a single LLM? This work explores an orthogonal direction focusing on post-training LLMs for autoregressive searching (i.e., an extended reasoning process with self-reflection and self-exploration of new strategies). To achieve this, we propose the Chain-of-Action-Thought (COAT) reasoning and a two-stage training paradigm: 1) a small-scale format tuning stage to internalize the COAT reasoning format and 2) a large-scale self-improvement stage leveraging reinforcement learning. Our approach results in Satori, a 7B LLM trained on open-source models and data. Extensive empirical evaluations demonstrate that Satori achieves state-of-the-art performance on mathematical reasoning benchmarks while exhibits strong generalization to out-of-domain tasks. Code, data, and models will be fully open-sourced.

Harnessing the Power of Large Language Models for Natural Language to First-Order Logic Translation

Translating natural language sentences to first-order logic (NL-FOL translation) is a longstanding challenge in the NLP and formal logic literature. This paper introduces LogicLLaMA, a LLaMA-7B model fine-tuned for NL-FOL translation using LoRA on a single GPU. LogicLLaMA is capable of directly translating natural language into FOL rules, which outperforms GPT-3.5. LogicLLaMA is also equipped to correct FOL rules predicted by GPT-3.5, and can achieve similar performance as GPT-4 with a fraction of the cost. This correction ability was achieved by a novel supervised fine-tuning (SFT) + reinforcement learning with human feedback (RLHF) framework, which initially trains on synthetically perturbed NL-FOL pairs to encourage chain-of-thought reasoning and then fine-tunes with RLHF on GPT-3.5 outputs using a FOL verifier as the reward model. To train LogicLLaMA, we present MALLS (large language Model generAted NL-FOL pairS), a dataset of 34K high-quality and diverse sentence-level NL-FOL pairs collected from GPT-4. The dataset was created by implementing a pipeline that prompts GPT-4 for pairs, and dynamically adjusts the prompts to ensure the collection of pairs with rich and diverse contexts at different levels of complexity, and verifies the validity of the generated FOL rules. Codes, weights, and data are available at https://github.com/gblackout/LogicLLaMA{{small https://github.com/gblackout/LogicLLaMA}}.

LLMs for Relational Reasoning: How Far are We?

Large language models (LLMs) have revolutionized many areas (e.g. natural language processing, software engineering, etc.) by achieving state-of-the-art performance on extensive downstream tasks. Aiming to achieve robust and general artificial intelligence, there has been a surge of interest in investigating the reasoning ability of the LLMs. Whereas the textual and numerical reasoning benchmarks adopted by previous works are rather shallow and simple, it is hard to conclude that the LLMs possess strong reasoning ability by merely achieving positive results on these benchmarks. Recent efforts have demonstrated that the LLMs are poor at solving sequential decision-making problems that require common-sense planning by evaluating their performance on the reinforcement learning benchmarks. In this work, we conduct an in-depth assessment of several state-of-the-art LLMs' reasoning ability based on the inductive logic programming (ILP) benchmark, which is broadly recognized as a representative and challenging measurement for evaluating logic program induction/synthesis systems as it requires inducing strict cause-effect logic to achieve robust deduction on independent and identically distributed (IID) and out-of-distribution (OOD) test samples. Our evaluations illustrate that compared with the neural program induction systems which are much smaller in model size, the state-of-the-art LLMs are much poorer in terms of reasoning ability by achieving much lower performance and generalization using either natural language prompting or truth-value matrix prompting.

Towards Large Reasoning Models: A Survey of Reinforced Reasoning with Large Language Models

Language has long been conceived as an essential tool for human reasoning. The breakthrough of Large Language Models (LLMs) has sparked significant research interest in leveraging these models to tackle complex reasoning tasks. Researchers have moved beyond simple autoregressive token generation by introducing the concept of "thought" -- a sequence of tokens representing intermediate steps in the reasoning process. This innovative paradigm enables LLMs' to mimic complex human reasoning processes, such as tree search and reflective thinking. Recently, an emerging trend of learning to reason has applied reinforcement learning (RL) to train LLMs to master reasoning processes. This approach enables the automatic generation of high-quality reasoning trajectories through trial-and-error search algorithms, significantly expanding LLMs' reasoning capacity by providing substantially more training data. Furthermore, recent studies demonstrate that encouraging LLMs to "think" with more tokens during test-time inference can further significantly boost reasoning accuracy. Therefore, the train-time and test-time scaling combined to show a new research frontier -- a path toward Large Reasoning Model. The introduction of OpenAI's o1 series marks a significant milestone in this research direction. In this survey, we present a comprehensive review of recent progress in LLM reasoning. We begin by introducing the foundational background of LLMs and then explore the key technical components driving the development of large reasoning models, with a focus on automated data construction, learning-to-reason techniques, and test-time scaling. We also analyze popular open-source projects at building large reasoning models, and conclude with open challenges and future research directions.

Can LLMs Reason in the Wild with Programs?

Large Language Models (LLMs) have shown superior capability to solve reasoning problems with programs. While being a promising direction, most of such frameworks are trained and evaluated in settings with a prior knowledge of task requirements. However, as LLMs become more capable, it is necessary to assess their reasoning abilities in more realistic scenarios where many real-world problems are open-ended with ambiguous scope, and often require multiple formalisms to solve. To investigate this, we introduce the task of reasoning in the wild, where an LLM is tasked to solve a reasoning problem of unknown type by identifying the subproblems and their corresponding formalisms, and writing a program to solve each subproblem, guided by a tactic. We create a large tactic-guided trajectory dataset containing detailed solutions to a diverse set of reasoning problems, ranging from well-defined single-form reasoning (e.g., math, logic), to ambiguous and hybrid ones (e.g., commonsense, combined math and logic). This allows us to test various aspects of LLMs reasoning at the fine-grained level such as the selection and execution of tactics, and the tendency to take undesired shortcuts. In experiments, we highlight that existing LLMs fail significantly on problems with ambiguous and mixed scope, revealing critical limitations and overfitting issues (e.g. accuracy on GSM8K drops by at least 50\%). We further show the potential of finetuning a local LLM on the tactic-guided trajectories in achieving better performance. Project repo is available at github.com/gblackout/Reason-in-the-Wild

Language Models as Compilers: Simulating Pseudocode Execution Improves Algorithmic Reasoning in Language Models

Algorithmic reasoning refers to the ability to understand the complex patterns behind the problem and decompose them into a sequence of reasoning steps towards the solution. Such nature of algorithmic reasoning makes it a challenge for large language models (LLMs), even though they have demonstrated promising performance in other reasoning tasks. Within this context, some recent studies use programming languages (e.g., Python) to express the necessary logic for solving a given instance/question (e.g., Program-of-Thought) as inspired by their strict and precise syntaxes. However, it is non-trivial to write an executable code that expresses the correct logic on the fly within a single inference call. Also, the code generated specifically for an instance cannot be reused for others, even if they are from the same task and might require identical logic to solve. This paper presents Think-and-Execute, a novel framework that decomposes the reasoning process of language models into two steps. (1) In Think, we discover a task-level logic that is shared across all instances for solving a given task and then express the logic with pseudocode; (2) In Execute, we further tailor the generated pseudocode to each instance and simulate the execution of the code. With extensive experiments on seven algorithmic reasoning tasks, we demonstrate the effectiveness of Think-and-Execute. Our approach better improves LMs' reasoning compared to several strong baselines performing instance-specific reasoning (e.g., CoT and PoT), suggesting the helpfulness of discovering task-level logic. Also, we show that compared to natural language, pseudocode can better guide the reasoning of LMs, even though they are trained to follow natural language instructions.

WILT: A Multi-Turn, Memorization-Robust Inductive Logic Benchmark for LLMs

While large language models have shown impressive capabilities across a wide range of domains, they still encounter significant challenges in reasoning tasks that require gathering evidence over multiple turns and drawing logical conclusions. These challenges present significant obstacles for LLM chat user interfaces, which rely on multi-turn interactions to facilitate effective collaboration. This limitation leads to real-world issues; for example, service chatbots must gather necessary information from customers over multiple turns to diagnose and resolve problems effectively. Despite the multi-turn nature of many real-world LLM use cases, most existing benchmarks rely on carefully curated single-turn tests, which often blur the line between memorization and genuine reasoning. To address this, we introduce the Wason Inductive Logic Test (WILT), a simple yet challenging multi-turn reasoning benchmark designed to resist memorization. WILT is inspired by the Wason 2-4-6 task, where participants must infer a boolean function involving three variables (e.g., x < y < z) by proposing test cases (such as (2, 4, 6)). In WILT, each test starts from a clean slate, with only the initial instructions provided, preventing models from relying on pre-learned responses. Over several turns, models must interact with the environment by suggesting test cases to narrow the possible hypotheses and ultimately infer the hidden function based on the outcomes. Our findings reveal that LLMs struggle with this task, exhibiting distinct strengths and weaknesses: some are better at narrowing down the hypothesis space by proposing valuable test cases, while others are more adept at deducing the hidden function from observed cases. Despite these variations, the best-performing model achieves only 28% accuracy, highlighting a significant gap in LLM performance on complex multi-turn reasoning tasks.

Are Large Language Models Really Good Logical Reasoners? A Comprehensive Evaluation and Beyond

Logical reasoning consistently plays a fundamental and significant role in the domains of knowledge engineering and artificial intelligence. Recently, Large Language Models (LLMs) have emerged as a noteworthy innovation in natural language processing (NLP), exhibiting impressive achievements across various classic NLP tasks. However, the question of whether LLMs can effectively address the task of logical reasoning, which requires gradual cognitive inference similar to human intelligence, remains unanswered. To this end, we aim to bridge this gap and provide comprehensive evaluations in this paper. Firstly, to offer systematic evaluations, we select fifteen typical logical reasoning datasets and organize them into deductive, inductive, abductive and mixed-form reasoning settings. Considering the comprehensiveness of evaluations, we include three representative LLMs (i.e., text-davinci-003, ChatGPT and BARD) and evaluate them on all selected datasets under zero-shot, one-shot and three-shot settings. Secondly, different from previous evaluations relying only on simple metrics (e.g., accuracy), we propose fine-level evaluations from objective and subjective manners, covering both answers and explanations. Additionally, to uncover the logical flaws of LLMs, problematic cases will be attributed to five error types from two dimensions, i.e., evidence selection process and reasoning process. Thirdly, to avoid the influences of knowledge bias and purely focus on benchmarking the logical reasoning capability of LLMs, we propose a new dataset with neutral content. It contains 3,000 samples and covers deductive, inductive and abductive settings. Based on the in-depth evaluations, this paper finally forms a general evaluation scheme of logical reasoning capability from six dimensions. It reflects the pros and cons of LLMs and gives guiding directions for future works.

Diving into Self-Evolving Training for Multimodal Reasoning

Reasoning ability is essential for Large Multimodal Models (LMMs). In the absence of multimodal chain-of-thought annotated data, self-evolving training, where the model learns from its own outputs, has emerged as an effective and scalable approach for enhancing reasoning abilities. Despite its growing usage, a comprehensive understanding of self-evolving training, particularly in the context of multimodal reasoning, remains limited. In this paper, we delve into the intricacies of self-evolving training for multimodal reasoning, pinpointing three key factors: Training Method, Reward Model, and Prompt Variation. We systematically examine each factor and explore how various configurations affect the training's effectiveness. Our analysis leads to a set of best practices for each factor, aimed at optimizing multimodal reasoning. Furthermore, we explore the Self-Evolution Dynamics during training and the impact of automatic balancing mechanisms in boosting performance. After all the investigations, we present a final recipe for self-evolving training in multimodal reasoning, encapsulating these design choices into a framework we call MSTaR (Multimodal Self-evolving Training for Reasoning), which is universally effective for models with different sizes on various benchmarks, e.g., surpassing the pre-evolved model significantly on 5 multimodal reasoning benchmarks without using additional human annotations, as demonstrated on MiniCPM-V-2.5 (8B), Phi-3.5-Vision (4B) and InternVL2 (2B). We believe this study fills a significant gap in the understanding of self-evolving training for multimodal reasoning and offers a robust framework for future research. Our policy and reward models, as well as the collected data, is released to facilitate further investigation in multimodal reasoning.

MalAlgoQA: Pedagogical Evaluation of Counterfactual Reasoning in Large Language Models and Implications for AI in Education

This paper introduces MalAlgoQA, a novel dataset designed to evaluate the counterfactual reasoning capabilities of Large Language Models (LLMs) through a pedagogical approach. The dataset comprises mathematics and reading comprehension questions, each accompanied by four answer choices and their corresponding rationales. At the heart of MalAlgoQA are ``malgorithms'' - rationales behind incorrect answer choices that represent flawed yet logically coherent reasoning paths. These malgorithms serve as counterfactual scenarios, allowing us to assess an LLM's ability to identify and analyze flawed reasoning patterns. We propose the Malgorithm Identification task, where LLMs are assessed based on their ability to identify corresponding malgorithm given an incorrect answer choice. To evaluate the model performance, we introduce two metrics: Algorithm Identification Accuracy (AIA) for correct answer rationale identification, and Malgorithm Identification Accuracy (MIA) for incorrect answer rationale identification. Our experiments reveal that state-of-the-art LLMs exhibit significant performance drops in MIA compared to AIA, highlighting the challenges in counterfactual reasoning. Surprisingly, we find that the chain-of-thought prompting technique not only fails to consistently enhance MIA but can sometimes lead to underperformance compared to simple prompting. These findings have important implications for developing LLMs with improved counterfactual reasoning, particularly relevant for AI-powered tutoring systems, where identifying and addressing student misconceptions is essential. MalAlgoQA dataset is available https://github.com/luffycodes/MalAlgoQA-Dataset{here}.

Quiet-STaR: Language Models Can Teach Themselves to Think Before Speaking

When writing and talking, people sometimes pause to think. Although reasoning-focused works have often framed reasoning as a method of answering questions or completing agentic tasks, reasoning is implicit in almost all written text. For example, this applies to the steps not stated between the lines of a proof or to the theory of mind underlying a conversation. In the Self-Taught Reasoner (STaR, Zelikman et al. 2022), useful thinking is learned by inferring rationales from few-shot examples in question-answering and learning from those that lead to a correct answer. This is a highly constrained setting -- ideally, a language model could instead learn to infer unstated rationales in arbitrary text. We present Quiet-STaR, a generalization of STaR in which LMs learn to generate rationales at each token to explain future text, improving their predictions. We address key challenges, including 1) the computational cost of generating continuations, 2) the fact that the LM does not initially know how to generate or use internal thoughts, and 3) the need to predict beyond individual next tokens. To resolve these, we propose a tokenwise parallel sampling algorithm, using learnable tokens indicating a thought's start and end, and an extended teacher-forcing technique. Encouragingly, generated rationales disproportionately help model difficult-to-predict tokens and improve the LM's ability to directly answer difficult questions. In particular, after continued pretraining of an LM on a corpus of internet text with Quiet-STaR, we find zero-shot improvements on GSM8K (5.9%rightarrow10.9%) and CommonsenseQA (36.3%rightarrow47.2%) and observe a perplexity improvement of difficult tokens in natural text. Crucially, these improvements require no fine-tuning on these tasks. Quiet-STaR marks a step towards LMs that can learn to reason in a more general and scalable way.

Knowledge Solver: Teaching LLMs to Search for Domain Knowledge from Knowledge Graphs

Large language models (LLMs), such as ChatGPT and GPT-4, are versatile and can solve different tasks due to their emergent ability and generalizability. However, LLMs sometimes lack domain-specific knowledge to perform tasks, which would also cause hallucination during inference. In some previous works, additional modules like graph neural networks (GNNs) are trained on retrieved knowledge from external knowledge bases, aiming to mitigate the problem of lacking domain-specific knowledge. However, incorporating additional modules: 1) would need retraining additional modules when encountering novel domains; 2) would become a bottleneck since LLMs' strong abilities are not fully utilized for retrieval. In this paper, we propose a paradigm, termed Knowledge Solver (KSL), to teach LLMs to search for essential knowledge from external knowledge bases by harnessing their own strong generalizability. Specifically, we design a simple yet effective prompt to transform retrieval into a multi-hop decision sequence, which empowers LLMs with searching knowledge ability in zero-shot manner. Additionally, KSL is able to provide complete retrieval paths and therefore increase explainability of LLMs' reasoning processes. We conduct experiments on three datasets: CommonsenseQA, OpenbookQA, and MedQA-USMLE, and found that our approach improves LLM baseline performance by a relatively large margin.

Demystifying Long Chain-of-Thought Reasoning in LLMs

Scaling inference compute enhances reasoning in large language models (LLMs), with long chains-of-thought (CoTs) enabling strategies like backtracking and error correction. Reinforcement learning (RL) has emerged as a crucial method for developing these capabilities, yet the conditions under which long CoTs emerge remain unclear, and RL training requires careful design choices. In this study, we systematically investigate the mechanics of long CoT reasoning, identifying the key factors that enable models to generate long CoT trajectories. Through extensive supervised fine-tuning (SFT) and RL experiments, we present four main findings: (1) While SFT is not strictly necessary, it simplifies training and improves efficiency; (2) Reasoning capabilities tend to emerge with increased training compute, but their development is not guaranteed, making reward shaping crucial for stabilizing CoT length growth; (3) Scaling verifiable reward signals is critical for RL. We find that leveraging noisy, web-extracted solutions with filtering mechanisms shows strong potential, particularly for out-of-distribution (OOD) tasks such as STEM reasoning; and (4) Core abilities like error correction are inherently present in base models, but incentivizing these skills effectively for complex tasks via RL demands significant compute, and measuring their emergence requires a nuanced approach. These insights provide practical guidance for optimizing training strategies to enhance long CoT reasoning in LLMs. Our code is available at: https://github.com/eddycmu/demystify-long-cot.

Challenge LLMs to Reason About Reasoning: A Benchmark to Unveil Cognitive Depth in LLMs

In this work, we introduce a novel evaluation paradigm for Large Language Models, one that challenges them to engage in meta-reasoning. This approach addresses critical shortcomings in existing math problem-solving benchmarks, traditionally used to evaluate the cognitive capabilities of agents. Our paradigm shifts the focus from result-oriented assessments, which often overlook the reasoning process, to a more holistic evaluation that effectively differentiates the cognitive capabilities among models. For example, in our benchmark, GPT-4 demonstrates a performance ten times more accurate than GPT3-5. The significance of this new paradigm lies in its ability to reveal potential cognitive deficiencies in LLMs that current benchmarks, such as GSM8K, fail to uncover due to their saturation and lack of effective differentiation among varying reasoning abilities. Our comprehensive analysis includes several state-of-the-art math models from both open-source and closed-source communities, uncovering fundamental deficiencies in their training and evaluation approaches. This paper not only advocates for a paradigm shift in the assessment of LLMs but also contributes to the ongoing discourse on the trajectory towards Artificial General Intelligence (AGI). By promoting the adoption of meta-reasoning evaluation methods similar to ours, we aim to facilitate a more accurate assessment of the true cognitive abilities of LLMs.

Democratizing Reasoning Ability: Tailored Learning from Large Language Model

Large language models (LLMs) exhibit impressive emergent abilities in natural language processing, but their democratization is hindered due to huge computation requirements and closed-source nature. Recent research on advancing open-source smaller LMs by distilling knowledge from black-box LLMs has obtained promising results in the instruction-following ability. However, the reasoning ability which is more challenging to foster, is relatively rarely explored. In this paper, we propose a tailored learning approach to distill such reasoning ability to smaller LMs to facilitate the democratization of the exclusive reasoning ability. In contrast to merely employing LLM as a data annotator, we exploit the potential of LLM as a reasoning teacher by building an interactive multi-round learning paradigm. This paradigm enables the student to expose its deficiencies to the black-box teacher who then can provide customized training data in return. Further, to exploit the reasoning potential of the smaller LM, we propose self-reflection learning to motivate the student to learn from self-made mistakes. The learning from self-reflection and LLM are all tailored to the student's learning status, thanks to the seamless integration with the multi-round learning paradigm. Comprehensive experiments and analysis on mathematical and commonsense reasoning tasks demonstrate the effectiveness of our method. The code will be available at https://github.com/Raibows/Learn-to-Reason.

System-2 Mathematical Reasoning via Enriched Instruction Tuning

Solving complex mathematical problems via system-2 reasoning is a natural human skill, yet it remains a significant challenge for current large language models (LLMs). We identify the scarcity of deliberate multi-step reasoning data as a primary limiting factor. To this end, we introduce Enriched Instruction Tuning (EIT), a method that enriches existing human-annotated mathematical datasets by synergizing human and AI feedback to create fine-grained reasoning trajectories. These datasets are then used to fine-tune open-source LLMs, enhancing their mathematical reasoning abilities without reliance on any symbolic verification program. Concretely, EIT is composed of two critical steps: Enriching with Reasoning Plan (ERP) and Enriching with Reasoning Step (ERS). The former generates a high-level plan that breaks down complex instructions into a sequence of simpler objectives, while ERS fills in reasoning contexts often overlooked by human annotators, creating a smoother reasoning trajectory for LLM fine-tuning. Unlike existing CoT prompting methods that generate reasoning chains only depending on LLM's internal knowledge, our method leverages human-annotated initial answers as ``meta-knowledge'' to help LLMs generate more detailed and precise reasoning processes, leading to a more trustworthy LLM expert for complex mathematical problems. In experiments, EIT achieves an accuracy of 84.1% on GSM8K and 32.5% on MATH, surpassing state-of-the-art fine-tuning and prompting methods, and even matching the performance of tool-augmented methods.

Seemingly Plausible Distractors in Multi-Hop Reasoning: Are Large Language Models Attentive Readers?

State-of-the-art Large Language Models (LLMs) are accredited with an increasing number of different capabilities, ranging from reading comprehension, over advanced mathematical and reasoning skills to possessing scientific knowledge. In this paper we focus on their multi-hop reasoning capability: the ability to identify and integrate information from multiple textual sources. Given the concerns with the presence of simplifying cues in existing multi-hop reasoning benchmarks, which allow models to circumvent the reasoning requirement, we set out to investigate, whether LLMs are prone to exploiting such simplifying cues. We find evidence that they indeed circumvent the requirement to perform multi-hop reasoning, but they do so in more subtle ways than what was reported about their fine-tuned pre-trained language model (PLM) predecessors. Motivated by this finding, we propose a challenging multi-hop reasoning benchmark, by generating seemingly plausible multi-hop reasoning chains, which ultimately lead to incorrect answers. We evaluate multiple open and proprietary state-of-the-art LLMs, and find that their performance to perform multi-hop reasoning is affected, as indicated by up to 45% relative decrease in F1 score when presented with such seemingly plausible alternatives. We conduct a deeper analysis and find evidence that while LLMs tend to ignore misleading lexical cues, misleading reasoning paths indeed present a significant challenge.

Mellow: a small audio language model for reasoning

Multimodal Audio-Language Models (ALMs) can understand and reason over both audio and text. Typically, reasoning performance correlates with model size, with the best results achieved by models exceeding 8 billion parameters. However, no prior work has explored enabling small audio-language models to perform reasoning tasks, despite the potential applications for edge devices. To address this gap, we introduce Mellow, a small Audio-Language Model specifically designed for reasoning. Mellow achieves state-of-the-art performance among existing small audio-language models and surpasses several larger models in reasoning capabilities. For instance, Mellow scores 52.11 on MMAU, comparable to SoTA Qwen2 Audio (which scores 52.5) while using 50 times fewer parameters and being trained on 60 times less data (audio hrs). To train Mellow, we introduce ReasonAQA, a dataset designed to enhance audio-grounded reasoning in models. It consists of a mixture of existing datasets (30% of the data) and synthetically generated data (70%). The synthetic dataset is derived from audio captioning datasets, where Large Language Models (LLMs) generate detailed and multiple-choice questions focusing on audio events, objects, acoustic scenes, signal properties, semantics, and listener emotions. To evaluate Mellow's reasoning ability, we benchmark it on a diverse set of tasks, assessing on both in-distribution and out-of-distribution data, including audio understanding, deductive reasoning, and comparative reasoning. Finally, we conduct extensive ablation studies to explore the impact of projection layer choices, synthetic data generation methods, and language model pretraining on reasoning performance. Our training dataset, findings, and baseline pave the way for developing small ALMs capable of reasoning.

ReWOO: Decoupling Reasoning from Observations for Efficient Augmented Language Models

Augmented Language Models (ALMs) blend the reasoning capabilities of Large Language Models (LLMs) with tools that allow for knowledge retrieval and action execution. Existing ALM systems trigger LLM thought processes while pulling observations from these tools in an interleaved fashion. Specifically, an LLM reasons to call an external tool, gets halted to fetch the tool's response, and then decides the next action based on all preceding response tokens. Such a paradigm, though straightforward and easy to implement, often leads to huge computation complexity from redundant prompts and repeated execution. This study addresses such challenges for the first time, proposing a modular paradigm ReWOO (Reasoning WithOut Observation) that detaches the reasoning process from external observations, thus significantly reducing token consumption. Comprehensive evaluations across six public NLP benchmarks and a curated dataset reveal consistent performance enhancements with our proposed methodology. Notably, ReWOO achieves 5x token efficiency and 4% accuracy improvement on HotpotQA, a multi-step reasoning benchmark. Furthermore, ReWOO demonstrates robustness under tool-failure scenarios. Beyond prompt efficiency, decoupling parametric modules from non-parametric tool calls enables instruction fine-tuning to offload LLMs into smaller language models, thus substantially reducing model parameters. Our illustrative work offloads reasoning ability from 175B GPT3.5 into 7B LLaMA, demonstrating the significant potential for truly efficient and scalable ALM systems.

One Example Shown, Many Concepts Known! Counterexample-Driven Conceptual Reasoning in Mathematical LLMs

Leveraging mathematical Large Language Models (LLMs) for proof generation is a fundamental topic in LLMs research. We argue that the ability of current LLMs to prove statements largely depends on whether they have encountered the relevant proof process during training. This reliance limits their deeper understanding of mathematical theorems and related concepts. Inspired by the pedagogical method of "proof by counterexamples" commonly used in human mathematics education, our work aims to enhance LLMs' ability to conduct mathematical reasoning and proof through counterexamples. Specifically, we manually create a high-quality, university-level mathematical benchmark, CounterMATH, which requires LLMs to prove mathematical statements by providing counterexamples, thereby assessing their grasp of mathematical concepts. Additionally, we develop a data engineering framework to automatically obtain training data for further model improvement. Extensive experiments and detailed analyses demonstrate that CounterMATH is challenging, indicating that LLMs, such as OpenAI o1, have insufficient counterexample-driven proof capabilities. Moreover, our exploration into model training reveals that strengthening LLMs' counterexample-driven conceptual reasoning abilities is crucial for improving their overall mathematical capabilities. We believe that our work offers new perspectives on the community of mathematical LLMs.

CHAMP: A Competition-level Dataset for Fine-Grained Analyses of LLMs' Mathematical Reasoning Capabilities

Recent large language models (LLMs) have shown indications of mathematical reasoning ability. However it has not been clear how they would fare on more challenging competition-level problems. And while self-generated verbalizations of intermediate reasoning steps (i.e., chain-of-thought prompting) have been shown to be helpful, whether LLMs can make use of helpful side information such as problem-specific hints has not been investigated before. In this paper, we propose a challenging benchmark dataset for enabling such analyses. The Concept and Hint-Annotated Math Problems (CHAMP) consists of high school math competition problems, annotated with concepts, or general math facts, and hints, or problem-specific tricks. These annotations allow us to explore the effects of additional information, such as relevant hints, misleading concepts, or related problems. This benchmark is difficult, with the best model only scoring 58.1% in standard settings. With concepts and hints, performance sometimes improves, indicating that some models can make use of such side information. We further annotate model-generated solutions for their correctness. Using this corpus, we find that models often arrive at the correct final answer through wrong reasoning steps. In addition, we test whether models are able to verify these solutions, and find that most models struggle. The dataset and code are available on the project website.

LLMs Can Easily Learn to Reason from Demonstrations Structure, not content, is what matters!

Large reasoning models (LRMs) tackle complex reasoning problems by following long chain-of-thoughts (Long CoT) that incorporate reflection, backtracking, and self-validation. However, the training techniques and data requirements to elicit Long CoT remain poorly understood. In this work, we find that a Large Language model (LLM) can effectively learn Long CoT reasoning through data-efficient supervised fine-tuning (SFT) and parameter-efficient low-rank adaptation (LoRA). With just 17k long CoT training samples, the Qwen2.5-32B-Instruct model achieves significant improvements on a wide range of math and coding benchmarks, including 56.7% (+40.0%) on AIME 2024 and 57.0% (+8.1%) on LiveCodeBench, competitive to the proprietary o1-preview model's score of 44.6% and 59.1%. More importantly, we find that the structure of Long CoT is critical to the learning process, whereas the content of individual reasoning steps has minimal impact. Perturbations affecting content, such as training on incorrect samples or removing reasoning keywords, have little impact on performance. In contrast, structural modifications that disrupt logical consistency in the Long CoT, such as shuffling or deleting reasoning steps, significantly degrade accuracy. For example, a model trained on Long CoT samples with incorrect answers still achieves only 3.2% lower accuracy compared to training with fully correct samples. These insights deepen our understanding of how to elicit reasoning capabilities in LLMs and highlight key considerations for efficiently training the next generation of reasoning models. This is the academic paper of our previous released Sky-T1-32B-Preview model. Codes are available at https://github.com/NovaSky-AI/SkyThought.

GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models

Recent advancements in Large Language Models (LLMs) have sparked interest in their formal reasoning capabilities, particularly in mathematics. The GSM8K benchmark is widely used to assess the mathematical reasoning of models on grade-school-level questions. While the performance of LLMs on GSM8K has significantly improved in recent years, it remains unclear whether their mathematical reasoning capabilities have genuinely advanced, raising questions about the reliability of the reported metrics. To address these concerns, we conduct a large-scale study on several SOTA open and closed models. To overcome the limitations of existing evaluations, we introduce GSM-Symbolic, an improved benchmark created from symbolic templates that allow for the generation of a diverse set of questions. GSM-Symbolic enables more controllable evaluations, providing key insights and more reliable metrics for measuring the reasoning capabilities of models.Our findings reveal that LLMs exhibit noticeable variance when responding to different instantiations of the same question. Specifically, the performance of all models declines when only the numerical values in the question are altered in the GSM-Symbolic benchmark. Furthermore, we investigate the fragility of mathematical reasoning in these models and show that their performance significantly deteriorates as the number of clauses in a question increases. We hypothesize that this decline is because current LLMs cannot perform genuine logical reasoning; they replicate reasoning steps from their training data. Adding a single clause that seems relevant to the question causes significant performance drops (up to 65%) across all state-of-the-art models, even though the clause doesn't contribute to the reasoning chain needed for the final answer. Overall, our work offers a more nuanced understanding of LLMs' capabilities and limitations in mathematical reasoning.

Towards Effective and Efficient Continual Pre-training of Large Language Models

Continual pre-training (CPT) has been an important approach for adapting language models to specific domains or tasks. To make the CPT approach more traceable, this paper presents a technical report for continually pre-training Llama-3 (8B), which significantly enhances the Chinese language ability and scientific reasoning ability of the backbone model. To enhance the new abilities while retaining the original abilities, we design specific data mixture and curriculum strategies by utilizing existing datasets and synthesizing high-quality datasets. Specifically, we synthesize multidisciplinary scientific question and answer (QA) pairs based on related web pages, and subsequently incorporate these synthetic data to improve the scientific reasoning ability of Llama-3. We refer to the model after CPT as Llama-3-SynE (Synthetic data Enhanced Llama-3). We also present the tuning experiments with a relatively small model -- TinyLlama, and employ the derived findings to train the backbone model. Extensive experiments on a number of evaluation benchmarks show that our approach can largely improve the performance of the backbone models, including both the general abilities (+8.81 on C-Eval and +6.31 on CMMLU) and the scientific reasoning abilities (+12.00 on MATH and +4.13 on SciEval), without hurting the original capacities. Our model, data, and codes are available at https://github.com/RUC-GSAI/Llama-3-SynE.

Answering Unseen Questions With Smaller Language Models Using Rationale Generation and Dense Retrieval

When provided with sufficient explanatory context, smaller Language Models have been shown to exhibit strong reasoning ability on challenging short-answer question-answering tasks where the questions are unseen in training. We evaluate two methods for further improvement in this setting. Both methods focus on combining rationales generated by a larger Language Model with longer contexts created from a multi-hop dense retrieval system. The first method (RR) involves training a Rationale Ranking model to score both generated rationales and retrieved contexts with respect to relevance and truthfulness. We then use the scores to derive combined contexts from both knowledge sources using a number of combinatory strategies. For the second method (RATD) we utilise retrieval-augmented training datasets developed by Hartill et al. 2023 to train a smaller Reasoning model such that it becomes proficient at utilising relevant information from longer text sequences that may be only partially evidential and frequently contain many irrelevant sentences. We find that both methods significantly improve results. Our single best Reasoning model materially improves upon strong comparable prior baselines for unseen evaluation datasets (StrategyQA 58.9 rightarrow 61.7 acc., CommonsenseQA 63.6 rightarrow 72.7 acc., ARC-DA 31.6 rightarrow 52.1 F1, IIRC 25.5 rightarrow 27.3 F1) and a version utilising our prior knowledge of each type of question in selecting a context combination strategy does even better. Our proposed models also generally outperform direct prompts against much larger models (BLOOM 175B and StableVicuna 13B) in both few-shot chain-of-thought and standard few-shot settings.

MoreHopQA: More Than Multi-hop Reasoning

Most existing multi-hop datasets are extractive answer datasets, where the answers to the questions can be extracted directly from the provided context. This often leads models to use heuristics or shortcuts instead of performing true multi-hop reasoning. In this paper, we propose a new multi-hop dataset, MoreHopQA, which shifts from extractive to generative answers. Our dataset is created by utilizing three existing multi-hop datasets: HotpotQA, 2WikiMultihopQA, and MuSiQue. Instead of relying solely on factual reasoning, we enhance the existing multi-hop questions by adding another layer of questioning that involves one, two, or all three of the following types of reasoning: commonsense, arithmetic, and symbolic. Our dataset is created through a semi-automated process, resulting in a dataset with 1,118 samples that have undergone human verification. We then use our dataset to evaluate five different large language models: Mistral 7B, Gemma 7B, Llama 3 (8B and 70B), and GPT-4. We also design various cases to analyze the reasoning steps in the question-answering process. Our results show that models perform well on initial multi-hop questions but struggle with our extended questions, indicating that our dataset is more challenging than previous ones. Our analysis of question decomposition reveals that although models can correctly answer questions, only a portion - 38.7% for GPT-4 and 33.4% for Llama3-70B - achieve perfect reasoning, where all corresponding sub-questions are answered correctly. Evaluation code and data are available at https://github.com/Alab-NII/morehopqa

Enhancing the Reasoning Capabilities of Small Language Models via Solution Guidance Fine-Tuning

Large language models (LLMs) have demonstrated remarkable performance across a wide range of tasks. Advances in prompt engineering and fine-tuning techniques have further enhanced their ability to address complex reasoning challenges. However, these advanced capabilities are often exclusive to models exceeding 100 billion parameters. Although Chain-of-Thought (CoT) fine-tuning methods have been explored for smaller models (under 10 billion parameters), they typically depend on extensive CoT training data, which can introduce inconsistencies and limit effectiveness in low-data settings. To overcome these limitations, this paper introduce a new reasoning strategy Solution Guidance (SG) and a plug-and-play training paradigm Solution-Guidance Fine-Tuning (SGFT) for enhancing the reasoning capabilities of small language models. SG focuses on problem understanding and decomposition at the semantic and logical levels, rather than specific computations, which can effectively improve the SLMs' generalization and reasoning abilities. With only a small amount of SG training data, SGFT can fine-tune a SLM to produce accurate problem-solving guidances, which can then be flexibly fed to any SLM as prompts, enabling it to generate correct answers directly. Experimental results demonstrate that our method significantly improves the performance of SLMs on various reasoning tasks, enhancing both their practicality and efficiency within resource-constrained environments.

MindMerger: Efficient Boosting LLM Reasoning in non-English Languages

Reasoning capabilities are crucial for Large Language Models (LLMs), yet a notable gap exists between English and non-English languages. To bridge this disparity, some works fine-tune LLMs to relearn reasoning capabilities in non-English languages, while others replace non-English inputs with an external model's outputs such as English translation text to circumvent the challenge of LLM understanding non-English. Unfortunately, these methods often underutilize the built-in skilled reasoning and useful language understanding capabilities of LLMs. In order to better utilize the minds of reasoning and language understanding in LLMs, we propose a new method, namely MindMerger, which merges LLMs with the external language understanding capabilities from multilingual models to boost the multilingual reasoning performance. Furthermore, a two-step training scheme is introduced to first train to embeded the external capabilities into LLMs and then train the collaborative utilization of the external capabilities and the built-in capabilities in LLMs. Experiments on three multilingual reasoning datasets and a language understanding dataset demonstrate that MindMerger consistently outperforms all baselines, especially in low-resource languages. Without updating the parameters of LLMs, the average accuracy improved by 6.7% and 8.0% across all languages and low-resource languages on the MGSM dataset, respectively.

Think Beyond Size: Adaptive Prompting for More Effective Reasoning

Pretrained large language models (LLMs) are increasingly utilized across a wide range of natural language processing (NLP) tasks due to their impressive capabilities as few-shot learners. Recent techniques, such as chain-of-thought (CoT) prompting, have significantly advanced multi-step reasoning by introducing step-by-step decomposition, achieving state-of-the-art results on complex reasoning benchmarks. However, these approaches often rely on static prompting templates that do not adapt to task complexity or errors during the reasoning process. In this work, we introduce Adaptive Prompting, a dynamic and iterative framework designed to enhance reasoning by incorporating real-time adjustments to prompt structures and validation mechanisms.Experimental results demonstrate that Adaptive Prompting significantly improves performance on diverse reasoning benchmarks, including arithmetic reasoning (GSM8K, MultiArith), logical reasoning and commonsense tasks, achieving substantial accuracy gains compared to static prompting baselines. By integrating guided prompts, intermediate validation, and self-corrective steps, our approach enables smaller models to achieve competitive performance with larger counterparts, such as GPT-4, while maintaining computational efficiency. The framework achieves this without requiring fine-tuning or task-specific training data, highlighting the untapped potential of iterative reasoning methods.

Teaching Transformers Causal Reasoning through Axiomatic Training

For text-based AI systems to interact in the real world, causal reasoning is an essential skill. Since interventional data is costly to generate, we study to what extent an agent can learn causal reasoning from passive data. Specifically, we consider an axiomatic training setup where an agent learns from multiple demonstrations of a causal axiom (or rule), rather than incorporating the axiom as an inductive bias or inferring it from data values. A key question is whether the agent would learn to generalize from the axiom demonstrations to new scenarios. For example, if a transformer model is trained on demonstrations of the causal transitivity axiom over small graphs, would it generalize to applying the transitivity axiom over large graphs? Our results, based on a novel axiomatic training scheme, indicate that such generalization is possible. We consider the task of inferring whether a variable causes another variable, given a causal graph structure. We find that a 67 million parameter transformer model, when trained on linear causal chains (along with some noisy variations) can generalize well to new kinds of graphs, including longer causal chains, causal chains with reversed order, and graphs with branching; even when it is not explicitly trained for such settings. Our model performs at par (or even better) than many larger language models such as GPT-4, Gemini Pro, and Phi-3. Overall, our axiomatic training framework provides a new paradigm of learning causal reasoning from passive data that can be used to learn arbitrary axioms, as long as sufficient demonstrations can be generated.

Large Language Models are Zero-Shot Reasoners

Pretrained large language models (LLMs) are widely used in many sub-fields of natural language processing (NLP) and generally known as excellent few-shot learners with task-specific exemplars. Notably, chain of thought (CoT) prompting, a recent technique for eliciting complex multi-step reasoning through step-by-step answer examples, achieved the state-of-the-art performances in arithmetics and symbolic reasoning, difficult system-2 tasks that do not follow the standard scaling laws for LLMs. While these successes are often attributed to LLMs' ability for few-shot learning, we show that LLMs are decent zero-shot reasoners by simply adding "Let's think step by step" before each answer. Experimental results demonstrate that our Zero-shot-CoT, using the same single prompt template, significantly outperforms zero-shot LLM performances on diverse benchmark reasoning tasks including arithmetics (MultiArith, GSM8K, AQUA-RAT, SVAMP), symbolic reasoning (Last Letter, Coin Flip), and other logical reasoning tasks (Date Understanding, Tracking Shuffled Objects), without any hand-crafted few-shot examples, e.g. increasing the accuracy on MultiArith from 17.7% to 78.7% and GSM8K from 10.4% to 40.7% with large InstructGPT model (text-davinci-002), as well as similar magnitudes of improvements with another off-the-shelf large model, 540B parameter PaLM. The versatility of this single prompt across very diverse reasoning tasks hints at untapped and understudied fundamental zero-shot capabilities of LLMs, suggesting high-level, multi-task broad cognitive capabilities may be extracted by simple prompting. We hope our work not only serves as the minimal strongest zero-shot baseline for the challenging reasoning benchmarks, but also highlights the importance of carefully exploring and analyzing the enormous zero-shot knowledge hidden inside LLMs before crafting finetuning datasets or few-shot exemplars.

RCOT: Detecting and Rectifying Factual Inconsistency in Reasoning by Reversing Chain-of-Thought

Large language Models (LLMs) have achieved promising performance on arithmetic reasoning tasks by incorporating step-by-step chain-of-thought (CoT) prompting. However, LLMs face challenges in maintaining factual consistency during reasoning, exhibiting tendencies to condition overlooking, question misinterpretation, and condition hallucination over given problems. Existing methods use coarse-grained feedback (e.g., whether the answer is correct) to improve factual consistency. In this work, we propose RCoT (Reversing Chain-of-Thought), a novel method to improve LLMs' reasoning abilities by automatically detecting and rectifying factual inconsistency in LLMs' generated solutions. To detect factual inconsistency, RCoT first asks LLMs to reconstruct the problem based on generated solutions. Then fine-grained comparisons between the original problem and the reconstructed problem expose the factual inconsistency in the original solutions. To rectify the solution, RCoT formulates detected factual inconsistency into fine-grained feedback to guide LLMs in revising solutions. Experimental results demonstrate consistent improvements of RCoT over standard CoT across seven arithmetic datasets. Moreover, we find that manually written fine-grained feedback can dramatically improve LLMs' reasoning abilities (e.g., ChatGPT reaches 94.6% accuracy on GSM8K), encouraging the community to further explore the fine-grained feedback generation methods.

Efficient Tool Use with Chain-of-Abstraction Reasoning

To achieve faithful reasoning that aligns with human expectations, large language models (LLMs) need to ground their reasoning to real-world knowledge (e.g., web facts, math and physical rules). Tools help LLMs access this external knowledge, but there remains challenges for fine-tuning LLM agents (e.g., Toolformer) to invoke tools in multi-step reasoning problems, where inter-connected tool calls require holistic and efficient tool usage planning. In this work, we propose a new method for LLMs to better leverage tools in multi-step reasoning. Our method, Chain-of-Abstraction (CoA), trains LLMs to first decode reasoning chains with abstract placeholders, and then call domain tools to reify each reasoning chain by filling in specific knowledge. This planning with abstract chains enables LLMs to learn more general reasoning strategies, which are robust to shifts of domain knowledge (e.g., math results) relevant to different reasoning questions. It also allows LLMs to perform decoding and calling of external tools in parallel, which avoids the inference delay caused by waiting for tool responses. In mathematical reasoning and Wiki QA domains, we show that our method consistently outperforms previous chain-of-thought and tool-augmented baselines on both in-distribution and out-of-distribution test sets, with an average ~6% absolute QA accuracy improvement. LLM agents trained with our method also show more efficient tool use, with inference speed being on average ~1.4x faster than baseline tool-augmented LLMs.

Inference Scaling vs Reasoning: An Empirical Analysis of Compute-Optimal LLM Problem-Solving

Recent advances in large language models (LLMs) have predominantly focused on maximizing accuracy and reasoning capabilities, often overlooking crucial computational efficiency considerations. While this approach has yielded impressive accuracy improvements, it has led to methods that may be impractical for real-world deployment due to computational overhead and latency constraints. This paper investigates the potential synergy between reasoning enhancement and computational efficiency by analyzing the integration of two contrasting approaches: Quiet-STaR (Self-Taught Reasoner) and REBASE (REward BAlanced SEarch). Through comprehensive empirical analysis using the Mistral-7B model on the GSM8K dataset, we demonstrate that while each method excels in its primary objective-Quiet-STaR achieving superior accuracy (32.03%) despite high computational cost (554.66s runtime, 12.73T FLOPs), and REBASE providing exceptional efficiency (8.47s runtime, 2.35T FLOPs) while maintaining baseline-comparable accuracy (10.94%)-their integration reveals fundamental challenges in reconciling reasoning depth with computational efficiency. The combined approach unexpectedly results in degraded performance (9.38% accuracy, 143.66s runtime), highlighting critical insights about the complex interplay between reasoning enhancement and efficiency optimization in LLMs. Our findings illuminate the need for novel architectures and algorithms specifically designed to bridge the gap between these competing objectives, while providing concrete directions for future research in compute-efficient reasoning methods.

On Memorization of Large Language Models in Logical Reasoning

Large language models (LLMs) achieve good performance on challenging reasoning benchmarks, yet could also make basic reasoning mistakes. This contrasting behavior is puzzling when it comes to understanding the mechanisms behind LLMs' reasoning capabilities. One hypothesis is that the increasingly high and nearly saturated performance on common reasoning benchmarks could be due to the memorization of similar problems. In this paper, we systematically investigate this hypothesis with a quantitative measurement of memorization in reasoning tasks, using a dynamically generated logical reasoning benchmark based on Knights and Knaves (K&K) puzzles. We found that LLMs could interpolate the training puzzles (achieving near-perfect accuracy) after fine-tuning, yet fail when those puzzles are slightly perturbed, suggesting that the models heavily rely on memorization to solve those training puzzles. On the other hand, we show that while fine-tuning leads to heavy memorization, it also consistently improves generalization performance. In-depth analyses with perturbation tests, cross difficulty-level transferability, probing model internals, and fine-tuning with wrong answers suggest that the LLMs learn to reason on K&K puzzles despite training data memorization. This phenomenon indicates that LLMs exhibit a complex interplay between memorization and genuine reasoning abilities. Finally, our analysis with per-sample memorization score sheds light on how LLMs switch between reasoning and memorization in solving logical puzzles. Our code and data are available at https://memkklogic.github.io.

Flow of Reasoning: Efficient Training of LLM Policy with Divergent Thinking

Divergent thinking, the cognitive process of generating diverse solutions, is a hallmark of human creativity and problem-solving. For machines, sampling diverse solution trajectories in complex reasoning problems is crucial for robust outcomes, data augmentation, and enhanced model generalization. Large language models (LLMs) often struggle with generating high-quality, diverse reasoning. While supervised fine-tuning helps with quality, it requires extensive supervision data to capture the full diversity of solutions. Alternatively, reinforcement learning methods like PPO aim to find limited highest-reward solutions while neglecting the solution diversity, akin to convergent thinking. To address these limitations, we propose Flow of Reasoning (FoR) -- an efficient LLM training approach enabling diverse reasoning with minimal data. FoR formulates multi-step LLM reasoning as a Markovian flow from an initial state to terminal states. The formulation allows to adapt principled GFlowNet approaches to train the LLM as a policy, which is able to sample multiple reasoning paths with probabilities proportional to the unnormalized reward. Empirical results show that, with limited training data (e.g., 15 examples), FoR can discover diverse high-quality solutions that excel greatly beyond current state-of-the-art methods across three tasks, including embodied reasoning (BlocksWorld), math puzzle solving (Game24), and logical reasoning (PrOntoQA). Code is available at https://github.com/Yu-Fangxu/FoR.

Orca 2: Teaching Small Language Models How to Reason

Orca 1 learns from rich signals, such as explanation traces, allowing it to outperform conventional instruction-tuned models on benchmarks like BigBench Hard and AGIEval. In Orca 2, we continue exploring how improved training signals can enhance smaller LMs' reasoning abilities. Research on training small LMs has often relied on imitation learning to replicate the output of more capable models. We contend that excessive emphasis on imitation may restrict the potential of smaller models. We seek to teach small LMs to employ different solution strategies for different tasks, potentially different from the one used by the larger model. For example, while larger models might provide a direct answer to a complex task, smaller models may not have the same capacity. In Orca 2, we teach the model various reasoning techniques (step-by-step, recall then generate, recall-reason-generate, direct answer, etc.). More crucially, we aim to help the model learn to determine the most effective solution strategy for each task. We evaluate Orca 2 using a comprehensive set of 15 diverse benchmarks (corresponding to approximately 100 tasks and over 36,000 unique prompts). Orca 2 significantly surpasses models of similar size and attains performance levels similar or better to those of models 5-10x larger, as assessed on complex tasks that test advanced reasoning abilities in zero-shot settings. We open-source Orca 2 to encourage further research on the development, evaluation, and alignment of smaller LMs.

Reasoning with Large Language Models, a Survey

Scaling up language models to billions of parameters has opened up possibilities for in-context learning, allowing instruction tuning and few-shot learning on tasks that the model was not specifically trained for. This has achieved breakthrough performance on language tasks such as translation, summarization, and question-answering. Furthermore, in addition to these associative "System 1" tasks, recent advances in Chain-of-thought prompt learning have demonstrated strong "System 2" reasoning abilities, answering a question in the field of artificial general intelligence whether LLMs can reason. The field started with the question whether LLMs can solve grade school math word problems. This paper reviews the rapidly expanding field of prompt-based reasoning with LLMs. Our taxonomy identifies different ways to generate, evaluate, and control multi-step reasoning. We provide an in-depth coverage of core approaches and open problems, and we propose a research agenda for the near future. Finally, we highlight the relation between reasoning and prompt-based learning, and we discuss the relation between reasoning, sequential decision processes, and reinforcement learning. We find that self-improvement, self-reflection, and some metacognitive abilities of the reasoning processes are possible through the judicious use of prompts. True self-improvement and self-reasoning, to go from reasoning with LLMs to reasoning by LLMs, remains future work.

AlphaMath Almost Zero: process Supervision without process

Recent advancements in large language models (LLMs) have substantially enhanced their mathematical reasoning abilities. However, these models still struggle with complex problems that require multiple reasoning steps, frequently leading to logical or numerical errors. While numerical mistakes can be largely addressed by integrating a code interpreter, identifying logical errors within intermediate steps is more challenging. Moreover, manually annotating these steps for training is not only expensive but also labor-intensive, requiring the expertise of professional annotators. In our study, we introduce an innovative approach that bypasses the need for process annotations (from human or GPTs) by utilizing the Monte Carlo Tree Search (MCTS) framework. This technique automatically generates both the process supervision and the step-level evaluation signals. Our method iteratively trains the policy and value models, leveraging the capabilities of a well-pretrained LLM to progressively enhance its mathematical reasoning skills. Furthermore, we propose an efficient inference strategy-step-level beam search, where the value model is crafted to assist the policy model (i.e., LLM) in navigating more effective reasoning paths, rather than solely relying on prior probabilities. The experimental results on both in-domain and out-of-domain datasets demonstrate that even without GPT-4 or human-annotated process supervision, our AlphaMath framework achieves comparable or superior results to previous state-of-the-art methods.

SMART: Self-learning Meta-strategy Agent for Reasoning Tasks

Tasks requiring deductive reasoning, especially those involving multiple steps, often demand adaptive strategies such as intermediate generation of rationales or programs, as no single approach is universally optimal. While Language Models (LMs) can enhance their outputs through iterative self-refinement and strategy adjustments, they frequently fail to apply the most effective strategy in their first attempt. This inefficiency raises the question: Can LMs learn to select the optimal strategy in the first attempt, without a need for refinement? To address this challenge, we introduce SMART (Self-learning Meta-strategy Agent for Reasoning Tasks), a novel framework that enables LMs to autonomously learn and select the most effective strategies for various reasoning tasks. We model the strategy selection process as a Markov Decision Process and leverage reinforcement learning-driven continuous self-improvement to allow the model to find the suitable strategy to solve a given task. Unlike traditional self-refinement methods that rely on multiple inference passes or external feedback, SMART allows an LM to internalize the outcomes of its own reasoning processes and adjust its strategy accordingly, aiming for correct solutions on the first attempt. Our experiments across various reasoning datasets and with different model architectures demonstrate that SMART significantly enhances the ability of models to choose optimal strategies without external guidance (+15 points on the GSM8K dataset). By achieving higher accuracy with a single inference pass, SMART not only improves performance but also reduces computational costs for refinement-based strategies, paving the way for more efficient and intelligent reasoning in LMs.

Evaluating and Improving Tool-Augmented Computation-Intensive Math Reasoning

Chain-of-thought prompting~(CoT) and tool augmentation have been validated in recent work as effective practices for improving large language models~(LLMs) to perform step-by-step reasoning on complex math-related tasks. However, most existing math reasoning datasets may be not able to fully evaluate and analyze the ability of LLMs in manipulating tools and performing reasoning, as they may only require very few invocations of tools or miss annotations for evaluating intermediate reasoning steps. To address the issue, we construct CARP, a new Chinese dataset consisting of 4,886 computation-intensive algebra problems with formulated annotations on intermediate steps. In CARP, we test four LLMs with CoT prompting, and find that they are all prone to make mistakes at the early steps of the solution, leading to wrong answers. Based on this finding, we propose a new approach that can deliberate the reasoning steps with tool interfaces, namely DELI. In DELI, we first initialize a step-by-step solution based on retrieved exemplars, then iterate two deliberation procedures that check and refine the intermediate steps of the generated solution, from the perspectives of tool manipulation and natural language reasoning, until obtaining converged solutions or reaching the maximum turn. Experimental results on CARP and six other datasets show that the proposed DELI mostly outperforms competitive baselines, and can further boost the performance of existing CoT methods. Our data and code are available in https://github.com/RUCAIBox/CARP.

Autonomous Tree-search Ability of Large Language Models

Large Language Models have excelled in remarkable reasoning capabilities with advanced prompting techniques, but they fall short on tasks that require exploration, strategic foresight, and sequential decision-making. Recent works propose to utilize external programs to define search logic, such that LLMs can perform passive tree search to solve more challenging reasoning tasks. Though impressive results have been achieved, there are several fundamental limitations of these approaches. First, passive tree searches are not efficient as they usually require multiple rounds of LLM API calls to solve one single problem. Moreover, passive search methods are not flexible since they need task-specific program designs. Then a natural question arises: can we maintain the tree-search capability of LLMs without the aid of external programs, and can still generate responses that clearly demonstrate the process of a tree-structure search? To this end, we propose a new concept called autonomous tree-search ability of LLM, which can automatically generate a response containing search trajectories for the correct answer. Concretely, we perform search trajectories using capable LLM API via a fixed system prompt, allowing them to perform autonomous tree-search (ATS) right out of the box. Experiments on 4 puzzle games demonstrate our method can achieve huge improvements. The ATS-BFS method outperforms the Chain of Thought approach by achieving an average accuracy improvement of 33%. Compared to Tree of Thoughts, it requires 65.6% or 47.7% less GPT-api cost to attain a comparable level of accuracy. Moreover, we have collected data using the ATS prompt method and fine-tuned LLaMA. This approach yield a greater improvement compared to the ones fine-tuned on CoT data. Specifically, it outperforms CoT-tuned LLaMAs by an average of 40.6% and 38.5% for LLaMA2-7B and LLaMA2-13B, respectively.

RL on Incorrect Synthetic Data Scales the Efficiency of LLM Math Reasoning by Eight-Fold

Training on model-generated synthetic data is a promising approach for finetuning LLMs, but it remains unclear when it helps or hurts. In this paper, we investigate this question for math reasoning via an empirical study, followed by building a conceptual understanding of our observations. First, we find that while the typical approach of finetuning a model on synthetic correct or positive problem-solution pairs generated by capable models offers modest performance gains, sampling more correct solutions from the finetuned learner itself followed by subsequent fine-tuning on this self-generated data doubles the efficiency of the same synthetic problems. At the same time, training on model-generated positives can amplify various spurious correlations, resulting in flat or even inverse scaling trends as the amount of data increases. Surprisingly, we find that several of these issues can be addressed if we also utilize negative responses, i.e., model-generated responses that are deemed incorrect by a final answer verifier. Crucially, these negatives must be constructed such that the training can appropriately recover the utility or advantage of each intermediate step in the negative response. With this per-step scheme, we are able to attain consistent gains over only positive data, attaining performance similar to amplifying the amount of synthetic data by 8 times. We show that training on per-step negatives can help to unlearn spurious correlations in the positive data, and is equivalent to advantage-weighted reinforcement learning (RL), implying that it inherits robustness benefits of RL over imitating positive data alone.

TART: A plug-and-play Transformer module for task-agnostic reasoning

Large language models (LLMs) exhibit in-context learning abilities which enable the same model to perform several tasks without any task-specific training. In contrast, traditional adaptation approaches, such as fine-tuning, modify the underlying models for each specific task. In-context learning, however, consistently underperforms task-specific tuning approaches even when presented with the same examples. While most existing approaches (e.g., prompt engineering) focus on the LLM's learned representations to patch this performance gap, our analysis actually reveal that LLM representations contain sufficient information to make good predictions. As such, we focus on the LLM's reasoning abilities and demonstrate that this performance gap exists due to their inability to perform simple probabilistic reasoning tasks. This raises an intriguing question: Are LLMs actually capable of learning how to reason in a task-agnostic manner? We answer this in the affirmative and propose TART which generically improves an LLM's reasoning abilities using a synthetically trained Transformer-based reasoning module. TART trains this reasoning module in a task-agnostic manner using only synthetic logistic regression tasks and composes it with an arbitrary real-world pre-trained model without any additional training. With a single inference module, TART improves performance across different model families (GPT-Neo, Pythia, BLOOM), model sizes (100M - 6B), tasks (14 NLP binary classification tasks), and even across different modalities (audio and vision). Additionally, on the RAFT Benchmark, TART improves GPT-Neo (125M)'s performance such that it outperforms BLOOM (176B), and is within 4% of GPT-3 (175B). Our code and models are available at https://github.com/HazyResearch/TART .

How susceptible are LLMs to Logical Fallacies?

This paper investigates the rational thinking capability of Large Language Models (LLMs) in multi-round argumentative debates by exploring the impact of fallacious arguments on their logical reasoning performance. More specifically, we present Logic Competence Measurement Benchmark (LOGICOM), a diagnostic benchmark to assess the robustness of LLMs against logical fallacies. LOGICOM involves two agents: a persuader and a debater engaging in a multi-round debate on a controversial topic, where the persuader tries to convince the debater of the correctness of its claim. First, LOGICOM assesses the potential of LLMs to change their opinions through reasoning. Then, it evaluates the debater's performance in logical reasoning by contrasting the scenario where the persuader employs logical fallacies against one where logical reasoning is used. We use this benchmark to evaluate the performance of GPT-3.5 and GPT-4 using a dataset containing controversial topics, claims, and reasons supporting them. Our findings indicate that both GPT-3.5 and GPT-4 can adjust their opinion through reasoning. However, when presented with logical fallacies, GPT-3.5 and GPT-4 are erroneously convinced 41% and 69% more often, respectively, compared to when logical reasoning is used. Finally, we introduce a new dataset containing over 5k pairs of logical vs. fallacious arguments. The source code and dataset of this work are made publicly available.

Light-R1: Curriculum SFT, DPO and RL for Long COT from Scratch and Beyond

This paper presents our work on the Light-R1 series, with models, data, and code all released. We first focus on training long COT models from scratch, specifically starting from models initially lacking long COT capabilities. Using a curriculum training recipe consisting of two-stage SFT and semi-on-policy DPO, we train our model Light-R1-32B from Qwen2.5-32B-Instruct, resulting in superior math performance compared to DeepSeek-R1-Distill-Qwen-32B. Despite being trained exclusively on math data, Light-R1-32B shows strong generalization across other domains. In the subsequent phase of this work, we highlight the significant benefit of the 3k dataset constructed for the second SFT stage on enhancing other models. By fine-tuning DeepSeek-R1-Distilled models using this dataset, we obtain new SOTA models in 7B and 14B, while the 32B model, Light-R1-32B-DS performed comparably to QwQ-32B and DeepSeek-R1. Furthermore, we extend our work by applying reinforcement learning, specifically GRPO, on long-COT models to further improve reasoning performance. We successfully train our final Light-R1-14B-DS with RL, achieving SOTA performance among 14B parameter models in math. With AIME24 & 25 scores of 74.0 and 60.2 respectively, Light-R1-14B-DS surpasses even many 32B models and DeepSeek-R1-Distill-Llama-70B. Its RL training also exhibits well expected behavior, showing simultaneous increase in response length and reward score. The Light-R1 series of work validates training long-COT models from scratch, showcases the art in SFT data and releases SOTA models from RL.

Automatic Curriculum Expert Iteration for Reliable LLM Reasoning

Hallucinations (i.e., generating plausible but inaccurate content) and laziness (i.e. excessive refusals or defaulting to "I don't know") persist as major challenges in LLM reasoning. Current efforts to reduce hallucinations primarily focus on factual errors in knowledge-grounded tasks, often neglecting hallucinations related to faulty reasoning. Meanwhile, some approaches render LLMs overly conservative, limiting their problem-solving capabilities. To mitigate hallucination and laziness in reasoning tasks, we propose Automatic Curriculum Expert Iteration (Auto-CEI) to enhance LLM reasoning and align responses to the model's capabilities--assertively answering within its limits and declining when tasks exceed them. In our method, Expert Iteration explores the reasoning trajectories near the LLM policy, guiding incorrect paths back on track to reduce compounding errors and improve robustness; it also promotes appropriate "I don't know" responses after sufficient reasoning attempts. The curriculum automatically adjusts rewards, incentivizing extended reasoning before acknowledging incapability, thereby pushing the limits of LLM reasoning and aligning its behaviour with these limits. We compare Auto-CEI with various SOTA baselines across logical reasoning, mathematics, and planning tasks, where Auto-CEI achieves superior alignment by effectively balancing assertiveness and conservativeness.

On the Emergence of Thinking in LLMs I: Searching for the Right Intuition

Recent AI advancements, such as OpenAI's new models, are transforming LLMs into LRMs (Large Reasoning Models) that perform reasoning during inference, taking extra time and compute for higher-quality outputs. We aim to uncover the algorithmic framework for training LRMs. Methods like self-consistency, PRM, and AlphaZero suggest reasoning as guided search. We ask: what is the simplest, most scalable way to enable search in LLMs? We propose a post-training framework called Reinforcement Learning via Self-Play (RLSP). RLSP involves three steps: (1) supervised fine-tuning with human or synthetic demonstrations of the reasoning process, (2) using an exploration reward signal to encourage diverse and efficient reasoning behaviors, and (3) RL training with an outcome verifier to ensure correctness while preventing reward hacking. Our key innovation is to decouple exploration and correctness signals during PPO training, carefully balancing them to improve performance and efficiency. Empirical studies in the math domain show that RLSP improves reasoning. On the Llama-3.1-8B-Instruct model, RLSP can boost performance by 23% in MATH-500 test set; On AIME 2024 math problems, Qwen2.5-32B-Instruct improved by 10% due to RLSP. However, a more important finding of this work is that the models trained using RLSP, even with the simplest exploration reward that encourages the model to take more intermediate steps, showed several emergent behaviors such as backtracking, exploration of ideas, and verification. These findings demonstrate that RLSP framework might be enough to enable emergence of complex reasoning abilities in LLMs when scaled. Lastly, we propose a theory as to why RLSP search strategy is more suitable for LLMs inspired by a remarkable result that says CoT provably increases computational power of LLMs, which grows as the number of steps in CoT li2024chain,merrill2023expresssive.

MARIO: MAth Reasoning with code Interpreter Output -- A Reproducible Pipeline

Large language models (LLMs) have seen considerable advancements in natural language understanding tasks, yet there remains a gap to bridge before attaining true artificial general intelligence, especially concerning shortcomings in mathematical reasoning capabilities. We postulate that the inherent nature of LLM training, which focuses on predicting probabilities of next token, presents challenges in effectively modeling mathematical reasoning that demands exact calculations, both from data-driven and theoretical standpoints. In this paper, we address this challenge by enriching the data landscape and introducing a novel math dataset, enhanced with a capability to utilize a Python code interpreter. This dataset is derived from GSM8K and MATH and has been further refined through a combination of GPT-4 annotations, human review, and self-training processes, where the errors in the original GSM8K training set have been fixed. Additionally, we propose a tentative, easily replicable protocol for the fine-tuning of math-specific LLMs, which has led to a significant improvement in the performance of a 7B-parameter LLM on the GSM8K and MATH datasets. We are committed to advancing the field of mathematical reasoning in LLMs and, to that end, we have made the model checkpoints and will make the dataset publicly available. We hope this will facilitate further research and development within the community.

ProcBench: Benchmark for Multi-Step Reasoning and Following Procedure

Reasoning is central to a wide range of intellectual activities, and while the capabilities of large language models (LLMs) continue to advance, their performance in reasoning tasks remains limited. The processes and mechanisms underlying reasoning are not yet fully understood, but key elements include path exploration, selection of relevant knowledge, and multi-step inference. Problems are solved through the synthesis of these components. In this paper, we propose a benchmark that focuses on a specific aspect of reasoning ability: the direct evaluation of multi-step inference. To this end, we design a special reasoning task where multi-step inference is specifically focused by largely eliminating path exploration and implicit knowledge utilization. Our dataset comprises pairs of explicit instructions and corresponding questions, where the procedures necessary for solving the questions are entirely detailed within the instructions. This setup allows models to solve problems solely by following the provided directives. By constructing problems that require varying numbers of steps to solve and evaluating responses at each step, we enable a thorough assessment of state-of-the-art LLMs' ability to follow instructions. To ensure the robustness of our evaluation, we include multiple distinct tasks. Furthermore, by comparing accuracy across tasks, utilizing step-aware metrics, and applying separately defined measures of complexity, we conduct experiments that offer insights into the capabilities and limitations of LLMs in reasoning tasks. Our findings have significant implications for the development of LLMs and highlight areas for future research in advancing their reasoning abilities. Our dataset is available at https://huggingface.co/datasets/ifujisawa/procbench and code at https://github.com/ifujisawa/proc-bench.

Toward Self-Improvement of LLMs via Imagination, Searching, and Criticizing

Despite the impressive capabilities of Large Language Models (LLMs) on various tasks, they still struggle with scenarios that involves complex reasoning and planning. Recent work proposed advanced prompting techniques and the necessity of fine-tuning with high-quality data to augment LLMs' reasoning abilities. However, these approaches are inherently constrained by data availability and quality. In light of this, self-correction and self-learning emerge as viable solutions, employing strategies that allow LLMs to refine their outputs and learn from self-assessed rewards. Yet, the efficacy of LLMs in self-refining its response, particularly in complex reasoning and planning task, remains dubious. In this paper, we introduce AlphaLLM for the self-improvements of LLMs, which integrates Monte Carlo Tree Search (MCTS) with LLMs to establish a self-improving loop, thereby enhancing the capabilities of LLMs without additional annotations. Drawing inspiration from the success of AlphaGo, AlphaLLM addresses the unique challenges of combining MCTS with LLM for self-improvement, including data scarcity, the vastness search spaces of language tasks, and the subjective nature of feedback in language tasks. AlphaLLM is comprised of prompt synthesis component, an efficient MCTS approach tailored for language tasks, and a trio of critic models for precise feedback. Our experimental results in mathematical reasoning tasks demonstrate that AlphaLLM significantly enhances the performance of LLMs without additional annotations, showing the potential for self-improvement in LLMs.

Making Large Language Models Better Reasoners with Alignment

Reasoning is a cognitive process of using evidence to reach a sound conclusion. The reasoning capability is essential for large language models (LLMs) to serve as the brain of the artificial general intelligence agent. Recent studies reveal that fine-tuning LLMs on data with the chain of thought (COT) reasoning process can significantly enhance their reasoning capabilities. However, we find that the fine-tuned LLMs suffer from an Assessment Misalignment problem, i.e., they frequently assign higher scores to subpar COTs, leading to potential limitations in their reasoning abilities. To address this problem, we introduce an Alignment Fine-Tuning (AFT) paradigm, which involves three steps: 1) fine-tuning LLMs with COT training data; 2) generating multiple COT responses for each question, and categorizing them into positive and negative ones based on whether they achieve the correct answer; 3) calibrating the scores of positive and negative responses given by LLMs with a novel constraint alignment loss. Specifically, the constraint alignment loss has two objectives: a) Alignment, which guarantees that positive scores surpass negative scores to encourage answers with high-quality COTs; b) Constraint, which keeps the negative scores confined to a reasonable range to prevent the model degradation. Beyond just the binary positive and negative feedback, the constraint alignment loss can be seamlessly adapted to the ranking situations when ranking feedback is accessible. Furthermore, we also delve deeply into recent ranking-based alignment methods, such as DPO, RRHF, and PRO, and discover that the constraint, which has been overlooked by these approaches, is also crucial for their performance. Extensive experiments on four reasoning benchmarks with both binary and ranking feedback demonstrate the effectiveness of AFT.

Chain of Thoughtlessness: An Analysis of CoT in Planning

Large language model (LLM) performance on reasoning problems typically does not generalize out of distribution. Previous work has claimed that this can be mitigated by modifying prompts to include examples with chains of thought--demonstrations of solution procedures--with the intuition that it is possible to in-context teach an LLM an algorithm for solving the problem. This paper presents a case study of chain of thought on problems from Blocksworld, a classical planning domain, and examine the performance of two state-of-the-art LLMs across two axes: generality of examples given in prompt, and complexity of problems queried with each prompt. While our problems are very simple, we only find meaningful performance improvements from chain of thought prompts when those prompts are exceedingly specific to their problem class, and that those improvements quickly deteriorate as the size n of the query-specified stack grows past the size of stacks shown in the examples. Our results hint that, contrary to previous claims in the literature, CoT's performance improvements do not stem from the model learning general algorithmic procedures via demonstrations and depend on carefully engineering highly problem specific prompts. This spotlights drawbacks of chain of thought, especially because of the sharp tradeoff between possible performance gains and the amount of human labor necessary to generate examples with correct reasoning traces.

Knowledge Infused Decoding

Pre-trained language models (LMs) have been shown to memorize a substantial amount of knowledge from the pre-training corpora; however, they are still limited in recalling factually correct knowledge given a certain context. Hence, they tend to suffer from counterfactual or hallucinatory generation when used in knowledge-intensive natural language generation (NLG) tasks. Recent remedies to this problem focus on modifying either the pre-training or task fine-tuning objectives to incorporate knowledge, which normally require additional costly training or architecture modification of LMs for practical applications. We present Knowledge Infused Decoding (KID) -- a novel decoding algorithm for generative LMs, which dynamically infuses external knowledge into each step of the LM decoding. Specifically, we maintain a local knowledge memory based on the current context, interacting with a dynamically created external knowledge trie, and continuously update the local memory as a knowledge-aware constraint to guide decoding via reinforcement learning. On six diverse knowledge-intensive NLG tasks, task-agnostic LMs (e.g., GPT-2 and BART) armed with KID outperform many task-optimized state-of-the-art models, and show particularly strong performance in few-shot scenarios over seven related knowledge-infusion techniques. Human evaluation confirms KID's ability to generate more relevant and factual language for the input context when compared with multiple baselines. Finally, KID also alleviates exposure bias and provides stable generation quality when generating longer sequences. Code for KID is available at https://github.com/microsoft/KID.

Divide and Conquer for Large Language Models Reasoning

Large language models (LLMs) have shown impressive performance in various reasoning benchmarks with the emergence of Chain-of-Thought (CoT) and its derivative methods, particularly in tasks involving multi-choice questions (MCQs). However, current works all process data uniformly without considering the problem-solving difficulty, which means an excessive focus on simple questions while insufficient to intricate ones. To address this challenge, we inspired by humans using heuristic strategies to categorize tasks and handle them individually, propose to apply the Divide and Conquer to LLMs reasoning. First, we divide questions into different subsets based on the statistical confidence score (CS), then fix nearly resolved sets and conquer demanding nuanced process ones with elaborately designed methods, including Prior Knowledge based Reasoning (PKR) and Filter Choices based Reasoning (FCR), as well as their integration variants. Our experiments demonstrate that this proposed strategy significantly boosts the models' reasoning abilities across nine datasets involving arithmetic, commonsense, and logic tasks. For instance, compared to baseline, we make a striking improvement on low confidence subsets of 8.72\% for AQuA, 15.07\% for ARC Challenge and 7.71\% for RiddleSense. In addition, through extensive analysis on length of rationale and number of options, we verify that longer reasoning paths in PKR could prevent models from referring infer-harmful shortcuts, and also find that removing irrelevant choices in FCR would substantially avoid models' confusion. The code is at https://github.com/AiMijie/Divide-and-Conquer