ICLR 2025 论文列表

Large language models (LLMs) have achieved remarkable performance in recent years but are fundamentally limited by the underlying training data. To improve models beyond the training data, recent works have explored how LLMs can be used to generate synthetic data for autonomous self-improvement. However, successive steps of self-improvement can reach a point of diminishing returns. In this work, we propose a complementary approach towards self-improvement where finetuning is applied to a multiagent society of language models. A group of language models, all starting from the same base model, are independently specialized by updating each one using data generated through multiagent interactions among the models. By training each model on independent sets of data, we illustrate how this approach enables specialization across models and diversification over the set of models. As a result, our overall system is able to preserve diverse reasoning chains and autonomously improve over many more rounds of fine-tuning than single-agent self-improvement methods. We quantitatively illustrate the efficacy of the approach across a wide suite of reasoning tasks.

Recent advancements in large language models (LLMs) have resulted in increasingly anthropomorphic language concerning the ability of LLMs to reason. Whether \textit{reasoning} in LLMs should be understood to be inherently different is, however, widely debated. We propose utilizing a representation engineering approach wherein model activations are read from the residual stream of an LLM when processing a reasoning task. The activations are used to derive a control vector that is applied to the model as an inference-time intervention, modulating the representational space of the model, to improve performance on the specified task. We publish the code for deriving control vectors and analyzing model representations. The method allows us to improve performance on reasoning benchmarks and assess how control vectors influence the final logit distribution of a model via metrics such as KL divergence and entropy. We apply control vectors to Mistral-7B-Instruct and a range of Pythia models on an inductive, a deductive and mathematical reasoning task. We show that an LLM can, to a certain degree, be controlled to improve its perceived reasoning ability by modulating activations. The intervention is dependent upon the ability to reliably extract the model's typical state when correctly solving a task. Our results suggest that reasoning performance can be modulated in the same manner as other information-processing tasks performed by LLMs and demonstrate that we are capable of improving performance on specific tasks via a simple intervention on the residual stream with no additional training.

Mathematical reasoning remains a challenging area for large language models (LLMs), prompting the development of math-specific LLMs such as LLEMMA, DeepSeekMath, and Qwen2-Math, among others. These models typically follow a two-stage training paradigm: pre-training with math-related corpora and post-training with problem datasets for supervised fine-tuning (SFT). Despite these efforts, the improvements in mathematical reasoning achieved through continued pre-training (CPT) are often less significant compared to those obtained via SFT. This study addresses this discrepancy by exploring alternative strategies during the pre-training phase, focusing on the use of problem-solving data over general mathematical corpora. We investigate three primary research questions: (1) Can problem-solving data enhance the model's mathematical reasoning capabilities more effectively than general mathematical corpora during CPT? (2) Are synthetic data from the same source equally effective, and which synthesis methods are most efficient? (3) How do the capabilities developed from the same problem-solving data differ between the CPT and SFT stages, and what factors contribute to these differences? Our findings indicate that problem-solving data significantly enhances the model's mathematical capabilities compared to general mathematical corpora. We also identify effective data synthesis methods, demonstrating that the tutorship amplification synthesis method achieves the best performance. Furthermore, while SFT facilitates instruction-following abilities, it underperforms compared to CPT with the same data, which can be partially attributed to its poor learning capacity for more challenging problem-solving data. These insights provide valuable guidance for optimizing the mathematical reasoning capabilities of LLMs, culminating in our development of a powerful mathematical base model called MathGPT-8B.

Large language models (LLMs) can prove mathematical theorems formally by generating proof steps (\textit{a.k.a.} tactics) within a proof system. However, the space of possible tactics is vast and complex, while the available training data for formal proofs is limited, posing a significant challenge to LLM-based tactic generation. To address this, we introduce a neuro-symbolic tactic generator that synergizes the mathematical intuition learned by LLMs with domain-specific insights encoded by symbolic methods. The key aspect of this integration is identifying which parts of mathematical reasoning are best suited to LLMs and which to symbolic methods. While the high-level idea of neuro-symbolic integration is broadly applicable to various mathematical problems, in this paper, we focus specifically on Olympiad inequalities (Figure~1). We analyze how humans solve these problems and distill the techniques into two types of tactics: (1) scaling, handled by symbolic methods, and (2) rewriting, handled by LLMs. In addition, we combine symbolic tools with LLMs to prune and rank the proof goals for efficient proof search. We evaluate our framework on 161 challenging inequalities from multiple mathematics competitions, achieving state-of-the-art performance and significantly outperforming existing LLM and symbolic approaches without requiring additional training data.

Vision-Language Models (VLMs) have shown broad effectiveness due to extensive training that aligns visual inputs with corresponding language responses. However, this conclusive alignment training causes models to overlook essential visual reasoning, leading to failures in handling detailed visual tasks and producing unfaithful responses. Drawing inspiration from human cognition in solving visual problems (e.g., marking, zoom in), this paper introduces Chain of Manipulations, a mechanism that enables VLMs to tackle problems step-by-step with evidence. After training, models can solve various visual problems by eliciting intrinsic manipulations (e.g., grounding, zoom in) with results (e.g., boxes, image) actively without relying external tools, while also allowing users to trace error causes. In this paper, we study the comprehensive methodology that includes: (1) a flexible design of manipulations based on extensive analysis, (2) an efficient automated data generation pipeline, (3) a compatible VLM architecture capable of multi-turn, multi-image, and (4) a model training process for versatile capabilities. With the design, we also manually annotate **6K** high-quality samples for challenging graphical mathematical problems. Our trained model, CogCoM, equipped with this mechanism and 17B parameters, achieves SOTA performance across **9** benchmarks in **4** categories, demonstrating its effectiveness while maintaining interpretability. Code, model, and data are available at https://github.com/THUDM/CogCoM.

Temporal Knowledge Graph(TKG) serves as an efficacious way to store dynamic facts in real-world. Extrapolation reasoning on TKGs, which aims at predicting possible future events, has attracted consistent research interest. Recently, some rule-based methods have been proposed, which are considered more interpretable compared with embedding-based methods. Existing rule-based methods apply rules through path matching or subgraph extraction, which falls short in inference ability and suffers from missing facts in TKGs. Besides, during rule application period, these methods consider the standing of facts as a binary 0 or 1 problem and ignores the validity as well as frequency of historical facts under temporal settings. In this paper, by designing a novel paradigm for rule application, we propose INFER, a neural-symbolic model for TKG extrapolation. With the introduction of Temporal Validity Function, INFER firstly considers the frequency and validity of historical facts and extends the truth value of facts into continuous real number to better adapt for temporal settings. INFER builds Temporal Weight Matrices with a pre-trained static KG embedding model to enhance its inference ability. Moreover, to facilitates potential integration with existing embedding-based methods, INFER adopts a rule projection module which enables it apply rules through conducting matrices operation on GPU. This feature also improves the efficiency of rule application. Experimental results show that INFER achieves state-of-the-art performance on various TKG datasets and significantly outperforms existing rule-based models on our modified, more sparse TKG datasets, which demonstrates the superiority of our model in inference ability.

Math Word Problems (MWPs) play a vital role in assessing the capabilities of Large Language Models (LLMs), yet current research primarily focuses on questions with concise contexts. The impact of longer contexts on mathematical reasoning remains under-explored. This study pioneers the investigation of Context Length Generalizability (CoLeG), which refers to the ability of LLMs to solve MWPs with extended narratives. We introduce Extended Grade-School Math (E-GSM), a collection of MWPs featuring lengthy narratives, and propose two novel metrics to evaluate the efficacy and resilience of LLMs in tackling these problems. Our analysis of existing zero-shot prompting techniques with proprietary LLMs along with open-source LLMs reveals a general deficiency in CoLeG. To alleviate these issues, we propose tailored approaches for different categories of LLMs. For proprietary LLMs, we introduce a new instructional prompt designed to mitigate the impact of long contexts. For open-source LLMs, we develop a novel auxiliary task for fine-tuning to enhance CoLeG. Our comprehensive results demonstrate the effectiveness of our proposed methods, showing improved performance on E-GSM. Additionally, we conduct an in-depth analysis to differentiate the effects of semantic understanding and reasoning efficacy, showing that our methods improves the latter. We also establish the generalizability of our methods across several other MWP benchmarks. Our findings highlight the limitations of current LLMs and offer practical solutions correspondingly, paving the way for further exploration of model generalizability and training methodologies.

Large language models (LLMs) can solve an increasing number of complex reasoning tasks while making surprising mistakes in basic numerical understanding and processing (such as $9.11 > 9.9$). The latter ability is essential for tackling complex arithmetic and mathematical problems and serves as a foundation for most reasoning tasks, but previous work paid little attention to it or only discussed several restricted tasks (like integer addition). In this paper, we comprehensively investigate the numerical understanding and processing ability (NUPA) of LLMs. Firstly, we introduce a benchmark covering four common numerical representations and 17 distinct numerical tasks in four major categories, resulting in 41 meaningful combinations in total. These tasks are derived from primary and secondary education curricula, encompassing nearly all everyday numerical understanding and processing scenarios, and the rules of these tasks are very simple and clear. Through the benchmark, we find that current LLMs fail frequently in many of the tasks. To study the problem, we train small models with existing and potential techniques for enhancing NUPA (such as tokenizers, PEs, and number formats), comprehensively evaluating their effectiveness using our testbed. We also finetune practical-scale LLMs on our proposed NUPA tasks and find that 1) naive finetuning can improve NUPA a lot on many but not all tasks, and 2) surprisingly, techniques designed to enhance NUPA prove ineffective for finetuning pretrained models. We further explore the impact of chain-of-thought techniques on NUPA. Our work provides a more detailed and comprehensive understanding of NUPA in LLMs.

Recent advancements in Large Language Models (LLMs) have sparked interest in their mathematical reasoning capabilities. While performance on the widely popular GSM8K benchmark has improved, questions remain about whether reported evaluation metrics are reliable, and reasoning abilities of LLMs have advanced. 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 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 demonstrate that their performance significantly deteriorates as the number of clauses in a question increases. We hypothesize that this decline is due to the fact that current LLMs are not capable of genuine logical reasoning; instead, they attempt to replicate the reasoning steps observed in their training data. When we add a single clause that appears relevant to the question, we observe significant performance drops (up to 65%) across all state-of-the-art models, even though the added clause does not contribute to the reasoning chain needed to reach the final answer. Overall, our work provides a more nuanced understanding of LLMs' capabilities and limitations in mathematical reasoning.

Multimodal Large Language Models (MLLMs) have emerged as a central focus in both industry and academia, but often suffer from biases introduced by visual and language priors, which can lead to multimodal hallucination. These biases arise from the visual encoder and the Large Language Model (LLM) backbone, affecting the attention mechanism responsible for aligning multimodal inputs. Existing decoding-based mitigation methods focus on statistical correlations and overlook the causal relationships between attention mechanisms and model output, limiting their effectiveness in addressing these biases. To tackle this issue, we propose a causal inference framework termed CausalMM that applies structural causal modeling to MLLMs, treating modality priors as a confounder between attention mechanisms and output. Specifically, by employing backdoor adjustment and counterfactual reasoning at both the visual and language attention levels, our method mitigates the negative effects of modality priors and enhances the alignment of MLLM's inputs and outputs, with a maximum score improvement of 65.3% on 6 VLind-Bench indicators and 164 points on MME Benchmark compared to conventional methods. Extensive experiments validate the effectiveness of our approach while being a plug-and-play solution. Our code is available at: https://github.com/The-Martyr/CausalMM.

Language models are increasingly being used in important decision pipelines, so ensuring the correctness of their outputs is crucial. Recent work has proposed evaluating the “factuality” of claims decomposed from a language model generation and applying conformal prediction techniques to filter out those claims that are not factual. This can be effective for tasks such as information retrieval, where constituent claims may be evaluated in isolation for factuality, but is not appropriate for reasoning tasks, as steps of a logical argument can be evaluated for correctness only within the context of the claims that precede them. To capture this, we define “coherent factuality” and develop a conformal-prediction-based method to guarantee coherent factuality for language model outputs. Our approach applies split conformal prediction to subgraphs within a "deducibility" graph that represents the steps of a reasoning problem. We evaluate our method on mathematical reasoning problems from the MATH and FELM datasets and find that our algorithm consistently produces correct and substantiated orderings of claims, achieving coherent factuality across target coverage levels. Moreover, we achieve 90\% factuality on our stricter definition while retaining 80\% or more of the original claims, highlighting the utility of our deducibility-graph-guided approach.

This paper introduces rStar, a self-play mutual reasoning approach that significantly improves reasoning capabilities of small language models (SLMs) without fine-tuning or superior models. rStar decouples reasoning into a self-play mutual generation-discrimination process. First, a target SLM augments the Monte Carlo Tree Search (MCTS) with a rich set of human-like reasoning actions to construct higher quality reasoning trajectories. Next, another SLM, with capabilities similar to the target SLM, acts as a discriminator to verify each trajectory generated by the target SLM. The mutually agreed reasoning trajectories are considered mutual consistent, thus are more likely to be correct. Extensive experiments across five SLMs demonstrate rStar can effectively solve diverse reasoning problems, including GSM8K, GSM-Hard, MATH, SVAMP, and StrategyQA. Remarkably, rStar boosts GSM8K accuracy from 12.51\% to 63.91\% for LLaMA2-7B, from 36.46\% to 81.88\% for Mistral-7B, from 74.53\% to 91.13\% for LLaMA3-8B-Instruct. Code is available at https://github.com/zhentingqi/rStar.

Despite their proficiency in general tasks, Multi-modal Large Language Models (MLLMs) struggle with automatic Geometry Problem Solving (GPS), which demands understanding diagrams, interpreting symbols, and performing complex reasoning. This limitation arises from their pre-training on natural images and texts, along with the lack of automated verification in the problem-solving process. Besides, current geometric specialists are limited by their task-specific designs, making them less effective for broader geometric problems. To this end, we present GeoX, a multi-modal large model focusing on geometric understanding and reasoning tasks. Given the significant differences between geometric diagram-symbol and natural image-text, we introduce unimodal pre-training to develop a diagram encoder and symbol decoder, enhancing the understanding of geometric images and corpora. Furthermore, we introduce geometry-language alignment, an effective pre-training paradigm that bridges the modality gap between unimodal geometric experts. We propose a Generator-And-Sampler Transformer (GS-Former) to generate discriminative queries and eliminate uninformative representations from unevenly distributed geometric signals. Finally, GeoX benefits from visual instruction tuning, empowering it to take geometric images and questions as input and generate verifiable solutions. Experiments show that GeoX outperforms both generalists and geometric specialists on publicly recognized benchmarks, such as GeoQA, UniGeo, Geometry3K, and PGPS9k. Our data and code will be released soon to accelerate future research on automatic GPS.

With the rapid advancement of test-time compute search strategies to improve the mathematical problem-solving capabilities of large language models (LLMs), the need for building robust verifiers has become increasingly important. However, all these inference strategies rely on existing verifiers originally designed for Best-of-N search, which makes them sub-optimal for tree search techniques at test time. During tree search, existing verifiers can only offer indirect and implicit assessments of partial solutions or under-value prospective intermediate steps, thus resulting in the premature pruning of promising intermediate steps. To overcome these limitations, we propose token-supervised value models (TVMs) -- a new class of verifiers that assign each token a probability that reflects the likelihood of reaching the correct final answer. This new token-level supervision enables TVMs to directly and explicitly evaluate partial solutions, effectively distinguishing between promising and incorrect intermediate steps during tree search at test time. Experimental results demonstrate that combining tree-search-based inference strategies with TVMs significantly improves the accuracy of LLMs in mathematical problem-solving tasks, surpassing the performance of existing verifiers.

Large language models (LLMs) can solve arithmetic word problems with high accuracy, but little is known about how well they generalize to more complex problems. This is difficult to study, as (i) much of the available evaluation data has already been seen by the most capable models during training, and (ii) existing benchmarks do not capture how problem proofs may be arbitrarily complex in various ways. In this paper, we present a data-generation framework for evaluating LLMs on problems with arbitrarily complex arithmetic proofs, called MathGAP. MathGAP generates problem statements and chain-of-thought reasoning traces according to specifications about their arithmetic proof structure, enabling systematic studies on easy-to-hard generalization with respect to complexity of proof trees. Using MathGAP, we find that LLMs show a significant decrease in performance as proofs get deeper and wider. This effect is more pronounced in complex, nonlinear proof structures, which are challenging even for the most capable models. The models are also sensitive to simple changes in sentence ordering. However, they remain capable of solving some complex problems, suggesting that reasoning generalization is noisy.

Enabling LLMs to improve their outputs by using more test-time compute is a critical step towards building self-improving agents that can operate on open-ended natural language. In this paper, we scale up inference-time computation in LLMs, with a focus on answering: if an LLM is allowed to use a fixed but non-trivial amount of inference-time compute, how much can it improve its performance on a challenging prompt? Answering this question has implications not only on performance, but also on the future of LLM pretraining and how to tradeoff inference-time and pre-training compute. Little research has attempted to understand the scaling behaviors of test-time inference methods, with current work largely providing negative results for a number of these strategies. In this work, we analyze two primary mechanisms to scale test-time computation: (1) searching against dense, process-based verifier reward models (PRMs); and (2) updating the model's distribution over a response adaptively, given the prompt at test time. We find that in both cases, the effectiveness of different approaches to scaling test-time compute critically varies depending on the difficulty of the prompt. This observation motivates applying a "compute-optimal" scaling strategy, which acts to, as effectively as possible, allocate test-time compute per prompt in an adaptive manner. Using this compute-optimal strategy, we can improve the efficiency of test-time compute scaling for math reasoning problems by more than 4x compared to a best-of-N baseline. Additionally, in a FLOPs-matched evaluation, we find that on problems where a smaller base model attains somewhat non-trivial success rates, test-time compute can be used to outperform a 14x larger model.

Training on high-quality synthetic data from strong language models (LMs) is a common strategy to improve the reasoning performance of LMs. In this work, we revisit whether this strategy is compute-optimal under a fixed inference budget (e.g., FLOPs). To do so, we investigate the trade-offs between generating synthetic data using a stronger but more expensive (SE) model versus a weaker but cheaper (WC) model. We evaluate the generated data across three key metrics: coverage, diversity, and false positive rate, and show that the data from WC models may have higher coverage and diversity, but also exhibit higher false positive rates. We then finetune LMs on data from SE and WC models in different settings: knowledge distillation, self-improvement, and a novel weak-to-strong improvement setup where a weaker LM teaches reasoning to a stronger LM. Our findings reveal that models finetuned on WC-generated data consistently outperform those trained on SE-generated data across multiple benchmarks and multiple choices of WC and SE models. These results challenge the prevailing practice of relying on SE models for synthetic data generation, suggesting that WC may be the compute-optimal approach for training advanced LM reasoners.

Decoder-only Transformers often struggle with complex reasoning tasks, particularly arithmetic reasoning requiring multiple sequential operations. In this work, we identify representation collapse in the model’s intermediate layers as a key factor limiting their reasoning capabilities. To address this, we propose Sequential Variance-Covariance Regularization (Seq-VCR), which enhances the entropy of intermediate representations and prevents collapse. Combined with dummy pause tokens as substitutes for chain-of-thought (CoT) tokens, our method significantly improves performance in arithmetic reasoning problems. In the challenging 5 × 5 integer multiplication task, our approach achieves 99.5% exact match accuracy, outperforming models of the same size (which yield 0% accuracy) and GPT-4 with five-shot CoT prompting (44%). We also demonstrate superior results on arithmetic expression and longest increasing subsequence (LIS) datasets. Our findings highlight the importance of preventing intermediate layer representation collapse to enhance the reasoning capabilities of Transformers and show that Seq-VCR offers an effective solution without requiring explicit CoT supervision.

The capabilities and limitations of Large Language Models (LLMs) have been sketched out in great detail in recent years, providing an intriguing yet conflicting picture. On the one hand, LLMs demonstrate a general ability to solve problems. On the other hand, they show surprising reasoning gaps when compared to humans, casting doubt on the robustness of their generalisation strategies. The sheer volume of data used in the design of LLMs has precluded us from applying the method traditionally used to measure generalisation: train-test set separation. To overcome this, we study what kind of generalisation strategies LLMs employ when performing reasoning tasks by investigating the pretraining data they rely on. For two models of different sizes (7B and 35B) and 2.5B of their pretraining tokens, we identify what documents influence the model outputs for three simple mathematical reasoning tasks and contrast this to the data that are influential for answering factual questions. We find that, while the models rely on mostly distinct sets of data for each factual question, a document often has a similar influence across different reasoning questions within the same task, indicating the presence of procedural knowledge. We further find that the answers to factual questions often show up in the most influential data. However, for reasoning questions the answers usually do not show up as highly influential, nor do the answers to the intermediate reasoning steps. When we characterise the top ranked documents for the reasoning questions qualitatively, we confirm that the influential documents often contain procedural knowledge, like demonstrating how to obtain a solution using formulae or code. Our findings indicate that the approach to reasoning the models use is unlike retrieval, and more like a generalisable strategy that synthesises procedural knowledge from documents doing a similar form of reasoning.