Large language models (LLMs) have demonstrated remarkable capabilities in solving complex reasoning tasks, particularly in mathematics. However, the domain of physics reasoning presents unique challenges that have received significantly less attention. Existing benchmarks often fall short in evaluating LLMs' abilities on the breadth and depth of undergraduate-level physics, underscoring the need for a comprehensive evaluation. To fill this gap, we introduce UGPhysics, a large-scale and comprehensive benchmark specifically designed to evaluate UnderGraduate-level Physics (UGPhysics) reasoning with LLMs. UGPhysics includes 5,520 undergraduate-level physics problems in both English and Chinese, covering 13 subjects with seven different answer types and four distinct physics reasoning skills, all rigorously screened for data leakage. Additionally, we develop a Model-Assistant Rule-based Judgment (MARJ) pipeline specifically tailored for assessing answer correctness of physics problems, ensuring accurate evaluation. Our evaluation of 31 leading LLMs shows that the highest overall accuracy, 49.8% (achieved by OpenAI-o1-mini), emphasizes the necessity for models with stronger physics reasoning skills, beyond math abilities. We hope UGPhysics, along with MARJ, will drive future advancements in AI for physics reasoning. Codes and data are available at https://github.com/YangLabHKUST/UGPhysics .
Large Language Models (LLMs), such as OpenAI's o1 and DeepSeek's R1, excel at advanced reasoning tasks like math and coding via Reinforcement Learning with Verifiable Rewards (RLVR), but still struggle with puzzles solvable by humans without domain knowledge. We introduce Enigmata, the first comprehensive suite tailored for improving LLMs with puzzle reasoning skills. It includes 36 tasks across seven categories, each with 1) a generator that produces unlimited examples with controllable difficulty and 2) a rule-based verifier for automatic evaluation. This generator-verifier design supports scalable, multi-task RL training, fine-grained analysis, and seamless RLVR integration. We further propose Enigmata-Eval, a rigorous benchmark, and develop optimized multi-task RLVR strategies. Our trained model, Qwen2.5-32B-Enigmata, consistently surpasses o3-mini-high and o1 on the puzzle reasoning benchmarks like Enigmata-Eval, ARC-AGI (32.8%), and ARC-AGI 2 (0.6%). It also generalizes well to out-of-domain puzzle benchmarks and mathematical reasoning, with little multi-tasking trade-off. When trained on larger models like Seed1.5-Thinking (20B activated parameters and 200B total parameters), puzzle data from Enigmata further boosts SoTA performance on advanced math and STEM reasoning tasks such as AIME (2024-2025), BeyondAIME and GPQA (Diamond), showing nice generalization benefits of Enigmata. This work offers a unified, controllable framework for advancing logical reasoning in LLMs. Resources of this work can be found at https://seed-enigmata.github.io.
Researchers working on low-resource languages face persistent challenges due to limited data availability and restricted access to computational resources. Although most large language models (LLMs) are predominantly trained in high-resource languages, adapting them to low-resource contexts, particularly African languages, requires specialized techniques. Several strategies have emerged for adapting models to low-resource languages in todays LLM landscape, defined by multi-stage pre-training and post-training paradigms. However, the most effective approaches remain uncertain. This work systematically investigates which adaptation strategies yield the best performance when extending existing LLMs to African languages. We conduct extensive experiments and ablation studies to evaluate different combinations of data types (translated versus synthetically generated), training stages (pre-training versus post-training), and other model adaptation configurations. Our experiments focuses on mathematical reasoning tasks, using the Llama 3.1 model family as our base model.
Large Language Models (LLMs) are prone to hallucination, especially during multi-hop and reasoning-intensive tasks such as mathematical problem solving. While Outcome Reward Models verify only final answers, Process Reward Models (PRMs) score each intermediate step to steer generation toward coherent solutions. We introduce PathFinder-PRM, a novel hierarchical, error-aware discriminative PRM that first classifies math and consistency errors at each step, then combines these fine-grained signals to estimate step correctness. To train PathFinder-PRM, we construct a 400K-sample dataset by enriching the human-annotated PRM800K corpus and RLHFlow Mistral traces with three-dimensional step-level labels. On PRMBench, PathFinder-PRM achieves a new state-of-the-art PRMScore of 67.7, outperforming the prior best (65.5) while using 3 times less data. When applied to reward guided greedy search, our model yields prm@8 48.3, a +1.5 point gain over the strongest baseline. These results demonstrate that decoupled error detection and reward estimation not only boost fine-grained error detection but also substantially improve end-to-end, reward-guided mathematical reasoning with greater data efficiency.
Long chain-of-thought (CoT) significantly enhances large language models' (LLM) reasoning capabilities. However, the extensive reasoning traces lead to inefficiencies and an increased time-to-first-token (TTFT). We propose a novel training paradigm that uses reinforcement learning (RL) to guide reasoning LLMs to interleave thinking and answering for multi-hop questions. We observe that models inherently possess the ability to perform interleaved reasoning, which can be further enhanced through RL. We introduce a simple yet effective rule-based reward to incentivize correct intermediate steps, which guides the policy model toward correct reasoning paths by leveraging intermediate signals generated during interleaved reasoning. Extensive experiments conducted across five diverse datasets and three RL algorithms (PPO, GRPO, and REINFORCE++) demonstrate consistent improvements over traditional think-answer reasoning, without requiring external tools. Specifically, our approach reduces TTFT by over 80% on average and improves up to 19.3% in Pass@1 accuracy. Furthermore, our method, trained solely on question answering and logical reasoning datasets, exhibits strong generalization ability to complex reasoning datasets such as MATH, GPQA, and MMLU. Additionally, we conduct in-depth analysis to reveal several valuable insights into conditional reward modeling.
Test-Time Scaling (TTS) has proven effective in improving the performance of Large Language Models (LLMs) during inference. However, existing research has overlooked the efficiency of TTS from a latency-sensitive perspective. Through a latency-aware evaluation of representative TTS methods, we demonstrate that a compute-optimal TTS does not always result in the lowest latency in scenarios where latency is critical. To address this gap and achieve latency-optimal TTS, we propose two key approaches by optimizing the concurrency configurations: (1) branch-wise parallelism, which leverages multiple concurrent inference branches, and (2) sequence-wise parallelism, enabled by speculative decoding. By integrating these two approaches and allocating computational resources properly to each, our latency-optimal TTS enables a 32B model to reach 82.3% accuracy on MATH-500 within 1 minute and a smaller 3B model to achieve 72.4% within 10 seconds. Our work emphasizes the importance of latency-aware TTS and demonstrates its ability to deliver both speed and accuracy in latency-sensitive scenarios.
In-context learning (ICL) is a crucial capability of current large language models (LLMs), where the selection of examples plays a key role in performance. While most existing approaches focus on selecting the most similar examples to the query, the impact of diversity in example selection remains underexplored. We systematically investigate the role of diversity in in-context example selection through experiments across a range of tasks, from sentiment classification to more challenging math and code problems. Experiments on Llama-3.1, Gemma-2, and Mistral-v0.3 families of models show that diversity-aware selection methods improve performance, particularly on complex tasks like math and code, and enhance robustness to out-of-distribution queries. To support these findings, we introduce a theoretical framework that explains the benefits of incorporating diversity in in-context example selection.
The advent of large reasoning models, such as OpenAI o1 and DeepSeek R1, has significantly advanced complex reasoning tasks. However, their capabilities in multilingual complex reasoning remain underexplored, with existing efforts largely focused on simpler tasks like MGSM. To address this gap, we introduce MMATH, a benchmark for multilingual complex reasoning spanning 374 high-quality math problems across 10 typologically diverse languages. Using MMATH, we observe that even advanced models like DeepSeek R1 exhibit substantial performance disparities across languages and suffer from a critical off-target issue-generating responses in unintended languages. To address this, we explore strategies including prompting and training, demonstrating that reasoning in English and answering in target languages can simultaneously enhance performance and preserve target-language consistency. Our findings offer new insights and practical strategies for advancing the multilingual reasoning capabilities of large language models. Our code and data could be found at https://github.com/RUCAIBox/MMATH.
Existing mathematical reasoning benchmarks are predominantly English only or translation-based, which can introduce semantic drift and mask languagespecific reasoning errors. To address this, we present AI4Math, a benchmark of 105 original university level math problems natively authored in Spanish. The dataset spans seven advanced domains (Algebra, Calculus, Geometry, Probability, Number Theory, Combinatorics, and Logic), and each problem is accompanied by a step by step human solution. We evaluate six large language models GPT 4o, GPT 4o mini, o3 mini, LLaMA 3.3 70B, DeepSeek R1 685B, and DeepSeek V3 685B under four configurations: zero shot and chain of thought, each in Spanish and English. The top models (o3 mini, DeepSeek R1 685B, DeepSeek V3 685B) achieve over 70% accuracy, whereas LLaMA 3.3 70B and GPT-4o mini remain below 40%. Most models show no significant performance drop between languages, with GPT 4o even performing better on Spanish problems in the zero shot setting. Geometry, Combinatorics, and Probability questions remain persistently challenging for all models. These results highlight the need for native-language benchmarks and domain-specific evaluations to reveal reasoning failures not captured by standard metrics.
We introduce Grade School Math with Distracting Context (GSM-DC), a synthetic benchmark to evaluate Large Language Models' (LLMs) reasoning robustness against systematically controlled irrelevant context (IC). GSM-DC constructs symbolic reasoning graphs with precise distractor injections, enabling rigorous, reproducible evaluation. Our experiments demonstrate that LLMs are significantly sensitive to IC, affecting both reasoning path selection and arithmetic accuracy. Additionally, training models with strong distractors improves performance in both in-distribution and out-of-distribution scenarios. We further propose a stepwise tree search guided by a process reward model, which notably enhances robustness in out-of-distribution conditions.
We present MSA-MathEval, our submission to the BEA 2025 Shared Task on evaluating AI tutor responses across four instructional dimensions: Mistake Identification, Mistake Location, Providing Guidance, and Actionability. Our approach uses a unified training pipeline to fine-tune a single instruction-tuned language model across all tracks, without any task-specific architectural changes. To improve prediction reliability, we introduce a disagreement-aware ensemble inference strategy that enhances coverage of minority labels. Our system achieves strong performance across all tracks, ranking 1st in Providing Guidance, 3rd in Actionability, and 4th in both Mistake Identification and Mistake Location. These results demonstrate the effectiveness of scalable instruction tuning and disagreement-driven modeling for robust, multi-dimensional evaluation of LLMs as educational tutors.
Diffusion Language Models (DLMs) promise parallel generation and bidirectional context, yet they underperform autoregressive (AR) models in both likelihood modeling and generated text quality. We identify that this performance gap arises when important tokens (e.g., key words or low-frequency words that anchor a sentence) are masked early in the forward process, limiting contextual information for accurate reconstruction. To address this, we introduce the Anchored Diffusion Language Model (ADLM), a novel two-stage framework that first predicts distributions over important tokens via an anchor network, and then predicts the likelihoods of missing tokens conditioned on the anchored predictions. ADLM significantly improves test perplexity on LM1B and OpenWebText, achieving up to 25.4% gains over prior DLMs, and narrows the gap with strong AR baselines. It also achieves state-of-the-art performance in zero-shot generalization across seven benchmarks and surpasses AR models in MAUVE score, which marks the first time a DLM generates better human-like text than an AR model. Theoretically, we derive an Anchored Negative Evidence Lower Bound (ANELBO) objective and show that anchoring improves sample complexity and likelihood modeling. Beyond diffusion, anchoring boosts performance in AR models and enhances reasoning in math and logic tasks, outperforming existing chain-of-thought approaches
We propose RaDeR, a set of reasoning-based dense retrieval models trained with data derived from mathematical problem solving using large language models (LLMs). Our method leverages retrieval-augmented reasoning trajectories of an LLM and self-reflective relevance evaluation, enabling the creation of both diverse and hard-negative samples for reasoning-intensive relevance. RaDeR retrievers, trained for mathematical reasoning, effectively generalize to diverse reasoning tasks in the BRIGHT and RAR-b benchmarks, consistently outperforming strong baselines in overall performance. Notably, RaDeR achieves significantly higher performance than baselines on the Math and Coding splits. In addition, RaDeR presents the first dense retriever that outperforms BM25 when queries are Chain-of-Thought reasoning steps, underscoring the critical role of reasoning-based retrieval to augment reasoning language models. Furthermore, RaDeR achieves comparable or superior performance while using only 2.5% of the training data used by the concurrent work REASONIR, highlighting the quality of our synthesized training data.
Large language models (LLMs) still struggle across tasks outside of high-resource languages. In this work, we investigate cross-lingual transfer to lower-resource languages where task-specific post-training data is scarce. Building on prior work, we first validate that the subsets of model parameters that matter most for mathematical reasoning and multilingual capabilities are distinctly non-overlapping. To exploit this implicit separability between task and target language parameterization, we develop and analyze numerous modular frameworks to improve the composition of the two during fine-tuning. These methods generally employ freezing parameters or post hoc model merging to assign math and language improvement to different key parts of the LLM. In the absence of in-language math data, we demonstrate that the modular approaches successfully improve upon baselines across three languages, four models, and two fine-tuning paradigms (full and LoRA). Furthermore, we identify the most consistently successful modular method to be fine-tuning separate language and math experts and model merging via Layer-Swapping, somewhat surprisingly. We offer possible explanations for this result via recent works on the linearity of task vectors. We further explain this by empirically showing that reverting less useful fine-tuning updates after training often outperforms freezing them from the start.
Benefiting from contrastively trained visual encoders on large-scale natural scene images, Large Multimodal Models (LMMs) have achieved remarkable performance across various visual perception tasks. However, the inherent limitations of contrastive learning upon summarized descriptions fundamentally restrict the capabilities of models in meticulous reasoning, particularly in crucial scenarios of geometric problem-solving. To enhance geometric understanding, we propose a novel hard negative contrastive learning framework for the vision encoder, which combines image-based contrastive learning using generation-based hard negatives created by perturbing diagram generation code, and text-based contrastive learning using rule-based negatives derived from modified geometric descriptions and retrieval-based negatives selected based on caption similarity. We train CLIP using our strong negative learning method, namely MMCLIP (Multimodal Math CLIP), and subsequently train an LMM for geometric problem-solving. Experiments show that our trained model, MMGeoLM, significantly outperforms other open-source models on three geometric reasoning benchmarks. Even with a size of 7B, it can rival powerful closed-source models like GPT-4o. We further study the impact of different negative sample construction methods and the number of negative samples on the geometric reasoning performance of LMM, yielding fruitful conclusions. The code and dataset are available at https://github.com/THU-KEG/MMGeoLM.
Recent progress in large language models (LLMs) has shown promise in formal theorem proving, yet existing benchmarks remain limited to isolated, static proof tasks, failing to capture the iterative, engineering-intensive workflows of real-world formal mathematics libraries. Motivated by analogous advances in software engineering, we introduce the paradigm of Automated Proof Engineering (APE), which aims to automate proof engineering tasks such as feature addition, proof refactoring, and bug fixing using LLMs. To facilitate research in this direction, we present APE-Bench I, the first realistic benchmark built from real-world commit histories of Mathlib4, featuring diverse file-level tasks described in natural language and verified via a hybrid approach combining the Lean compiler and LLM-as-a-Judge. We further develop Eleanstic, a scalable parallel verification infrastructure optimized for proof checking across multiple versions of Mathlib. Empirical results on state-of-the-art LLMs demonstrate strong performance on localized edits but substantial degradation on handling complex proof engineering. This work lays the foundation for developing agentic workflows in proof engineering, with future benchmarks targeting multi-file coordination, project-scale verification, and autonomous agents capable of planning, editing, and repairing formal libraries.
Guaranteeing the correctness and factuality of language model (LM) outputs is a major open problem. In this work, we propose conformal factuality, a framework that can ensure high probability correctness guarantees for LMs by connecting language modeling and conformal prediction. We observe that the correctness of an LM output is equivalent to an uncertainty quantification problem, where the uncertainty sets are defined as the entailment set of an LM's output. Using this connection, we show that conformal prediction in language models corresponds to a back-off algorithm that provides high probability correctness guarantees by progressively making LM outputs less specific (and expanding the associated uncertainty sets). This approach applies to any black-box LM and requires very few human-annotated samples. Evaluations of our approach on closed book QA (FActScore, NaturalQuestions) and reasoning tasks (MATH) show that our approach can provide 80-90% correctness guarantees while retaining the majority of the LM's original output.
Despite LLMs' explicit alignment against demographic stereotypes, they have been shown to exhibit biases under various social contexts. In this work, we find that LLMs exhibit concerning biases in how they associate solution veracity with demographics. Through experiments across five human value-aligned LLMs on mathematics, coding, commonsense, and writing problems, we reveal two forms of such veracity biases: Attribution Bias, where models disproportionately attribute correct solutions to certain demographic groups, and Evaluation Bias, where models' assessment of identical solutions varies based on perceived demographic authorship. Our results show pervasive biases: LLMs consistently attribute fewer correct solutions and more incorrect ones to African-American groups in math and coding, while Asian authorships are least preferred in writing evaluation. In additional studies, we show LLMs automatically assign racially stereotypical colors to demographic groups in visualization code, suggesting these biases are deeply embedded in models' reasoning processes. Our findings indicate that demographic bias extends beyond surface-level stereotypes and social context provocations, raising concerns about LLMs' deployment in educational and evaluation settings.
Process Reward Models (PRMs), which provide step-by-step feedback on the reasoning generated by Large Language Models (LLMs), are receiving increasing attention. However, two key research gaps remain: collecting accurate step-level error labels for training typically requires costly human annotation, and existing PRMs are limited to math reasoning problems. In response to these gaps, this paper aims to address the challenges of automatic dataset creation and the generalization of PRMs to diverse reasoning tasks. To achieve this goal, we propose FoVer, an approach for training PRMs on step-level error labels automatically annotated by formal verification tools, such as Z3 for formal logic and Isabelle for theorem proof, which provide automatic and accurate verification for symbolic tasks. Using this approach, we synthesize a training dataset with error labels on LLM responses for formal logic and theorem proof tasks without human annotation. Although this data synthesis is feasible only for tasks compatible with formal verification, we observe that LLM-based PRMs trained on our dataset exhibit cross-task generalization, improving verification across diverse reasoning tasks. Specifically, PRMs trained with FoVer significantly outperform baseline PRMs based on the original LLMs and achieve competitive or superior results compared to state-of-the-art PRMs trained on labels annotated by humans or stronger models, as measured by step-level verification on ProcessBench and Best-of-K performance across 12 reasoning benchmarks, including MATH, AIME, ANLI, MMLU, and BBH. The datasets, models, and code are provided at https://github.com/psunlpgroup/FoVer.
The rapid advancement of native multi-modal models and omni-models, exemplified by GPT-4o, Gemini, and o3, with their capability to process and generate content across modalities such as text and images, marks a significant milestone in the evolution of intelligence. Systematic evaluation of their multi-modal output capabilities in visual thinking processes (also known as multi-modal chain of thought, M-CoT) becomes critically important. However, existing benchmarks for evaluating multi-modal models primarily focus on assessing multi-modal inputs and text-only reasoning while neglecting the importance of reasoning through multi-modal outputs. In this paper, we present a benchmark, dubbed RBench-V, designed to assess models' vision-indispensable reasoning abilities. To construct RBench-V, we carefully hand-pick 803 questions covering math, physics, counting, and games. Unlike previous benchmarks that typically specify certain input modalities, RBench-V presents problems centered on multi-modal outputs, which require image manipulation such as generating novel images and constructing auxiliary lines to support the reasoning process. We evaluate numerous open- and closed-source models on RBench-V, including o3, Gemini 2.5 Pro, Qwen2.5-VL, etc. Even the best-performing model, o3, achieves only 25.8% accuracy on RBench-V, far below the human score of 82.3%, highlighting that current models struggle to leverage multi-modal reasoning. Data and code are available at https://evalmodels.github.io/rbenchv