NeurIPS 2025 论文列表

It is understood that different neural network architectures are suited to different tasks, but is there always a single best architecture for a given task? We compare the expressive power of transformers, RNNs, and transformers with chain of thought tokens on a simple and natural class of tasks we term Compositional Reasoning Questions (CRQ). This family captures multi-step problems with tree-like compositional structure, such as evaluating Boolean formulas. We prove that under standard hardness assumptions, *none* of these three architectures is capable of solving CRQs unless some hyperparameter (depth, embedding dimension, and number of chain of thought tokens, respectively) grows with the size of the input. We then provide constructions for solving CRQs with each architecture. For transformers, our construction uses depth that is logarithmic in the problem size. For RNNs, logarithmic embedding dimension is necessary and sufficient, so long as the inputs are provided in a certain order. For transformers with chain of thought, our construction uses $n$ CoT tokens. These results show that, while CRQs are inherently hard, there are several different ways for language models to overcome this hardness. Even for a single class of problems, each architecture has strengths and weaknesses, and none is strictly better than the others.

Protein language models (PLMs) are often assumed to capture evolutionary information by training on large protein sequence datasets. Yet it remains unclear whether PLMs can reason about evolution—that is, infer evolutionary relationships between sequences. We test this capability by evaluating whether standard PLM usage, frozen or fine-tuned embeddings with distance-based comparison, supports evolutionary reasoning. Existing PLMs consistently fail to recover phylogenetic structure, despite strong performance on sequence-level tasks such as masked-token and contact prediction. We present Phyla, a hybrid state-space and transformer model that jointly processes multiple sequences and is trained using a tree-based objective across 3,000 phylogenies spanning diverse protein families. Phyla outperforms the next-best PLM by 9\% on tree reconstruction and 23\% on taxonomic clustering while remaining alignment- and guide-tree-free. Although classical alignment pipelines achieve higher absolute accuracy, Phyla narrows the gap and achieves markedly lower end-to-end runtime. Applied to real data, Phyla reconstructs biologically accurate clades in the tree of life and resolves genome-scale relationships among Mycobacterium tuberculosis isolates. These findings suggest that, under standard usage, evolutionary reasoning does not reliably emerge from large-scale sequence modeling. Instead, Phyla shows that models trained with phylogenetic supervision can reason about evolution more effectively, offering a biologically grounded path toward evolutionary foundation models.

Geometry is a fundamental branch of mathematics and plays a crucial role in evaluating the reasoning capabilities of multimodal large language models (MLLMs). However, existing multimodal mathematics benchmarks mainly focus on plane geometry and largely ignore solid geometry, which requires spatial reasoning and is more challenging than plane geometry. To address this critical gap, we introduce **SolidGeo**, the first large-scale benchmark specifically designed to evaluate the performance of MLLMs on mathematical reasoning tasks in solid geometry. SolidGeo consists of 3,113 real-world K–12 and competition-level problems, each paired with visual context and annotated with difficulty levels and fine-grained solid geometry categories. Our benchmark covers a wide range of 3D reasoning subjects such as projection, unfolding, spatial measurement, and spatial vector, offering a rigorous testbed for assessing solid geometry. Through extensive experiments, we observe that MLLMs encounter substantial challenges in solid geometry math tasks, with a considerable performance gap relative to human capabilities on SolidGeo. Moreover, we analyze the performance, inference effiency and error patterns of various models, offering insights into the solid geometric mathematical reasoning capabilities of MLLMs. We hope SolidGeo serves as a catalyst for advancing MLLMs toward deeper geometric reasoning and spatial intelligence. The dataset is released at https://huggingface.co/datasets/HarryYancy/SolidGeo/

While large language models (LLMs) with Chain-of-Thought (CoT) reasoning excel in mathematics and coding, their potential for systematic reasoning in chemistry, a domain demanding rigorous structural analysis for real-world tasks like drug design and reaction engineering, remains untapped. Current benchmarks focus on simple knowledge retrieval, neglecting step-by-step reasoning required for complex tasks such as molecular optimization and reaction prediction. To address this, we introduce ChemCoTBench, a reasoning framework that bridges molecular structure understanding with arithmetic-inspired operations, including addition, deletion, and substitution, to formalize chemical problem-solving into transparent, step-by-step workflows. By treating molecular transformations as modular "chemical operations", the framework enables slow-thinking reasoning, mirroring the logic of mathematical proofs while grounding solutions in real-world chemical constraints. We evaluate models on two high-impact tasks: Molecular Property Optimization and Chemical Reaction Prediction. These tasks mirror real-world challenges while providing structured evaluability. We further provide ChemCoTDataset, a pioneering 22,000-instance chemical reasoning dataset with expert-annotated chains of thought to facilitate LLM fine-tuning. By providing annotated trainable datasets, a reasoning taxonomy, and baseline evaluations, our work bridges the gap between abstract reasoning methods and practical chemical discovery, establishing a foundation for advancing LLMs as tools for AI-driven scientific innovation.

Large Language Models (LLMs) offer promising capabilities for tackling complex reasoning tasks, including optimization problems. However, existing methods either rely on prompt engineering, which leads to poor generalization across problem types, or require costly supervised training. We introduce SolverLLM, a training-free framework that leverages test-time scaling to solve diverse optimization problems. Rather than solving directly, SolverLLM generates mathematical formulations and translates them into solver-ready code, guided by a novel Monte Carlo Tree Search (MCTS) strategy. To enhance the search process, we modify classical MCTS with (1) dynamic expansion for adaptive formulation generation, (2) prompt backpropagation to guide exploration via outcome-driven feedback, and (3) uncertainty backpropagation to incorporate reward reliability into decision-making. Experiments on six standard benchmark datasets demonstrate that SolverLLM outperforms both prompt-based and learning-based baselines, achieving strong generalization without additional training.

Large language models (LLMs) trained via reinforcement learning with verifiable reward (RLVR) have achieved breakthroughs on tasks with explicit, automatable verification, such as software programming and mathematical problems. Extending RLVR to electronic design automation (EDA), especially automatically generating hardware description languages (HDLs) like Verilog from natural-language (NL) specifications, however, poses three key challenges: the lack of automated and accurate verification environments, the scarcity of high-quality NL-code pairs, and the prohibitive computation cost of RLVR. To this end, we introduce CodeV-R1, an RLVR framework for training Verilog generation LLMs. First, we develop a rule-based testbench generator that performs robust equivalence checking against golden references. Second, we propose a round-trip data synthesis method that pairs open-source Verilog snippets with LLM-generated NL descriptions, verifies code–NL–code consistency via the generated testbench, and filters out inequivalent examples to yield a high-quality dataset. Third, we employ a two-stage "distill-then-RL" training pipeline: distillation for the cold start of reasoning abilities, followed by adaptive DAPO, our novel RLVR algorithm that can reduce training cost by adaptively adjusting sampling rate. The resulting model, CodeV-R1-7B, achieves 68.6 \% and 72.9 \% pass@1 on VerilogEval v2 and RTLLM v1.1, respectively, surpassing prior state-of-the-art by 12$\sim$20 \%, while even exceeding the performance of 671B DeepSeek-R1 on RTLLM. We have released our model, training code, and dataset to facilitate research in EDA and LLM communities.

Recent advances in natural language processing highlight two key factors for improving reasoning in large language models (LLMs): (i) allocating more test-time compute tends to help on harder problems but often introduces redundancy in the reasoning trace, and (ii) compute is most effective when reasoning is systematic and incremental, forming structured chains of thought (CoTs) akin to human problem-solving. To study these factors in isolation, we introduce a controlled setting based on shortest-path tasks in layered graphs. We train decoder-only transformers on question–trace–answer triples using a custom tokenizer, comparing models trained on optimal bottom-up dynamic programming traces with those trained on longer, valid traces involving backtracking. Surprisingly, under the same training-token budget, the latter models generalize better to unseen graphs. This benefit is not due to length alone—injecting arbitrary redundancy into reasoning traces fails to help and can even hurt performance. Instead, we find that generalization correlates with the model's confidence in next-token prediction, suggesting that long, coherent, and locally incremental traces make the training signal easier to optimize.

We introduce AutoJudge, a method that accelerates large language model (LLM) inference with task-specific lossy speculative decoding. Instead of matching the original model output distribution token-by-token, we identify the generated tokens that affect the downstream quality of the response, relaxing the distribution match guarantee so that the "unimportant" tokens can be generated faster. Our approach relies on a semi‑greedy search algorithm to test which of the mismatches between target and draft models should be corrected to preserve quality and which ones may be skipped. We then train a lightweight classifier based on existing LLM embeddings to predict, at inference time, which mismatching tokens can be safely accepted without compromising the final answer quality. We evaluate AutoJudge with multiple draft/target model pairs on mathematical reasoning and programming benchmarks, achieving significant speedups at the cost of a minor accuracy reduction. Notably, on GSM8K with the Llama 3.1 70B target model, our approach achieves up to ${\approx}2{\times}$ speedup \textit{over speculative decoding} at the cost of a ${\le} 1\%$ drop in accuracy. When applied to the LiveCodeBench benchmark, AutoJudge automatically detects programming-specific important tokens, accepting ${\ge}25$ tokens per speculation cycle at a$~ 2\%$ drop in Pass@1. Our approach requires no human annotation and is easy to integrate with modern LLM inference frameworks.

Large Language Models (LLMs) often struggle with mathematical reasoning tasks requiring precise, verifiable computation. While Reinforcement Learning (RL) from outcome-based rewards enhances text-based reasoning, understanding how agents autonomously learn to leverage external tools like code execution remains crucial. We investigate RL from outcome-based rewards for Tool-Integrated Reasoning, ZeroTIR, training base LLMs to spontaneously generate and execute Python code for mathematical problems without supervised tool-use examples. Our central contribution is we demonstrate that as RL training progresses, key metrics scale predictably. Specifically, we observe strong positive correlations where increased training steps lead to increases in the spontaneous code execution frequency, the average response length, and, critically, the final task accuracy. This suggests a quantifiable relationship between computational effort invested in training and the emergence of effective, tool-augmented reasoning strategies. We implement a robust framework featuring a decoupled code execution environment and validate our findings across standard RL algorithms and frameworks. Experiments show ZeroTIR significantly surpasses non-tool ZeroRL baselines on challenging math benchmarks. Our findings provide a foundational understanding of how autonomous tool use is acquired and scales within Agent RL, offering a reproducible benchmark for future studies. Code is released at \href{https://github.com/yyht/openrlhf_async_pipline}{https://github.com/yyht/openrlhf\_async\_pipline}.

Large reasoning models (LRMs) like OpenAI-o1 have shown impressive capabilities in natural language reasoning. However, these models frequently demonstrate inefficiencies or inaccuracies when tackling complex mathematical operations. While integrating computational tools such as Code Interpreters (CIs) offers a promising solution, it introduces a critical challenge: a conflict between the model's internal, probabilistic reasoning and the external, deterministic knowledge provided by the CI, which often leads models to unproductive deliberation. To overcome this, we introduce CoRT (Code-Optimized Reasoning Training), a post-training framework designed to teach LRMs to effectively utilize CIs. We propose **Hint-Engineering**, a new data synthesis strategy that strategically injects diverse hints at optimal points within reasoning paths. This approach generates high-quality, code-integrated reasoning data specifically tailored to optimize LRM-CI interaction. Using this method, we have synthesized 30 high-quality samples to post-train models ranging from 1.5B to 32B parameters through supervised fine-tuning. CoRT further refines the multi-round interleaving of external CI usage and internal thinking by employing rejection sampling and reinforcement learning. Our experimental evaluations demonstrate CoRT's effectiveness, yielding absolute improvements of 4\% and 8\% on DeepSeek-R1-Distill-Qwen-32B and DeepSeek-R1-Distill-Qwen-1.5B, respectively, across five challenging mathematical reasoning datasets. Moreover, CoRT significantly enhances efficiency, reducing token usage by approximately 30\% for the 32B model and 50\% for the 1.5B model compared to pure natural language reasoning baselines. The models and code are available at: [this url](https://github.com/ChengpengLi1003/CoRT).

Recent progress in large language models (LLMs) highlights the power of scaling test-time compute to achieve strong performance on complex tasks, such as mathematical reasoning and code generation. This raises a critical question: how should model training be modified to optimize performance under a subsequent test-time compute strategy and budget? To explore this, we focus on pass@N, a simple test-time strategy that searches for a correct answer in N independent samples. We show, surprisingly, that training with cross-entropy (CE) can be _misaligned_ with pass@N in that pass@N accuracy _decreases_ with longer CE training. We explain the origins of this misalignment in terms of model overconfidence induced by CE, and experimentally verify our prediction of overconfidence as an impediment to scaling test-time compute via pass@N. Furthermore we suggest a principled, modified training loss that is better aligned to pass@N by limiting model confidence and rescuing pass@N test performance. Our algorithm demonstrates improved mathematical reasoning on MATH and MiniF2F benchmarks under several scenarios: (1) providing answers to math questions both with and without Chain-of-Thought reasoning traces; and (2) proving theorems by searching over proof trees of varying shapes. Overall our work underscores the importance of co-designing two traditionally separate phases of LLM development: training-time protocols and test-time search and reasoning strategies.

Large Language Models (LLMs) have emerged with many intellectual capacities. While numerous benchmarks assess their intelligence, limited attention has been given to their ability to explore—an essential capacity for discovering new information and adapting to novel environments in both natural and artificial systems. The extent to which LLMs can effectively explore, particularly in open-ended tasks, remains unclear. This study investigates whether LLMs can surpass humans in exploration during an open-ended task, using Little Alchemy 2 as a paradigm, where agents combine elements to discover new ones. Results show most LLMs underperform compared to humans, except for the o1 model, with those traditional LLMs relying primarily on uncertainty-driven strategies, unlike humans who balance uncertainty and empowerment. Results indicate that traditional reasoning-focused LLMs, such as GPT-4o, exhibit a significantly faster and less detailed reasoning process, limiting their exploratory performance. In contrast, the DeepSeek reasoning model demonstrates prolonged, iterative thought processes marked by repetitive analysis of combinations and past trials, reflecting a more thorough and human-like exploration strategy. Representational analysis of the models with Sparse Autoencoders (SAE) revealed that uncertainty and choices are represented at earlier transformer blocks, while empowerment values are processed later, causing LLMs to think too fast and make premature decisions, hindering effective exploration. These findings shed light on the limitations of LLM exploration and suggest directions for improving their adaptability.

In this paper, we propose a simple and efficient method for value model training on long-context reasoning traces. Compared to existing process reward models (PRMs), our method does not require a fine-grained notion of ``step,'' which is difficult to define for long-context reasoning models. By collecting a dataset of 2.5 million reasoning traces, we train a 1.5B token-level value model and apply it to DeepSeek models for improved performance with test-time compute scaling. We find that block-wise value-guided search (\texttt{VGS}) with a final weighted majority vote achieves better test-time scaling than standard methods such as majority voting or best-of-$n$. Moreover, \texttt{VGS} significantly reduces the inference FLOPs required to achieve the same performance of majority voting. Our dataset, model and codebase are open-sourced at \codeurl.

Scaling test-time compute is crucial for enhancing the reasoning capabilities of large language models (LLMs). Existing approaches typically employ reinforcement learning (RL) to maximize a verifiable reward obtained at the end of reasoning traces. However, such methods optimize only the final performance under a large and fixed token budget, which hinders efficiency in both training and deployment. In this work, we present **AnytimeReasoner**, a novel framework for optimizing reasoning performance under varying thinking budget constraints. To achieve this, we truncate the complete thinking process to fit within sampled token budgets from a prior distribution, compelling the model to summarize the optimal answer for each truncated thinking for verification. This introduces verifiable dense rewards into the reasoning process, facilitating more effective credit assignment in RL optimization. We then optimize the thinking and summary policies in a decoupled manner to maximize the cumulative reward. Additionally, we introduce a novel variance reduction technique, **Budget Relative Policy Optimization (BRPO)**, to enhance the robustness and efficiency of the learning process when reinforcing the thinking policy. Empirical results in mathematical reasoning tasks demonstrate that our method consistently outperforms GRPO across all thinking budgets under various prior distributions, enhancing both training and token efficiency.

Large Language Models (LLMs) have demonstrated outstanding performance in mathematical reasoning capabilities. However, we argue that current large-scale reasoning models primarily rely on scaling up training datasets with diverse mathematical problems and long thinking chains, which raises questions about whether LLMs genuinely acquire mathematical concepts and reasoning principles or merely remember the training data. In contrast, humans tend to break down complex problems into multiple fundamental atomic capabilities. Inspired by this, we propose a new paradigm for evaluating mathematical atomic capabilities. Our work categorizes atomic abilities into two dimensions: (1) field-specific abilities across four major mathematical fields, algebra, geometry, analysis, and topology, and (2) logical abilities at different levels, including conceptual understanding, forward multi-step reasoning with formal math language, and counterexample-driven backward reasoning. We propose corresponding training and evaluation datasets for each atomic capability unit, and conduct extensive experiments about how different atomic capabilities influence others, to explore the strategies to elicit the required specific atomic capability. Evaluation and experimental results on advanced models show many interesting discoveries and inspirations about the different performances of models on various atomic capabilities and the interactions between atomic capabilities. Our findings highlight the importance of decoupling mathematical intelligence into atomic components, providing new insights into model cognition and guiding the development of training strategies toward a more efficient, transferable, and cognitively grounded paradigm of "atomic thinking".

Low-Rank Adaptation (LoRA) has become the de facto parameter-efficient fine-tuning (PEFT) method for large language models (LLMs) by constraining weight updates to low-rank matrices. Recent works such as Tied-LoRA, VeRA, and VB-LoRA push efficiency further by introducing additional constraints to reduce the trainable parameter space. In this paper, we show that the parameter space reduction strategies employed by these LoRA variants can be formulated within a unified framework, Uni-LoRA, where the LoRA parameter space, flattened as a high-dimensional vector space R^D, can be reconstructed through a projection from a subspace R^d, with d << D. We demonstrate that the fundamental difference among various LoRA methods lies in the choice of the projection matrix, P ∈ R^{D×d}. Most existing LoRA variants rely on layer-wise or structure-specific projections that limit cross-layer parameter sharing, thereby compromising parameter efficiency. In light of this, we introduce an efficient and theoretically grounded projection matrix that is isometric, enabling global parameter sharing and reducing computation overhead. Furthermore, under the unified view of Uni-LoRA, this design requires only a single trainable vector to reconstruct LoRA parameters for the entire LLM -- making Uni-LoRA both a unified framework and a “one-vector-only” solution. Extensive experiments on GLUE, mathematical reasoning, and instruction tuning benchmarks demonstrate that Uni-LoRA achieves state-of-the-art parameter efficiency while outperforming or matching prior approaches in predictive performance.

Natural Language to SQL (NL2SQL) enables intuitive interactions with databases by transforming natural language queries into structured SQL statements. Despite recent advancements in enhancing human-computer interaction within database applications, significant challenges persist, particularly regarding the inference performance in complex scenarios involving multi-table joins and nested queries. Current methodologies primarily utilize supervised fine-tuning (SFT) to train the NL2SQL model, which may limit adaptability and interpretability in new environments (e.g., finance and healthcare). In order to enhance the reasoning performance of the NL2SQL model in the above complex situations, we introduce SQL-R1, a novel NL2SQL reasoning model trained by the reinforcement learning (RL) algorithms. We design a specialized RL-based reward function tailored for NL2SQL tasks and discussed the impact of cold start and synthetic data on the effectiveness of intensive training. In addition, we achieve competitive accuracy using only a tiny amount of synthetic NL2SQL data for augmented training and further explore data engineering for RL. In existing experiments, SQL-R1 achieves execution accuracy of 88.6\% and 67.1\% on the benchmark Spider and BIRD, respectively. The code is available at https://github.com/IDEA-FinAI/SQL-R1.

Large reasoning models (LRMs) excel at complex reasoning tasks but typically generate lengthy sequential chains-of-thought, resulting in long inference times before arriving at the final answer. To address this challenge, we introduce SPRINT, a novel post-training and inference-time framework designed to enable LRMs to dynamically identify and exploit opportunities for parallelization during their reasoning process. SPRINT incorporates an innovative data curation pipeline that reorganizes natural language reasoning trajectories into structured rounds of long-horizon planning and parallel execution. By fine-tuning LRMs on a small amount of such curated data, the models learn to dynamically identify independent subtasks within extended reasoning processes and effectively execute them in parallel. Through extensive evaluations, we demonstrate that models fine-tuned with the SPRINT framework match the performance of reasoning models on complex domains such as mathematics while generating up to 39% fewer sequential tokens on problems requiring more than 8,000 output tokens. Finally, we observe consistent results transferred to two out-of-distribution tasks, namely GPQA and Countdown, with up to 45% and 65% reduction in average sequential tokens respectively for longer reasoning trajectories, while matching the performance of the fine-tuned reasoning model.

Large language models (LLMs) have shown impressive performance on reasoning benchmarks like math and logic. While many works have largely assumed well-defined tasks, real-world queries are often underspecified and only solvable by acquiring missing information. We formalize this information-gathering problem as a constraint satisfaction problem (CSP) with missing variable assignments. Using a special case where only one necessary variable assignment is missing, we can evaluate an LLM's ability to identify the minimal necessary question to ask. We present QuestBench, a set of underspecified reasoning tasks solvable by asking at most one question, which includes: (1) Logic-Q: logical reasoning tasks with one missing proposition, (2) Planning-Q: PDDL planning problems with partially-observed initial states, (3) GSM-Q: human-annotated grade school math problems with one unknown variable, and (4) GSME-Q: equation-based version of GSM-Q. The LLM must select the correct clarification question from multiple options. While current models excel at GSM-Q and GSME-Q, they achieve only 40-50% accuracy on Logic-Q and Planning-Q. Analysis shows that the ability to solve well-specified reasoning problems is not sufficient for success on our benchmark: models struggle to identify the right question even when they can solve the fully specified version. This highlights the need for specifically optimizing models' information acquisition capabilities.