Daily Papers

Many challenging reasoning tasks require not just rapid, intuitive responses, but a more deliberate, multi-step approach. Recent progress in large language models (LLMs) highlights an important shift from the "System 1" way of quick reactions to the "System 2" style of reflection-and-correction problem solving. However, current benchmarks heavily rely on the final-answer accuracy, leaving much of a model's intermediate reasoning steps unexamined. This fails to assess the model's ability to reflect and rectify mistakes within the reasoning process. To bridge this gap, we introduce FINEREASON, a logic-puzzle benchmark for fine-grained evaluation of LLMs' reasoning capabilities. Each puzzle can be decomposed into atomic steps, making it ideal for rigorous validation of intermediate correctness. Building on this, we introduce two tasks: state checking, and state transition, for a comprehensive evaluation of how models assess the current situation and plan the next move. To support broader research, we also provide a puzzle training set aimed at enhancing performance on general mathematical tasks. We show that models trained on our state checking and transition data demonstrate gains in math reasoning by up to 5.1% on GSM8K.

Large Reasoning Models (LRMs) have demonstrated impressive performance on complex tasks, including logical puzzle games that require deriving solutions satisfying all constraints. However, whether they can flexibly apply appropriate rules to varying conditions, particularly when faced with non-canonical game variants, remains an open question. Existing corpora focus on popular puzzles like 9x9 Sudoku, risking overfitting to canonical formats and memorization of solution patterns, which can mask deficiencies in understanding novel rules or adapting strategies to new variants. To address this, we introduce HardcoreLogic, a challenging benchmark of over 5,000 puzzles across 10 games, designed to test the robustness of LRMs on the "long-tail" of logical games. HardcoreLogic systematically transforms canonical puzzles through three dimensions: Increased Complexity (IC), Uncommon Elements (UE), and Unsolvable Puzzles (UP), reducing reliance on shortcut memorization. Evaluations on a diverse set of LRMs reveal significant performance drops, even for models achieving top scores on existing benchmarks, indicating heavy reliance on memorized stereotypes. While increased complexity is the dominant source of difficulty, models also struggle with subtle rule variations that do not necessarily increase puzzle difficulty. Our systematic error analysis on solvable and unsolvable puzzles further highlights gaps in genuine reasoning. Overall, HardcoreLogic exposes the limitations of current LRMs and establishes a benchmark for advancing high-level logical reasoning.

In this paper, we introduce Knowledge-Orthogonal Reasoning (KOR), which minimizes the impact of domain-specific knowledge for a more accurate evaluation of models' reasoning abilities in out-of-distribution scenarios. Based on this concept, we propose the Knowledge-Orthogonal Reasoning Benchmark (KOR-Bench), encompassing five task categories: Operation, Logic, Cipher, Puzzle, and Counterfactual. KOR-Bench emphasizes the effectiveness of models in applying new rule descriptions to solve novel rule-driven questions, revealing that top-performing models like Claude-3.5-Sonnet and GPT-4o only achieve 58.96% and 58.00% accuracy, respectively. We conduct thorough analyses to identify bottlenecks in the Cipher task using Stepwise Prompting, discovering that two rounds of Self-Correction yield optimal results. Complex Task Processing evaluates model performance across three integrated tasks, while we also explore the impact of Tricks on the Puzzle task and visualize rule-focused attention to enhance our understanding of model behavior. We aim for KOR-Bench to be a valuable resource for enhancing models' reasoning capabilities and fostering further research in this field.

We present a novel approach to formalise and solve search-based problems using large language models, which significantly improves upon previous state-of-the-art results. We demonstrate the efficacy of this approach on the logic puzzles benchmark ZebraLogicBench. Instead of letting the LLM attempt to directly solve the puzzles, our method prompts the model to formalise the problem in a logic-focused domain-specific language (DSL) called Logic.py. This formalised representation is then solved using a constraint solver, leveraging the strengths of both the language model and the solver. Our approach achieves a remarkable 65% absolute improvement over the baseline performance of Llama 3.1 70B on ZebraLogicBench, setting a new state-of-the-art with an accuracy of over 90%. This significant advancement demonstrates the potential of combining language models with domain-specific languages and auxiliary tools on traditionally challenging tasks for LLMs.

Existing reasoning benchmarks for large language models (LLMs) frequently fail to capture authentic creativity, often rewarding memorization of previously observed patterns. We address this shortcoming with Sudoku-Bench, a curated benchmark of challenging and unconventional Sudoku variants specifically selected to evaluate creative, multi-step logical reasoning. Sudoku variants form an unusually effective domain for reasoning research: each puzzle introduces unique or subtly interacting constraints, making memorization infeasible and requiring solvers to identify novel logical breakthroughs (``break-ins''). Despite their diversity, Sudoku variants maintain a common and compact structure, enabling clear and consistent evaluation. Sudoku-Bench includes a carefully chosen puzzle set, a standardized text-based puzzle representation, and flexible tools compatible with thousands of publicly available puzzles -- making it easy to extend into a general research environment. Baseline experiments show that state-of-the-art LLMs solve fewer than 15\% of puzzles unaided, highlighting significant opportunities to advance long-horizon, strategic reasoning capabilities.

Large Language Models have demonstrated strong performance on many established reasoning benchmarks. However, these benchmarks primarily evaluate structured skills like quantitative problem-solving, leaving a gap in assessing flexible, multifaceted reasoning abilities that are central to human intelligence. These abilities require integrating logical deduction with spatial awareness and constraint satisfaction, which current evaluations do not measure well. To address this, we introduce RiddleBench, a benchmark of 1,737 challenging puzzles in English designed to probe these core reasoning capabilities. Evaluation of state-of-the-art models on RiddleBench shows fundamental weaknesses. Even top proprietary models like Gemini 2.5 Pro, o3, and Claude 4 Sonnet achieve accuracy just above 60% (60.30%, 63.37%, and 63.16%). Analysis further reveals deep failures, including hallucination cascades (accepting flawed reasoning from other models) and poor self-correction due to a strong self-confirmation bias. Their reasoning is also fragile, with performance degrading significantly when constraints are reordered or irrelevant information is introduced. RiddleBench functions as a diagnostic tool for these issues and as a resource for guiding the development of more robust and reliable language models.

Logic reasoning in natural language has been recognized as an important measure of human intelligence for Large Language Models (LLMs). Popular benchmarks may entangle multiple reasoning skills and thus provide unfaithful evaluations on the logic reasoning skill. Meanwhile, existing logic reasoning benchmarks are limited in language diversity and their distributions are deviated from the distribution of an ideal logic reasoning benchmark, which may lead to biased evaluation results. This paper thereby proposes a new classical logic benchmark DivLogicEval, consisting of natural sentences composed of diverse statements in a counterintuitive way. To ensure a more reliable evaluation, we also introduce a new evaluation metric that mitigates the influence of bias and randomness inherent in LLMs. Through experiments, we demonstrate the extent to which logical reasoning is required to answer the questions in DivLogicEval and compare the performance of different popular LLMs in conducting logical reasoning.

Recent advancements in large language models (LLMs) have led to remarkable performance across a wide range of language understanding and mathematical tasks. As a result, increasing attention has been given to assessing the true reasoning capabilities of LLMs, driving research into commonsense, numerical, logical, and qualitative reasoning. However, with the rapid progress of reasoning-focused models such as OpenAI's o1 and DeepSeek's R1, there has been a growing demand for reasoning benchmarks that can keep pace with ongoing model developments. In this paper, we introduce MastermindEval, a simple, scalable, and interpretable deductive reasoning benchmark inspired by the board game Mastermind. Our benchmark supports two evaluation paradigms: (1) agentic evaluation, in which the model autonomously plays the game, and (2) deductive reasoning evaluation, in which the model is given a pre-played game state with only one possible valid code to infer. In our experimental results we (1) find that even easy Mastermind instances are difficult for current models and (2) demonstrate that the benchmark is scalable to possibly more advanced models in the future Furthermore, we investigate possible reasons why models cannot deduce the final solution and find that current models are limited in deducing the concealed code as the number of statement to combine information from is increasing.

Existing benchmarks for frontier models often test specialized, ``PhD-level'' knowledge that is difficult for non-experts to grasp. In contrast, we present a benchmark based on the NPR Sunday Puzzle Challenge that requires only general knowledge. Our benchmark is challenging for both humans and models, however correct solutions are easy to verify, and models' mistakes are easy to spot. Our work reveals capability gaps that are not evident in existing benchmarks: OpenAI o1 significantly outperforms other reasoning models that are on par on benchmarks that test specialized knowledge. Furthermore, our analysis of reasoning outputs uncovers new kinds of failures. DeepSeek R1, for instance, often concedes with ``I give up'' before providing an answer that it knows is wrong. R1 can also be remarkably ``uncertain'' in its output and in rare cases, it does not ``finish thinking,'' which suggests the need for an inference-time technique to ``wrap up'' before the context window limit is reached. We also quantify the effectiveness of reasoning longer with R1 and Gemini Thinking to identify the point beyond which more reasoning is unlikely to improve accuracy on our benchmark.

High-quality mathematical and logical datasets with verifiable answers are essential for strengthening the reasoning capabilities of large language models (LLMs). While recent data augmentation techniques have facilitated the creation of large-scale benchmarks, existing LLM-generated datasets often suffer from limited reliability, diversity, and scalability. To address these challenges, we introduce PuzzleClone, a formal framework for synthesizing verifiable data at scale using Satisfiability Modulo Theories (SMT). Our approach features three key innovations: (1) encoding seed puzzles into structured logical specifications, (2) generating scalable variants through systematic variable and constraint randomization, and (3) ensuring validity via a reproduction mechanism. Applying PuzzleClone, we construct a curated benchmark comprising over 83K diverse and programmatically validated puzzles. The generated puzzles span a wide spectrum of difficulty and formats, posing significant challenges to current state-of-the-art models. We conduct post training (SFT and RL) on PuzzleClone datasets. Experimental results show that training on PuzzleClone yields substantial improvements not only on PuzzleClone testset but also on logic and mathematical benchmarks. Post training raises PuzzleClone average from 14.4 to 56.2 and delivers consistent improvements across 7 logic and mathematical benchmarks up to 12.5 absolute percentage points (AMC2023 from 52.5 to 65.0). Our code and data are available at https://github.com/puzzleclone.

Inspired by the success of DeepSeek-R1, we explore the potential of rule-based reinforcement learning (RL) in large reasoning models. To analyze reasoning dynamics, we use synthetic logic puzzles as training data due to their controllable complexity and straightforward answer verification. We make some key technical contributions that lead to effective and stable RL training: a system prompt that emphasizes the thinking and answering process, a stringent format reward function that penalizes outputs for taking shortcuts, and a straightforward training recipe that achieves stable convergence. Our 7B model develops advanced reasoning skills-such as reflection, verification, and summarization-that are absent from the logic corpus. Remarkably, after training on just 5K logic problems, it demonstrates generalization abilities to the challenging math benchmarks AIME and AMC.

We introduce SATBench, a benchmark for evaluating the logical reasoning capabilities of large language models (LLMs) through logical puzzles derived from Boolean satisfiability (SAT) problems. Unlike prior work that focuses on inference rule-based reasoning, which often involves deducing conclusions from a set of premises, our approach leverages the search-based nature of SAT problems, where the objective is to find a solution that fulfills a specified set of logical constraints. Each instance in SATBench is generated from a SAT formula, then translated into a story context and conditions using LLMs. The generation process is fully automated and allows for adjustable difficulty by varying the number of clauses. All 2100 puzzles are validated through both LLM-assisted and solver-based consistency checks, with human validation on a subset. Experimental results show that even the strongest model, o4-mini, achieves only 65.0% accuracy on hard UNSAT problems, close to the random baseline of 50%. SATBench exposes fundamental limitations in the search-based logical reasoning abilities of current LLMs and provides a scalable testbed for future research in logical reasoning.

Large language models (LLMs) with Chain-of-Thought (CoT) prompting achieve strong reasoning but often produce unnecessarily long explanations, increasing cost and sometimes reducing accuracy. Fair comparison of efficiency-oriented approaches is hindered by fragmented evaluation practices. We introduce EffiReason-Bench, a unified benchmark for rigorous cross-paradigm evaluation of efficient reasoning methods across three categories: Reasoning Blueprints, Dynamic Execution, and Post-hoc Refinement. To enable step-by-step evaluation, we construct verified CoT annotations for CommonsenseQA and LogiQA via a pipeline that enforces standardized reasoning structures, comprehensive option-wise analysis, and human verification. We evaluate 7 methods across 6 open-source LLMs (1B-70B) on 4 datasets spanning mathematics, commonsense, and logic, and propose the E3-Score, a principled metric inspired by economic trade-off modeling that provides smooth, stable evaluation without discontinuities or heavy reliance on heuristics. Experiments show that no single method universally dominates; optimal strategies depend on backbone scale, task complexity, and architecture.

Thinking LLMs solve complex tasks at the expense of increased compute and overthinking on simpler problems, while non-thinking LLMs are faster and cheaper but underthink on harder reasoning problems. This has led to the development of separate thinking and non-thinking LLM variants, leaving the onus of selecting the optimal model for each query on the end user. In this work, we introduce OptimalThinkingBench, a unified benchmark that jointly evaluates overthinking and underthinking in LLMs and also encourages the development of optimally-thinking models that balance performance and efficiency. Our benchmark comprises two sub-benchmarks: OverthinkingBench, featuring simple queries in 72 domains, and UnderthinkingBench, containing 11 challenging reasoning tasks. Using novel thinking-adjusted accuracy metrics, we perform extensive evaluation of 33 different thinking and non-thinking models and show that no model is able to optimally think on our benchmark. Thinking models often overthink for hundreds of tokens on the simplest user queries without improving performance. In contrast, large non-thinking models underthink, often falling short of much smaller thinking models. We further explore several methods to encourage optimal thinking, but find that these approaches often improve on one sub-benchmark at the expense of the other, highlighting the need for better unified and optimal models in the future.

Reasoning ability has become a central focus in the advancement of Large Reasoning Models (LRMs). Although notable progress has been achieved on several reasoning benchmarks such as MATH500 and LiveCodeBench, existing benchmarks for algorithmic reasoning remain limited, failing to answer a critical question: Do LRMs truly master algorithmic reasoning? To answer this question, we propose AlgBench, an expert-curated benchmark that evaluates LRMs under an algorithm-centric paradigm. AlgBench consists of over 3,000 original problems spanning 27 algorithms, constructed by ACM algorithmic experts and organized under a comprehensive taxonomy, including Euclidean-structured, non-Euclidean-structured, non-optimized, local-optimized, global-optimized, and heuristic-optimized categories. Empirical evaluations on leading LRMs (e.g., Gemini-3-Pro, DeepSeek-v3.2-Speciale and GPT-o3) reveal substantial performance heterogeneity: while models perform well on non-optimized tasks (up to 92%), accuracy drops sharply to around 49% on globally optimized algorithms such as dynamic programming. Further analysis uncovers strategic over-shifts, wherein models prematurely abandon correct algorithmic designs due to necessary low-entropy tokens. These findings expose fundamental limitations of problem-centric reinforcement learning and highlight the necessity of an algorithm-centric training paradigm for robust algorithmic reasoning.

As large language models (LLMs) reach high scores on established mathematical benchmarks, such as GSM8K and MATH, the research community has turned to International Mathematical Olympiad (IMO) problems to push the evaluation frontier. However, existing Olympiad-level benchmarks suffer from practical constraints that introduce grading noise and potential bias, such as heterogeneous answer formats requiring model-based judges and a reliance on potentially flawed solutions. We introduce RIMO, a two-track benchmark designed to preserve peak Olympiad difficulty while eliminating this evaluation noise. The first track, RIMO-N, rewrites 335 IMO problems to admit a single, unique integer answer, allowing for deterministic correctness checking. The second track, RIMO-P, features 456 proof problems with expert-checked solutions, which are decomposed into a sequence of sub-problems to evaluate the step-by-step reasoning process via an automated grading system. Our benchmarking of ten frontier LLMs, including GPT-4o and Gemini 2.5 Flash, reveals that while these systems excel on older benchmarks, their performance drops sharply on RIMO. These results highlight a substantial gap between current LLM capabilities and actual Olympiad-level reasoning. By providing a challenging yet easy-to-evaluate suite, RIMO offers a high-resolution yardstick for future research, presenting a clear target for closing the profound reasoning gap our findings expose.

Knights and knaves problems represent a classic genre of logical puzzles where characters either tell the truth or lie. The objective is to logically deduce each character's identity based on their statements. The challenge arises from the truth-telling or lying behavior, which influences the logical implications of each statement. Solving these puzzles requires not only direct deductions from individual statements, but the ability to assess the truthfulness of statements by reasoning through various hypothetical scenarios. As such, knights and knaves puzzles serve as compelling examples of suppositional reasoning. In this paper, we introduce TruthQuest, a benchmark for suppositional reasoning based on the principles of knights and knaves puzzles. Our benchmark presents problems of varying complexity, considering both the number of characters and the types of logical statements involved. Evaluations on TruthQuest show that large language models like Llama 3 and Mixtral-8x7B exhibit significant difficulties solving these tasks. A detailed error analysis of the models' output reveals that lower-performing models exhibit a diverse range of reasoning errors, frequently failing to grasp the concept of truth and lies. In comparison, more proficient models primarily struggle with accurately inferring the logical implications of potentially false statements.

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.

Recent advancements in large language models (LLMs) have demonstrated significant progress in math and code reasoning capabilities. However, existing code benchmark are limited in their ability to evaluate the full spectrum of these capabilities, particularly at the competitive level. To bridge this gap, we introduce OJBench, a novel and challenging benchmark designed to assess the competitive-level code reasoning abilities of LLMs. OJBench comprises 232 programming competition problems from NOI and ICPC, providing a more rigorous test of models' reasoning skills. We conducted a comprehensive evaluation using OJBench on 37 models, including both closed-source and open-source models, reasoning-oriented and non-reasoning-oriented models. Our results indicate that even state-of-the-art reasoning-oriented models, such as o4-mini and Gemini-2.5-pro-exp, struggle with highly challenging competition-level problems. This highlights the significant challenges that models face in competitive-level code reasoning.

We introduce S1-Bench, a novel benchmark designed to evaluate Large Reasoning Models' (LRMs) performance on simple tasks that favor intuitive system 1 thinking rather than deliberative system 2 reasoning. While LRMs have achieved significant breakthroughs in complex reasoning tasks through explicit chains of thought, their reliance on deep analytical thinking may limit their system 1 thinking capabilities. Moreover, a lack of benchmark currently exists to evaluate LRMs' performance in tasks that require such capabilities. To fill this gap, S1-Bench presents a set of simple, diverse, and naturally clear questions across multiple domains and languages, specifically designed to assess LRMs' performance in such tasks. Our comprehensive evaluation of 22 LRMs reveals significant lower efficiency tendencies, with outputs averaging 15.5 times longer than those of traditional small LLMs. Additionally, LRMs often identify correct answers early but continue unnecessary deliberation, with some models even producing numerous errors. These findings highlight the rigid reasoning patterns of current LRMs and underscore the substantial development needed to achieve balanced dual-system thinking capabilities that can adapt appropriately to task complexity.

Large language models (LLMs) have demonstrated solid zero-shot reasoning capabilities, which is reflected in their performance on the current test tasks. This calls for a more challenging benchmark requiring highly advanced reasoning ability to be solved. In this paper, we introduce such a benchmark, consisting of 191 long-form (1200 words on average) mystery narratives constructed as detective puzzles. Puzzles are sourced from the "5 Minute Mystery" platform and include a multiple-choice question for evaluation. Only 47% of humans solve a puzzle successfully on average, while the best human solvers achieve over 80% success rate. We show that GPT-3 models barely outperform random on this benchmark (with 28% accuracy) while state-of-the-art GPT-4 solves only 38% of puzzles. This indicates that there is still a significant gap in the deep reasoning abilities of LLMs and humans and highlights the need for further research in this area. Our work introduces a challenging benchmark for future studies on reasoning in language models and contributes to a better understanding of the limits of LLMs' abilities.

We introduce Pencil Puzzle Bench, a framework for evaluating large language model reasoning through pencil puzzles, a family of constraint-satisfaction problems closely related to NP-complete problems, with deterministic, step-level verification. From a database of 62,231 puzzles across 94 varieties with verified unique solutions, we select a benchmark of 300 puzzles spanning 20 varieties and evaluate 51 models from 11 providers in two modes: direct ask (single-shot) and agentic (multi-turn with iterative verification). A key differentiator of our benchmark is that every intermediate board state can be checked against variety-specific constraints, localizing errors to the exact rule violated, providing the infrastructure for dense, per-move reward signals for process supervision and reinforcement learning. Our evaluation reveals two distinct axes of capability: (1) reasoning effort scaling, where GPT-5.2 improves 81x from no reasoning to maximum effort; and (2) agentic iteration, where Claude Opus 4.6 rises from 0.3% to 30.0% through iterative checking, while GPT-5.2@xhigh improves from 20.2% to 56.0%. Agentic attempts span a median of 29 turns over 17 minutes, with the longest exceeding 1,221 turns and 14.3 hours - a demanding test of long-context utilization, not just reasoning.

In recent years, the rapid development of large reasoning models has resulted in the saturation of existing benchmarks for evaluating mathematical reasoning, highlighting the urgent need for more challenging and rigorous evaluation frameworks. To address this gap, we introduce OlymMATH, a novel Olympiad-level mathematical benchmark, designed to rigorously test the complex reasoning capabilities of LLMs. OlymMATH features 200 meticulously curated problems, each manually verified and available in parallel English and Chinese versions. The problems are systematically organized into two distinct difficulty tiers: (1) AIME-level problems (easy) that establish a baseline for mathematical reasoning assessment, and (2) significantly more challenging problems (hard) designed to push the boundaries of current state-of-the-art models. In our benchmark, these problems span four core mathematical fields, each including a verifiable numerical solution to enable objective, rule-based evaluation. Empirical results underscore the significant challenge presented by OlymMATH, with state-of-the-art models including DeepSeek-R1 and OpenAI's o3-mini demonstrating notably limited accuracy on the hard subset. Furthermore, the benchmark facilitates comprehensive bilingual assessment of mathematical reasoning abilities-a critical dimension that remains largely unaddressed in mainstream mathematical reasoning benchmarks. We release the OlymMATH benchmark at the STILL project: https://github.com/RUCAIBox/Slow_Thinking_with_LLMs.

We introduce PRISM-Bench, a benchmark of puzzle-based visual challenges designed to evaluate not only whether models can solve problems, but how their reasoning unfolds. Unlike prior evaluations that measure only final-answer accuracy, PRISM-Bench introduces a diagnostic task: given a visual puzzle and a step-by-step chain-of-thought (CoT) containing exactly one error, models must identify the first incorrect step. This setting enables fine-grained assessment of logical consistency, error detection, and visual reasoning. The puzzles in PRISM-Bench require multi-step symbolic, geometric, and analogical reasoning, resisting shortcuts based on superficial pattern matching. Evaluations across state-of-the-art MLLMs reveal a persistent gap between fluent generation and faithful reasoning: models that produce plausible CoTs often fail to locate simple logical faults. By disentangling answer generation from reasoning verification, PRISM-Bench offers a sharper lens on multimodal reasoning competence and underscores the need for diagnostic evaluation protocols in the development of trustworthy MLLMs.

With the advancement of large language models (LLMs), solving complex reasoning tasks has gained increasing attention. Inference-time computation methods (e.g., Best-of-N, beam search, et al.) are particularly valuable as they can enhance reasoning performance without modifying model parameters or requiring additional training. However, these techniques come with implementation challenges, and most existing methods remain at the proof-of-concept stage with limited practical adoption due to their computational complexity and varying effectiveness across different tasks. In this paper, we investigate and benchmark diverse inference-time computation strategies across reasoning tasks of varying complexity. Since most current methods rely on a proposer-verifier pipeline that first generates candidate solutions (e.g., reasoning solutions) and then selects the best one based on reward signals (e.g., RLHF rewards, process rewards), our research focuses on optimizing both candidate solution generation (e.g., instructing prompts, hyperparameters such as temperature and top-p) and reward mechanisms (e.g., self-evaluation, reward types). Through extensive experiments (more than 20,000 A100-80G GPU hours with over 1,000 experiments) across a variety of models (e.g., Llama, Qwen, and Mistral families) of various sizes, our ablation studies reveal that previously overlooked strategies can significantly enhance performance (e.g., tuning temperature can improve reasoning task performance by up to 5%). Furthermore, we establish a standardized benchmark for inference-time computation by systematically evaluating six representative methods across eight reasoning tasks. These findings provide a stronger foundation for future research. The code is available at https://github.com/usail-hkust/benchmark_inference_time_computation_LLM

Complex reasoning tasks often rely on the ability to consistently and accurately apply simple rules across incremental steps, a foundational capability which we term "level-0" reasoning. To systematically evaluate this capability, we introduce L0-Bench, a language model benchmark for testing procedural correctness -- the ability to generate correct reasoning processes, complementing existing benchmarks that primarily focus on outcome correctness. Given synthetic Python functions with simple operations, L0-Bench grades models on their ability to generate step-by-step, error-free execution traces. The synthetic nature of L0-Bench enables systematic and scalable generation of test programs along various axes (e.g., number of trace steps). We evaluate a diverse array of recent closed-source and open-weight models on a baseline test set. All models exhibit degradation as the number of target trace steps increases, while larger models and reasoning-enhanced models better maintain correctness over multiple steps. Additionally, we use L0-Bench to explore test-time scaling along three dimensions: input context length, number of solutions for majority voting, and inference steps. Our results suggest substantial room to improve "level-0" reasoning and potential directions to build more reliable reasoning systems.

As a seemingly self-explanatory task, problem-solving has been a significant component of science and engineering. However, a general yet concrete formulation of problem-solving itself is missing. With the recent development of AI-based problem-solving agents, the demand for process-level verifiability is rapidly increasing yet underexplored. To fill these gaps, we present a principled formulation of problem-solving as a deterministic Markov decision process; a novel framework, FPS (Formal Problem-Solving), which utilizes existing FTP (formal theorem proving) environments to perform process-verified problem-solving; and D-FPS (Deductive FPS), decoupling solving and answer verification for better human-alignment. The expressiveness, soundness and completeness of the frameworks are proven. We construct three benchmarks on problem-solving: FormalMath500, a formalization of a subset of the MATH500 benchmark; MiniF2F-Solving and PutnamBench-Solving, adaptations of FTP benchmarks MiniF2F and PutnamBench. For faithful, interpretable, and human-aligned evaluation, we propose RPE (Restricted Propositional Equivalence), a symbolic approach to determine the correctness of answers by formal verification. We evaluate four prevalent FTP models and two prompting methods as baselines, solving at most 23.77% of FormalMath500, 27.47% of MiniF2F-Solving, and 0.31% of PutnamBench-Solving.

As the application of Large Language Models (LLMs) expands, the demand for reliable evaluations increases. Existing LLM evaluation benchmarks primarily rely on static datasets, making it challenging to assess model performance in dynamic interactions with users. Moreover, these benchmarks often depend on specific background knowledge, complicating the measurement of a model's logical reasoning capabilities. Other dynamic evaluation methods based on strong models or manual efforts may introduce biases and incur high costs and time demands, hindering large-scale application. To address these issues, we propose TurtleBench. TurtleBench collects real user guesses from our online Turtle Soup Puzzle platform that we developed. This approach allows for the relatively dynamic generation of evaluation datasets, mitigating the risk of model cheating while aligning assessments more closely with genuine user needs for reasoning capabilities, thus enhancing the reliability of evaluations. TurtleBench includes 1,532 user guesses along with the correctness of guesses after annotation. Using this dataset, we thoroughly evaluated nine of the most advanced LLMs available today. Notably, the OpenAI o1 series models did not achieve leading results in these evaluations. We propose several hypotheses for further research, such as "the latent reasoning of o1 utilizes trivial Chain-of-Thought (CoT) techniques" and "increasing CoT length not only provides reasoning benefits but also incurs noise costs."

Large language models (LLMs) have shown increasing capability in problem-solving and decision-making, largely based on the step-by-step chain-of-thought reasoning processes. However, it has been increasingly challenging to evaluate the reasoning capability of LLMs. Concretely, existing outcome-based benchmarks begin to saturate and become less sufficient to monitor the progress. To this end, we present a process-based benchmark MR-BEN that demands a meta reasoning skill, where LMs are asked to locate and analyse potential errors in automatically generated reasoning steps. MR-BEN is a comprehensive benchmark comprising 5,975 questions collected from human experts, covering various subjects such as physics, chemistry, logic, coding, and more. Through our designed metrics for assessing meta-reasoning on this benchmark, we identify interesting limitations and weaknesses of current LLMs (open-source and closed-source models). For example, open-source models are seemingly comparable to GPT-4 on outcome-based benchmarks, but they lag far behind on our benchmark, revealing the underlying reasoning capability gap between them. Our dataset and codes are available on https://randolph-zeng.github.io/Mr-Ben.github.io/.

This work investigates the reasoning and planning capabilities of foundation models and their scalability in complex, dynamic environments. We introduce PuzzlePlex, a benchmark designed to assess these capabilities through a diverse set of puzzles. PuzzlePlex consists of 15 types of puzzles, including deterministic and stochastic games of varying difficulty, as well as single-player and two-player scenarios. The PuzzlePlex framework provides a comprehensive environment for each game, and supports extensibility to generate more challenging instances as foundation models evolve. Additionally, we implement customized game-playing strategies for comparison. Building on this benchmark, we develop fine-grained metrics to measure performance and conduct an in-depth analysis of frontier foundation models across two settings: instruction-based and code-based. Furthermore, we systematically investigate their scaling limits. Our findings show that reasoning models outperform others in instruction-based settings, while code-based execution presents greater challenges but offers a scalable and efficient alternative. PuzzlePlex enables targeted evaluation and guides future improvements in reasoning, planning, and generalization for foundation models.

The effectiveness of Large Language Models (LLMs) is heavily influenced by the reasoning strategies, or styles of thought, employed in their prompts. However, the interplay between these reasoning styles, model architecture, and task type remains poorly understood. To address this, we introduce StyleBench, a comprehensive benchmark for systematically evaluating reasoning styles across diverse tasks and models. We assess five representative reasoning styles, including Chain of Thought (CoT), Tree of Thought (ToT), Algorithm of Thought (AoT), Sketch of Thought (SoT), and Chain-of-Draft (CoD) on five reasoning tasks, using 15 open-source models from major families (LLaMA, Qwen, Mistral, Gemma, GPT-OSS, Phi, and DeepSeek) ranging from 270M to 120B parameters. Our large-scale analysis reveals that no single style is universally optimal. We demonstrate that strategy efficacy is highly contingent on both model scale and task type: search-based methods (AoT, ToT) excel in open-ended problems but require large-scale models, while concise styles (SoT, CoD) achieve radical efficiency gains on well-defined tasks. Furthermore, we identify key behavioral patterns: smaller models frequently fail to follow output instructions and default to guessing, while reasoning robustness emerges as a function of scale. Our findings offer a crucial roadmap for selecting optimal reasoning strategies based on specific constraints, we open source the benchmark in https://github.com/JamesJunyuGuo/Style_Bench.

We present PutnamBench, a new multilingual benchmark for evaluating the ability of neural theorem-provers to solve competition mathematics problems. PutnamBench consists of 1697 hand-constructed formalizations of 640 theorems sourced from the William Lowell Putnam Mathematical Competition, the premier undergraduate-level mathematics competition in North America. All the theorems have formalizations in Lean 4 and Isabelle; a substantial subset also has Coq formalizations. Proving the theorems requires significant problem-solving ability and proficiency in a broad range of topics taught in undergraduate mathematics courses. We use PutnamBench to evaluate several established neural and symbolic theorem-provers. These approaches can only solve a handful of the PutnamBench problems, establishing the benchmark as a difficult open challenge for research on neural theorem-proving. PutnamBench is available at https://github.com/trishullab/PutnamBench.

We propose a framework for robust evaluation of reasoning capabilities of language models, using functional variants of benchmarks. Models that solve a reasoning test should exhibit no difference in performance over the static version of a problem compared to a snapshot of the functional variant. We have rewritten the relevant fragment of the MATH benchmark into its functional variant MATH(), with functionalization of other benchmarks to follow. When evaluating current state-of-the-art models over snapshots of MATH(), we find a reasoning gap -- the percentage difference between the static and functional accuracies. We find reasoning gaps from 58.35% to 80.31% among the state-of-the-art closed and open weights models that perform well on static benchmarks, with the caveat that the gaps are likely to be smaller with more sophisticated prompting strategies. Here we show that models which anecdotally have good reasoning performance over real-world tasks, have quantifiable lower gaps, motivating the open problem of building "gap 0" models. Code for evaluation and new evaluation datasets, three MATH() snapshots, are publicly available at https://github.com/consequentai/fneval/.

Puzzlehunts are a genre of complex, multi-step puzzles lacking well-defined problem definitions. In contrast to conventional reasoning benchmarks consisting of tasks with clear instructions, puzzlehunts require models to discover the underlying problem structure from multimodal evidence and iterative reasoning, mirroring real-world domains such as scientific discovery, exploratory data analysis, or investigative problem-solving. Despite recent progress in foundation models, their performance on such open-ended settings remains largely untested. In this paper, we introduce PuzzleWorld, a large-scale benchmark of 667 puzzlehunt-style problems designed to assess step-by-step, open-ended, and creative multimodal reasoning. Each puzzle is annotated with the final solution, detailed reasoning traces, and cognitive skill labels, enabling holistic benchmarking and fine-grained diagnostic analysis. Most state-of-the-art models achieve only 1-2% final answer accuracy, with the best model solving only 14% of puzzles and reaching 40% stepwise accuracy. To demonstrate the value of our reasoning annotations, we show that fine-tuning a small model on reasoning traces improves stepwise reasoning from 4% to 11%, while training on final answers alone degrades performance to near zero. Our error analysis reveals that current models exhibit myopic reasoning, are bottlenecked by the limitations of language-based inference, and lack sketching capabilities crucial for visual and spatial reasoning. We release PuzzleWorld at https://github.com/MIT-MI/PuzzleWorld to support future work on building more general, open-ended, and creative reasoning systems.

Large Language Models (LLMs) have made significant strides in mathematical reasoning, underscoring the need for a comprehensive and fair evaluation of their capabilities. However, existing benchmarks often fall short, either lacking extensive coverage of undergraduate-level mathematical problems or probably suffering from test-set contamination. To address these issues, we introduce UGMathBench, a diverse and dynamic benchmark specifically designed for evaluating undergraduate-level mathematical reasoning with LLMs. UGMathBench comprises 5,062 problems across 16 subjects and 111 topics, featuring 10 distinct answer types. Each problem includes three randomized versions, with additional versions planned for release as leading open-source LLMs become saturated in UGMathBench. Furthermore, we propose two key metrics: effective accuracy (EAcc), which measures the percentage of correctly solved problems across all three versions, and reasoning gap (Delta), which assesses reasoning robustness by calculating the difference between the average accuracy across all versions and EAcc. Our extensive evaluation of 23 leading LLMs reveals that the highest EAcc achieved is 56.3\% by OpenAI-o1-mini, with large Delta values observed across different models. This highlights the need for future research aimed at developing "large reasoning models" with high EAcc and Delta = 0. We anticipate that the release of UGMathBench, along with its detailed evaluation codes, will serve as a valuable resource to advance the development of LLMs in solving mathematical problems.

Reasoning has emerged as the next major frontier for language models (LMs), with rapid advances from both academic and industrial labs. However, this progress often outpaces methodological rigor, with many evaluations relying on benchmarking practices that lack transparency, robustness, or statistical grounding. In this work, we conduct a comprehensive empirical study and find that current mathematical reasoning benchmarks are highly sensitive to subtle implementation choices - including decoding parameters, random seeds, prompt formatting, and even hardware and software-framework configurations. Performance gains reported in recent studies frequently hinge on unclear comparisons or unreported sources of variance. To address these issues, we propose a standardized evaluation framework with clearly defined best practices and reporting standards. Using this framework, we reassess recent methods and find that reinforcement learning (RL) approaches yield only modest improvements - far below prior claims - and are prone to overfitting, especially on small-scale benchmarks like AIME24. In contrast, supervised finetuning (SFT) methods show consistently stronger generalization. To foster reproducibility, we release all code, prompts, and model outputs, for reasoning benchmarks, establishing more rigorous foundations for future work.

Existing visual reasoning benchmarks predominantly rely on natural language prompts, evaluate narrow reasoning modalities, or depend on subjective scoring procedures such as LLM-as-judge. We introduce the TACIT Benchmark, a programmatic visual reasoning benchmark comprising 10 tasks across 6 reasoning domains: spatial navigation, abstract pattern completion, causal simulation, logical constraint satisfaction, graph theory, and topology. The benchmark provides dual-track evaluation: a generative track in which models must produce solution images verified through deterministic computer-vision pipelines, and a discriminative track offering five-way multiple choice with structurally plausible near-miss distractors. Each distractor violates exactly one structural constraint, requiring models to reason about fine-grained visual differences rather than exploit superficial cues. Version 0.1.0 distributes 6,000 puzzles (108,000 PNG images across three resolutions) with fully deterministic seeded generation and reproducible verification. The dataset, generation code, and evaluation harness are released under the Apache 2.0 license on HuggingFace (DOI: 10.57967/hf/7904).

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.

Large language models (LLMs) have shown remarkable improvements in reasoning and many existing benchmarks have been addressed by models such as o1 and o3 either fully or partially. However, a majority of these benchmarks emphasize deductive reasoning, including mathematical and coding tasks in which rules such as mathematical axioms or programming syntax are clearly defined, based on which LLMs can plan and apply these rules to arrive at a solution. In contrast, inductive reasoning, where one infers the underlying rules from observed data, remains less explored. Such inductive processes lie at the heart of scientific discovery, as they enable researchers to extract general principles from empirical observations. To assess whether LLMs possess this capacity, we introduce InductionBench, a new benchmark designed to evaluate the inductive reasoning ability of LLMs. Our experimental findings reveal that even the most advanced models available struggle to master the simplest complexity classes within the subregular hierarchy of functions, highlighting a notable deficiency in current LLMs' inductive reasoning capabilities. Coda and data are available https://github.com/Wenyueh/inductive_reasoning_benchmark.

As language models (LMs) evolve from chat assistants to long-horizon agents capable of multi-step reasoning and tool use, existing benchmarks remain largely confined to structured or exam-style tasks that fall short of real-world professional demands. To this end, we introduce \OneMillion-Bench OneMillion-Bench, a benchmark of 400 expert-curated tasks spanning Law, Finance, Industry, Healthcare, and Natural Science, built to evaluate agents across economically consequential scenarios. Unlike prior work, the benchmark requires retrieving authoritative sources, resolving conflicting evidence, applying domain-specific rules, and making constraint decisions, where correctness depends as much on the reasoning process as the final answer. We adopt a rubric-based evaluation protocol scoring factual accuracy, logical coherence, practical feasibility, and professional compliance, focused on expert-level problems to ensure meaningful differentiation across agents. Together, \$OneMillion-Bench provides a unified testbed for assessing agentic reliability, professional depth, and practical readiness in domain-intensive scenarios.

This paper introduces a novel approach to evaluating deep learning models' capacity for in-diagram logic interpretation. Leveraging the intriguing realm of visual illusions, we establish a unique dataset, InDL, designed to rigorously test and benchmark these models. Deep learning has witnessed remarkable progress in domains such as computer vision and natural language processing. However, models often stumble in tasks requiring logical reasoning due to their inherent 'black box' characteristics, which obscure the decision-making process. Our work presents a new lens to understand these models better by focusing on their handling of visual illusions -- a complex interplay of perception and logic. We utilize six classic geometric optical illusions to create a comparative framework between human and machine visual perception. This methodology offers a quantifiable measure to rank models, elucidating potential weaknesses and providing actionable insights for model improvements. Our experimental results affirm the efficacy of our benchmarking strategy, demonstrating its ability to effectively rank models based on their logic interpretation ability. As part of our commitment to reproducible research, the source code and datasets will be made publicly available at https://github.com/rabbit-magic-wh/InDL

Large language models achieve near-ceiling performance on code generation benchmarks, yet these results increasingly reflect memorization rather than genuine reasoning. We introduce EsoLang-Bench, a benchmark using five esoteric programming languages (Brainfuck, Befunge-98, Whitespace, Unlambda, and Shakespeare) that lack benchmark gaming incentives due to their economic irrationality for pre-training. These languages require the same computational primitives as mainstream programming but have 1,000-100,000x fewer public repositories than Python (based on GitHub search counts). We evaluate five frontier models across five prompting strategies and find a dramatic capability gap: models achieving 85-95% on standard benchmarks score only 0-11% on equivalent esoteric tasks, with 0% accuracy beyond the Easy tier. Few-shot learning and self-reflection fail to improve performance, suggesting these techniques exploit training priors rather than enabling genuine learning. EsoLang-Bench provides the first benchmark designed to mimic human learning by acquiring new languages through documentation, interpreter feedback, and iterative experimentation, measuring transferable reasoning skills resistant to data contamination.

The rapid advancement of Large Language Models (LLMs) has demonstrated remarkable progress in complex reasoning tasks. However, a significant discrepancy persists between benchmark performances and real-world applications. We identify this gap as primarily stemming from current evaluation protocols and metrics, which inadequately capture the full spectrum of LLM capabilities, particularly in complex reasoning tasks where both accuracy and consistency are crucial. This work makes two key contributions. First, we introduce G-Pass@k, a novel evaluation metric that provides a continuous assessment of model performance across multiple sampling attempts, quantifying both the model's peak performance potential and its stability. Second, we present LiveMathBench, a dynamic benchmark comprising challenging, contemporary mathematical problems designed to minimize data leakage risks during evaluation. Through extensive experiments using G-Pass@k on state-of-the-art LLMs with LiveMathBench, we provide comprehensive insights into both their maximum capabilities and operational consistency. Our findings reveal substantial room for improvement in LLMs' "realistic" reasoning capabilities, highlighting the need for more robust evaluation methods. The benchmark and detailed results are available at: https://github.com/open-compass/GPassK.

Computing olympiads contain some of the most challenging problems for humans, requiring complex algorithmic reasoning, puzzle solving, in addition to generating efficient code. However, it has been understudied as a domain to evaluate language models (LMs). In this paper, we introduce the USACO benchmark with 307 problems from the USA Computing Olympiad, along with high-quality unit tests, reference code, and official analyses for each problem. These resources enable us to construct and test a range of LM inference methods for competitive programming for the first time. We find GPT-4 only achieves a 8.7% pass@1 accuracy with zero-shot chain-of-thought prompting, and our best inference method improves it to 20.2% using a combination of self-reflection and retrieval over episodic knowledge. However, this is far from solving the benchmark. To better understand the remaining challenges, we design a novel human-in-the-loop study and surprisingly find that a small number of targeted hints enable GPT-4 to solve 13 out of 15 problems previously unsolvable by any model and method. Our benchmark, baseline methods, quantitative results, and qualitative analysis serve as an initial step toward LMs with grounded, creative, and algorithmic reasoning.

As Large Language Models (LLMs) saturate elementary benchmarks, the research frontier has shifted from generation to the reliability of automated evaluation. We demonstrate that standard "LLM-as-a-Judge" protocols suffer from a systematic Alignment Gap when applied to upper-undergraduate to early graduate level mathematics. To quantify this, we introduce QEDBench, the first large-scale dual-rubric alignment benchmark to systematically measure alignment with human experts on university-level math proofs by contrasting course-specific rubrics against expert common knowledge criteria. By deploying a dual-evaluation matrix (7 judges x 5 solvers) against 1,000+ hours of human evaluation, we reveal that certain frontier evaluators like Claude Opus 4.5, DeepSeek-V3, Qwen 2.5 Max, and Llama 4 Maverick exhibit significant positive bias (up to +0.18, +0.20, +0.30, +0.36 mean score inflation, respectively). Furthermore, we uncover a critical reasoning gap in the discrete domain: while Gemini 3.0 Pro achieves state-of-the-art performance (0.91 average human evaluation score), other reasoning models like GPT-5 Pro and Claude Sonnet 4.5 see their performance significantly degrade in discrete domains. Specifically, their average human evaluation scores drop to 0.72 and 0.63 in Discrete Math, and to 0.74 and 0.50 in Graph Theory. In addition to these research results, we also release QEDBench as a public benchmark for evaluating and improving AI judges. Our benchmark is publicly published at https://github.com/qqliu/Yale-QEDBench.

As models become increasingly sophisticated, conventional algorithm benchmarks are increasingly saturated, underscoring the need for more challenging benchmarks to guide future improvements in algorithmic reasoning. This paper introduces OIBench, a high-quality, private, and challenging olympiad-level informatics dataset comprising 250 carefully curated original problems. We detail the construction methodology of the benchmark, ensuring a comprehensive assessment across various programming paradigms and complexities, and we demonstrate its contamination-resistant properties via experiments. We propose Time/Space Completion Curves for finer-grained efficiency analysis and enable direct human-model comparisons through high-level participant evaluations. Our experiments reveal that while open-source models lag behind closed-source counterparts, current SOTA models already outperform most human participants in both correctness and efficiency, while still being suboptimal compared to the canonical solutions. By releasing OIBench as a fully open-source resource (https://huggingface.co/datasets/AGI-Eval/OIBench), we hope this benchmark will contribute to advancing code reasoning capabilities for future LLMs.

Standard benchmarks have become increasingly unreliable due to saturation, subjectivity, and poor generalization. We argue that evaluating model's ability to acquire information actively is important to assess model's intelligence. We propose Interactive Benchmarks, a unified evaluation paradigm that assesses model's reasoning ability in an interactive process under budget constraints. We instantiate this framework across two settings: Interactive Proofs, where models interact with a judge to deduce objective truths or answers in logic and mathematics; and Interactive Games, where models reason strategically to maximize long-horizon utilities. Our results show that interactive benchmarks provide a robust and faithful assessment of model intelligence, revealing that there is still substantial room to improve in interactive scenarios. Project page: https://github.com/interactivebench/interactivebench

Formal mathematical reasoning remains a critical challenge for artificial intelligence, hindered by limitations of existing benchmarks in scope and scale. To address this, we present FormalMATH, a large-scale Lean4 benchmark comprising 5,560 formally verified problems spanning from high-school Olympiad challenges to undergraduate-level theorems across diverse domains (e.g., algebra, applied mathematics, calculus, number theory, and discrete mathematics). To mitigate the inefficiency of manual formalization, we introduce a novel human-in-the-loop autoformalization pipeline that integrates: (1) specialized large language models (LLMs) for statement autoformalization, (2) multi-LLM semantic verification, and (3) negation-based disproof filtering strategies using off-the-shelf LLM-based provers. This approach reduces expert annotation costs by retaining 72.09% of statements before manual verification while ensuring fidelity to the original natural-language problems. Our evaluation of state-of-the-art LLM-based theorem provers reveals significant limitations: even the strongest models achieve only 16.46% success rate under practical sampling budgets, exhibiting pronounced domain bias (e.g., excelling in algebra but failing in calculus) and over-reliance on simplified automation tactics. Notably, we identify a counterintuitive inverse relationship between natural-language solution guidance and proof success in chain-of-thought reasoning scenarios, suggesting that human-written informal reasoning introduces noise rather than clarity in the formal reasoning settings. We believe that FormalMATH provides a robust benchmark for benchmarking formal mathematical reasoning.

We present AMO-Bench, an Advanced Mathematical reasoning benchmark with Olympiad level or even higher difficulty, comprising 50 human-crafted problems. Existing benchmarks have widely leveraged high school math competitions for evaluating mathematical reasoning capabilities of large language models (LLMs). However, many existing math competitions are becoming less effective for assessing top-tier LLMs due to performance saturation (e.g., AIME24/25). To address this, AMO-Bench introduces more rigorous challenges by ensuring all 50 problems are (1) cross-validated by experts to meet at least the International Mathematical Olympiad (IMO) difficulty standards, and (2) entirely original problems to prevent potential performance leakages from data memorization. Moreover, each problem in AMO-Bench requires only a final answer rather than a proof, enabling automatic and robust grading for evaluation. Experimental results across 26 LLMs on AMO-Bench show that even the best-performing model achieves only 52.4% accuracy on AMO-Bench, with most LLMs scoring below 40%. Beyond these poor performances, our further analysis reveals a promising scaling trend with increasing test-time compute on AMO-Bench. These results highlight the significant room for improving the mathematical reasoning in current LLMs. We release AMO-Bench to facilitate further research into advancing the reasoning abilities of language models. https://amo-bench.github.io/

Large Language Models (LLMs) are increasingly used for code generation, yet quantum code generation is still evaluated mostly within single frameworks, making it difficult to separate quantum reasoning from framework familiarity. We introduce QuanBench+, a unified benchmark spanning Qiskit, PennyLane, and Cirq, with 42 aligned tasks covering quantum algorithms, gate decomposition, and state preparation. We evaluate models with executable functional tests, report Pass@1 and Pass@5, and use KL-divergence-based acceptance for probabilistic outputs. We additionally study Pass@1 after feedback-based repair, where a model may revise code after a runtime error or wrong answer. Across frameworks, the strongest one-shot scores reach 59.5% in Qiskit, 54.8% in Cirq, and 42.9% in PennyLane; with feedback-based repair, the best scores rise to 83.3%, 76.2%, and 66.7%, respectively. These results show clear progress, but also that reliable multi-framework quantum code generation remains unsolved and still depends strongly on framework-specific knowledge.

In recent years, large language models (LLMs) have made significant progress in code intelligence, yet systematically evaluating their code understanding and reasoning abilities remains challenging. Mainstream benchmarks such as HumanEval and MBPP primarily assess functional correctness, while reasoning benchmarks like CRUXEVAL are limited to single-function, low-complexity scenarios. As a result, advanced models achieve nearly saturated scores, limiting their discriminative power. To address this, we present STEPWISE-CODEX-Bench (SX-Bench), a novel benchmark designed for complex multi-function understanding and fine-grained execution reasoning. SX-Bench features tasks involving collaboration among multiple sub-functions (e.g., chained calls, nested loops), shifting evaluation towards overall control and data flow modeling. It defines "computation steps" as the minimal execution unit and requires models to predict the total number of steps in reasoning tasks, thereby assessing a model's in-depth understanding of dynamic execution beyond simple I/O matching. Evaluation on over 20 mainstream models (including 14 reasoning-enhanced models) demonstrates that SX-Bench is highly discriminative: even the state-of-the-art OpenAI-O3 achieves only 78.37 percent accuracy on Hard-Reasoning tasks, much lower than its saturated scores on previous benchmarks, thereby revealing bottlenecks in complex and fine-grained reasoning. We also release an automated pipeline combining program synthesis, symbolic execution, and LLM-aided validation for efficient benchmark generation and quality assurance. SX-Bench advances code evaluation from "single-function verification" to "multi-function dynamic reasoning," providing a key tool for the in-depth assessment of advanced code intelligence models.

Neurosymbolic approaches leveraging Large Language Models (LLMs) with formal methods have recently achieved strong results on mathematics-oriented theorem-proving benchmarks. However, success on competition-style mathematics does not by itself demonstrate the ability to construct proofs about real-world implementations. We address this gap with a benchmark derived from an industrial cryptographic library whose assembly routines are already verified in HOL Light. s2n-bignum is a library used at AWS for providing fast assembly routines for cryptography, and its correctness is established by formal verification. The task of formally verifying this library has been a significant achievement for the Automated Reasoning Group. It involved two tasks: (1) precisely specifying the correct behavior of a program as a mathematical proposition, and (2) proving that the proposition is correct. In the case of s2n-bignum, both tasks were carried out by human experts. In s2n-bignum-bench, we provide the formal specification and ask the LLM to generate a proof script that is accepted by HOL Light within a fixed proof-check timeout. To our knowledge, s2n-bignum-bench is the first public benchmark focused on machine-checkable proof synthesis for industrial low-level cryptographic assembly routines in HOL Light. This benchmark provides a challenging and practically relevant testbed for evaluating LLM-based theorem proving beyond competition mathematics. The code to set up and use the benchmark is available here: https://github.com/kings-crown/s2n-bignum-bench{s2n-bignum-bench}.

The rapid proliferation of benchmarks for evaluating large language models (LLMs) has created an urgent need for systematic methods to assess benchmark quality itself. We propose Benchmark^2, a comprehensive framework comprising three complementary metrics: (1) Cross-Benchmark Ranking Consistency, measuring whether a benchmark produces model rankings aligned with peer benchmarks; (2) Discriminability Score, quantifying a benchmark's ability to differentiate between models; and (3) Capability Alignment Deviation, identifying problematic instances where stronger models fail but weaker models succeed within the same model family. We conduct extensive experiments across 15 benchmarks spanning mathematics, reasoning, and knowledge domains, evaluating 11 LLMs across four model families. Our analysis reveals significant quality variations among existing benchmarks and demonstrates that selective benchmark construction based on our metrics can achieve comparable evaluation performance with substantially reduced test sets.

Reasoning benchmarks have played a crucial role in the progress of language models. Yet rigorous evaluation remains a significant challenge as static question-answer pairs provide only a snapshot of performance, compressing complex behavior into a single accuracy metric. This limitation is especially true in complex, rule-bound domains such as law, where existing benchmarks are costly to build and ill suited for isolating specific failure modes. To address this, we introduce OpenExempt, a framework and benchmark for diagnostic evaluation of legal reasoning. The OpenExempt Framework uses expert-crafted symbolic representations of U.S. Bankruptcy Code statutes to dynamically generate a large space of natural language reasoning tasks and their machine-computable solutions on demand. This gives users fine-grained control over task complexity and scope, allowing individual reasoning skills to be probed in isolation. Using this system, we construct the OpenExempt Benchmark, a diagnostic benchmark for legal reasoning with 9,765 samples across nine evaluation suites designed to carefully probe model capabilities. Experiments on 13 diverse language models reveal sharp performance cliffs that emerge only under longer reasoning paths and in the presence of obfuscating statements. We release the framework and benchmark publicly to support research aimed at understanding and improving the next generation of reasoning systems.

Large language models (LLMs) are capable of solving a wide range of tasks, yet they have struggled with reasoning. To address this, we propose Additional Logic Training (ALT), which aims to enhance LLMs' reasoning capabilities by program-generated logical reasoning samples. We first establish principles for designing high-quality samples by integrating symbolic logic theory and previous empirical insights. Then, based on these principles, we construct a synthetic corpus named Formal Logic Deduction Diverse (FLD^{times 2}), comprising numerous samples of multi-step deduction with unknown facts, diverse reasoning rules, diverse linguistic expressions, and challenging distractors. Finally, we empirically show that ALT on FLD^{times2} substantially enhances the reasoning capabilities of state-of-the-art LLMs, including LLaMA-3.1-70B. Improvements include gains of up to 30 points on logical reasoning benchmarks, up to 10 points on math and coding benchmarks, and 5 points on the benchmark suite BBH.

Recent generations of language models have introduced Large Reasoning Models (LRMs) that generate detailed thinking processes before providing answers. While these models demonstrate improved performance on reasoning benchmarks, their fundamental capabilities, scaling properties, and limitations remain insufficiently understood. Current evaluations primarily focus on established math and coding benchmarks, emphasizing final answer accuracy. However, this evaluation paradigm often suffers from contamination and does not provide insights into the reasoning traces. In this work, we systematically investigate these gaps with the help of controllable puzzle environments that allow precise manipulation of complexity while maintaining consistent logical structures. This setup enables the analysis of not only final answers but also the internal reasoning traces, offering insights into how LRMs think. Through extensive experiments, we show that LRMs face a complete accuracy collapse beyond certain complexities. Moreover, they exhibit a counterintuitive scaling limit: their reasoning effort increases with problem complexity up to a point, then declines despite having remaining token budget. By comparing LRMs with their standard LLM counterparts under same inference compute, we identify three performance regimes: (1) low-complexity tasks where standard models outperform LRMs, (2) medium-complexity tasks where LRMs demonstrates advantage, and (3) high-complexity tasks where both models face complete collapse. We found that LRMs have limitations in exact computation: they fail to use explicit algorithms and reason inconsistently across scales. We also investigate the reasoning traces in more depth, studying the patterns of explored solutions and analyzing the models' computational behavior, shedding light on their strengths, limitations, and raising questions about their reasoning capabilities.

Current mathematical reasoning benchmarks for large language models (LLMs) are approaching saturation, with some achieving > 90% accuracy, and are increasingly compromised by training-set contamination. We introduce Putnam-AXIOM, a benchmark of 522 university-level competition problems drawn from the prestigious William Lowell Putnam Mathematical Competition, and Putnam-AXIOM Variation, an unseen companion set of 100 functional variants generated by programmatically perturbing variables and constants. The variation protocol produces an unlimited stream of equally difficult, unseen instances -- yielding a contamination-resilient test bed. On the Original set, OpenAI's o1-preview -- the strongest evaluated model -- scores 41.9%, but its accuracy drops by 19.6% (46.8% relative decrease) on the paired Variations. The remaining eighteen models show the same downward trend, ten of them with non-overlapping 95% confidence intervals. These gaps suggest memorization and highlight the necessity of dynamic benchmarks. We complement "boxed" accuracy with Teacher-Forced Accuracy (TFA), a lightweight metric that directly scores reasoning traces and automates natural language proof evaluations. Putnam-AXIOM therefore provides a rigorous, contamination-resilient evaluation framework for assessing advanced mathematical reasoning of LLMs. Data and evaluation code are publicly available at https://github.com/brando90/putnam-axiom.

Evaluating the mathematical capability of Large Language Models (LLMs) is a critical yet challenging frontier. Existing benchmarks fall short, particularly for proof-centric problems, as manual creation is unscalable and costly, leaving the true mathematical abilities of LLMs largely unassessed. To overcome these barriers, we propose Proof2Hybrid, the first fully automated framework that synthesizes high-quality, proof-centric benchmarks from natural language mathematical corpora. The key novelty of our solution is Proof2X, a roadmap of converting mathematical proofs into various kinds of questions that are easy to verify. Instructed by this roadmap, we propose a new type of hybrid-formatted questions, named ``m-out-of-n multiple judge questions'', specifically designed to enable robust, automatic evaluation while being resilient to guessing and superficial pattern matching inherent in traditional formats. As a demonstration of our framework, we introduce AlgGeoTest, a benchmark for algebraic geometry--a frontier domain of modern mathematics--comprising 456 challenging items. Our extensive evaluations on state-of-the-art LLMs using AlgGeoTest reveal profound deficits in their comprehension of algebraic geometry, providing a more precise measure of their true mathematical capabilities. Our framework and benchmark pave the way for a new wave of in-depth research into the mathematical intelligence of AI systems.

In this paper, we introduce PolyMath, a multilingual mathematical reasoning benchmark covering 18 languages and 4 easy-to-hard difficulty levels. Our benchmark ensures difficulty comprehensiveness, language diversity, and high-quality translation, making it a highly discriminative multilingual mathematical benchmark in the era of reasoning LLMs. We conduct a comprehensive evaluation for advanced LLMs and find that even Deepseek-R1-671B and Qwen-QwQ-32B, achieve only 43.4 and 41.8 benchmark scores, with less than 30% accuracy under the highest level. From a language perspective, our benchmark reveals several key challenges of LLMs in multilingual reasoning: (1) Reasoning performance varies widely across languages for current LLMs; (2) Input-output language consistency is low in reasoning LLMs and may be correlated with performance; (3) The thinking length differs significantly by language for current LLMs. Additionally, we demonstrate that controlling the output language in the instructions has the potential to affect reasoning performance, especially for some low-resource languages, suggesting a promising direction for improving multilingual capabilities in LLMs.

Recent advancements in language models have led to significant improvements in mathematical reasoning across various benchmarks. However, most of these benchmarks rely on automatic evaluation methods that only compare final answers using heuristics, without verifying the underlying reasoning steps. This limitation results in false positive solutions, where models may produce correct final answers but with flawed deduction paths. In this paper, we systematically examine the prevalence of false positive solutions in mathematical problem solving for language models. We analyze the characteristics and extent of this issue across different open-source models, datasets of varying difficulty levels, and decoding strategies. Specifically, we explore how false positives influence the inference time scaling behavior of language models. Our experimental results reveal that: (1) false positive solutions persist across different models, datasets, and decoding methods, (2) sampling-based inference time scaling methods do not alleviate the problem, and (3) the pass@N evaluation metric is more susceptible to false positives, suggesting a significantly lower scaling ceiling than what automatic evaluations indicate. Additionally, we analyze specific instances of false positives and discuss potential limitations in self-improvement techniques and synthetic data generation under such conditions. Our data and code are publicly available at https://github.com/Wloner0809/False-Positives-in-Math.

Large language models (LLMs) have shown remarkable reasoning capabilities given chain-of-thought prompts (examples with intermediate reasoning steps). Existing benchmarks measure reasoning ability indirectly, by evaluating accuracy on downstream tasks such as mathematical reasoning. However, it is unclear how these models obtain the answers and whether they rely on simple heuristics rather than the generated chain-of-thought. To enable systematic exploration of the reasoning ability of LLMs, we present a new synthetic question-answering dataset called PrOntoQA, where each example is generated from a synthetic world model represented in first-order logic. This allows us to parse the generated chain-of-thought into symbolic proofs for formal analysis. Our analysis on InstructGPT and GPT-3 shows that LLMs are quite capable of making correct individual deduction steps, and so are generally capable of reasoning, even in fictional contexts. However, they have difficulty with proof planning: When multiple valid deduction steps are available, they are not able to systematically explore the different options.

Recent advances in large language models (LLMs) have demonstrated notable progress on many mathematical benchmarks. However, most of these benchmarks only feature problems grounded in junior and senior high school subjects, contain only multiple-choice questions, and are confined to a limited scope of elementary arithmetic operations. To address these issues, this paper introduces an expansive benchmark suite SciBench that aims to systematically examine the reasoning capabilities required for complex scientific problem solving. SciBench contains two carefully curated datasets: an open set featuring a range of collegiate-level scientific problems drawn from mathematics, chemistry, and physics textbooks, and a closed set comprising problems from undergraduate-level exams in computer science and mathematics. Based on the two datasets, we conduct an in-depth benchmark study of two representative LLMs with various prompting strategies. The results reveal that current LLMs fall short of delivering satisfactory performance, with an overall score of merely 35.80%. Furthermore, through a detailed user study, we categorize the errors made by LLMs into ten problem-solving abilities. Our analysis indicates that no single prompting strategy significantly outperforms others and some strategies that demonstrate improvements in certain problem-solving skills result in declines in other skills. We envision that SciBench will catalyze further developments in the reasoning abilities of LLMs, thereby ultimately contributing to scientific research and discovery.

The rapid evolution of code largelanguage models underscores the need for effective and transparent benchmarking of their reasoning capabilities. However, the current benchmarking approach heavily depends on publicly available, human-created datasets. The widespread use of these fixed benchmark datasets makes the benchmarking process to be static and thus particularly susceptible to data contamination, an unavoidable consequence of the extensive data collection processes used to train Code LLMs. Existing approaches that address data contamination often suffer from human effort limitations and imbalanced problem complexity. To tackle these challenges, we propose \tool, a novel benchmarking suite for evaluating Code LLMs under potential data contamination. Given a seed programming problem, \tool employs multiple agents to extract and modify the context without altering the core logic, generating semantically equivalent variations. We introduce a dynamic data generation methods and conduct empirical studies on two seed datasets across 21 Code LLMs. Results show that \tool effectively benchmarks reasoning capabilities under contamination risks while generating diverse problem sets to ensure consistent and reliable evaluations.

Large Vision-Language Models (LVLMs) struggle with puzzles, which require precise perception, rule comprehension, and logical reasoning. Assessing and enhancing their performance in this domain is crucial, as it reflects their ability to engage in structured reasoning - an essential skill for real-world problem-solving. However, existing benchmarks primarily evaluate pre-trained models without additional training or fine-tuning, often lack a dedicated focus on reasoning, and fail to establish a systematic evaluation framework. To address these limitations, we introduce VGRP-Bench, a Visual Grid Reasoning Puzzle Benchmark featuring 20 diverse puzzles. VGRP-Bench spans multiple difficulty levels, and includes extensive experiments not only on existing chat LVLMs (e.g., GPT-4o), but also on reasoning LVLMs (e.g., Gemini-Thinking). Our results reveal that even the state-of-the-art LVLMs struggle with these puzzles, highlighting fundamental limitations in their puzzle-solving capabilities. Most importantly, through systematic experiments, we identify and analyze key factors influencing LVLMs' puzzle-solving performance, including the number of clues, grid size, and rule complexity. Furthermore, we explore two Supervised Fine-Tuning (SFT) strategies that can be used in post-training: SFT on solutions (S-SFT) and SFT on synthetic reasoning processes (R-SFT). While both methods significantly improve performance on trained puzzles, they exhibit limited generalization to unseen ones. We will release VGRP-Bench to facilitate further research on LVLMs for complex, real-world problem-solving. Project page: https://yufan-ren.com/subpage/VGRP-Bench/.

Existing benchmarks for evaluating mathematical reasoning in large language models (LLMs) rely primarily on competition problems, formal proofs, or artificially challenging questions -- failing to capture the nature of mathematics encountered in actual research environments. We introduce RealMath, a novel benchmark derived directly from research papers and mathematical forums that assesses LLMs' abilities on authentic mathematical tasks. Our approach addresses three critical challenges: sourcing diverse research-level content, enabling reliable automated evaluation through verifiable statements, and designing a continually refreshable dataset to mitigate contamination risks. Experimental results across multiple LLMs reveal surprising capabilities in handling research mathematics compared to competition problems, suggesting current models may already serve as valuable assistants for working mathematicians despite limitations on highly challenging problems. The code and dataset for RealMath are publicly available.

Large reasoning models (LRMs) have demonstrated impressive reasoning capabilities across a broad range of tasks including Olympiad-level mathematical problems, indicating evidence of their complex reasoning abilities. While many reasoning benchmarks focus on the STEM domain, the ability of LRMs to reason correctly in broader task domains remains underexplored. In this work, we introduce TTT-Bench, a new benchmark that is designed to evaluate basic strategic, spatial, and logical reasoning abilities in LRMs through a suite of four two-player Tic-Tac-Toe-style games that humans can effortlessly solve from a young age. We propose a simple yet scalable programmatic approach for generating verifiable two-player game problems for TTT-Bench. Although these games are trivial for humans, they require reasoning about the intentions of the opponent, as well as the game board's spatial configurations, to ensure a win. We evaluate a diverse set of state-of-the-art LRMs, and discover that the models that excel at hard math problems frequently fail at these simple reasoning games. Further testing reveals that our evaluated reasoning models score on average downarrow 41\% \& downarrow 5\% lower on TTT-Bench compared to MATH 500 \& AIME 2024 respectively, with larger models achieving higher performance using shorter reasoning traces, where most of the models struggle on long-term strategic reasoning situations on simple and new TTT-Bench tasks.

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.

Instruction following has catalyzed the recent era of Large Language Models (LLMs) and is the foundational skill underpinning more advanced capabilities such as reasoning and agentic behaviors. As tasks grow more challenging, the logic structures embedded in natural language instructions becomes increasingly intricate. However, how well LLMs perform on such logic-rich instructions remains under-explored. We propose LogicIFGen and LogicIFEval. LogicIFGen is a scalable, automated framework for generating verifiable instructions from code functions, which can naturally express rich logic such as conditionals, nesting, recursion, and function calls. We further curate a collection of complex code functions and use LogicIFGen to construct LogicIFEval, a benchmark comprising 426 verifiable logic-rich instructions. Our experiments demonstrate that current state-of-the-art LLMs still struggle to correctly follow the instructions in LogicIFEval. Most LLMs can only follow fewer than 60% of the instructions, revealing significant deficiencies in the instruction-following ability. Code and Benchmark: https://github.com/mianzhang/LogicIF

Competitive programming problems increasingly serve as valuable benchmarks to evaluate the coding capabilities of large language models (LLMs) due to their complexity and ease of verification. Yet, current coding benchmarks face limitations such as lack of exceptionally challenging problems, insufficient test case coverage, reliance on online platform APIs that limit accessibility. To address these issues, we introduce LiveOIBench, a comprehensive benchmark featuring 403 expert-curated Olympiad-level competitive programming problems, each with an average of 60 expert-designed test cases. The problems are sourced directly from 72 official Informatics Olympiads in different regions conducted between 2023 and 2025. LiveOIBench distinguishes itself through four key features: (1) meticulously curated high-quality tasks with detailed subtask rubrics and extensive private test cases; (2) direct integration of elite contestant performance data to enable informative comparison against top-performing humans; (3) planned continuous, contamination-free updates from newly released Olympiad problems; and (4) a self-contained evaluation system facilitating offline and easy-to-reproduce assessments. Benchmarking 32 popular general-purpose and reasoning LLMs, we find that GPT-5 achieves a notable 81.76th percentile, a strong result that nonetheless falls short of top human contestant performance, who usually place above 90th. In contrast, among open-weight reasoning models, GPT-OSS-120B achieves only a 60th percentile, underscoring significant capability disparities from frontier closed models. Detailed analyses indicate that robust reasoning models prioritize precise problem analysis over excessive exploration, suggesting future models should emphasize structured analysis and minimize unnecessary exploration. All data, code, and leaderboard results will be made publicly available on our website.

Although many benchmarks evaluate the reasoning abilities of Large Language Models (LLMs) within domains such as mathematics, coding, or data wrangling, few abstract away from domain specifics to examine reasoning as a capability in and of itself. We contribute a novel type of benchmark evaluating the inductive reasoning capabilities of LLMs that is inspired by the forward reconstruction task from historical linguistics but is formulated in an extremely simple, general way (in the form of Programming by Examples). The task involves generating a cascade of simple string rewrite programs to transform a given list of input strings into a list of desired output strings. We present a fully automated pipeline that programmatically generates problems of this type with controllable difficulty, enabling scalable evaluation of reasoning models while avoiding contamination. Using this approach, we construct two benchmarks: PBEBench-Lite, which efficiently stratifies models of varying capabilities, and PBEBench, which requires models to induce programs similar in complexity to those constructed by historical linguists. Our experiments reveal a substantial performance gap between models that leverage test-time compute or LCoT (long chain-of-thought) reasoning and those that do not. Moreover, although recent models show promise, the solve rate for both of them drops below 5% for hard instances of the PBEBench dataset (ground truth cascade lengths of 20 and 30, respectively), falling well short of realistic historical linguistics requirements even with computationally expensive, popular scaling techniques from the PBE and reasoning literature. Additionally, we also study the effectiveness of different scaling strategies and the impact of various hyperparameters on the difficulty of the generated data using gpt-oss-120b, the best-performing open-source model.

Evaluating AI agents within complex, interactive environments that mirror real-world challenges is critical for understanding their practical capabilities. While existing agent benchmarks effectively assess skills like tool use or performance on structured tasks, they often do not fully capture an agent's ability to operate autonomously in exploratory environments that demand sustained, self-directed reasoning over a long and growing context. To spur the development of agents capable of more robust intrinsic reasoning over long horizons, we introduce TextQuests, a benchmark based on the Infocom suite of interactive fiction games. These text-based adventures, which can take human players over 30 hours and require hundreds of precise actions to solve, serve as an effective proxy for evaluating AI agents on focused, stateful tasks. The benchmark is specifically designed to assess an LLM agent's capacity for self-contained problem-solving by precluding the use of external tools, thereby focusing on intrinsic long-context reasoning capabilities in an exploratory environment characterized by the need for trial-and-error learning and sustained problem-solving within a single interactive session. We release TextQuests at https://textquests.ai.

Recent math benchmarks for large language models (LLMs) such as MathArena indicate that state-of-the-art reasoning models achieve impressive performance on mathematical competitions like AIME, with the leading model, o3-mini, achieving scores comparable to top human competitors. However, these benchmarks evaluate models solely based on final numerical answers, neglecting rigorous reasoning and proof generation which are essential for real-world mathematical tasks. To address this, we introduce the first comprehensive evaluation of full-solution reasoning for challenging mathematical problems. Using expert human annotators, we evaluated several state-of-the-art reasoning models on the six problems from the 2025 USAMO within hours of their release. Our results reveal that all tested models struggled significantly, achieving less than 5% on average. Through detailed analysis of reasoning traces, we identify the most common failure modes and find several unwanted artifacts arising from the optimization strategies employed during model training. Overall, our results suggest that current LLMs are inadequate for rigorous mathematical reasoning tasks, highlighting the need for substantial improvements in reasoning and proof generation capabilities.

The performance of large language models (LLMs) on existing reasoning benchmarks has significantly improved over the past years. In response, we present JEEBench, a considerably more challenging benchmark dataset for evaluating the problem solving abilities of LLMs. We curate 515 challenging pre-engineering mathematics, physics and chemistry problems from the highly competitive IIT JEE-Advanced exam. Long-horizon reasoning on top of deep in-domain knowledge is essential for solving problems in this benchmark. Our evaluation on various open-source and proprietary models reveals that the highest performance, even after using techniques like self-consistency, self-refinement and chain-of-thought prompting, is less than 40%. The typical failure modes of GPT-4, the best model, are errors in algebraic manipulation, difficulty in grounding abstract concepts into mathematical equations accurately and failure in retrieving relevant domain-specific concepts. We also observe that by mere prompting, GPT-4 is unable to assess risk introduced by negative marking for incorrect answers. For this, we develop a post-hoc confidence-thresholding method over self-consistency, which enables effective response selection. We hope that our challenging benchmark will guide future re-search in problem-solving using LLMs.

We demonstrate LLM agent specification gaming by instructing models to win against a chess engine. We find reasoning models like o1 preview and DeepSeek-R1 will often hack the benchmark by default, while language models like GPT-4o and Claude 3.5 Sonnet need to be told that normal play won't work to hack. We improve upon prior work like (Hubinger et al., 2024; Meinke et al., 2024; Weij et al., 2024) by using realistic task prompts and avoiding excess nudging. Our results suggest reasoning models may resort to hacking to solve difficult problems, as observed in OpenAI (2024)'s o1 Docker escape during cyber capabilities testing.

Large language models (LLMs) have demonstrated impressive performance on reasoning tasks, including mathematical reasoning. However, the current evaluation mostly focuses on carefully constructed benchmarks and neglects the consideration of real-world reasoning problems that present missing or contradictory conditions, known as ill-defined problems. To further study this problem, we develop a largescale benchmark called Problems with Missing and Contradictory conditions ( PMC) containing over 5,000 validated ill-defined mathematical problems. Our preliminary experiments through PMC reveal two challenges about existing methods: (1) traditional methods exhibit a trade-off between solving accuracy and rejection capabilities, and (2) formal methods struggle with modeling complex problems. To address these challenges, We develop Variable-Constraint Search (VCSEARCH), a trainingfree framework that leverages formal language to detect ill-defined problems, where a variableconstraint pair search strategy is incorporated to improve the modeling capability of formal language. Extensive experiments demonstrate that VCSEARCH improves the accuracy of identifying unsolvable problems by at least 12% across different LLMs, thus achieving stronger robust mathematical reasoning ability.

Critiques are important for enhancing the performance of Large Language Models (LLMs), enabling both self-improvement and constructive feedback for others by identifying flaws and suggesting improvements. However, evaluating the critique capabilities of LLMs presents a significant challenge due to the open-ended nature of the task. In this work, we introduce a new benchmark designed to assess the critique capabilities of LLMs. Unlike existing benchmarks, which typically function in an open-loop fashion, our approach employs a closed-loop methodology that evaluates the quality of corrections generated from critiques. Moreover, the benchmark incorporates features such as self-critique, cross-critique, and iterative critique, which are crucial for distinguishing the abilities of advanced reasoning models from more classical ones. We implement this benchmark using eight challenging reasoning tasks. We have several interesting findings. First, despite demonstrating comparable performance in direct chain-of-thought generation, classical LLMs significantly lag behind the advanced reasoning-based model o1-mini across all critique scenarios. Second, in self-critique and iterative critique settings, classical LLMs may even underperform relative to their baseline capabilities. We hope that this benchmark will serve as a valuable resource to guide future advancements. The code and data are available at https://github.com/tangzhy/RealCritic.

Large language models (LLMs) have recently shown strong performance on mathematical benchmarks. At the same time, they are prone to hallucination and sycophancy, often providing convincing but flawed proofs for incorrect mathematical statements provided by users. This significantly limits the applicability of LLMs in theorem proving, as verification of these flawed proofs must be done manually by expert mathematicians. However, existing benchmarks that measure sycophancy in mathematics are limited: they focus solely on final-answer problems, rely on very simple and often contaminated datasets, and construct benchmark samples using synthetic modifications that create ill-posed questions rather than well-posed questions that are demonstrably false. To address these issues, we introduce BrokenMath, the first benchmark for evaluating sycophantic behavior in LLMs within the context of natural language theorem proving. BrokenMath is built from advanced 2025 competition problems, which are perturbed with an LLM to produce false statements and subsequently refined through expert review. Using an LLM-as-a-judge framework, we evaluate state-of-the-art LLMs and agentic systems and find that sycophancy is widespread, with the best model, GPT-5, producing sycophantic answers 29% of the time. We further investigate several mitigation strategies, including test-time interventions and supervised fine-tuning on curated sycophantic examples. These approaches substantially reduce, but do not eliminate, sycophantic behavior.

Evaluation of reasoning language models gained importance after it was observed that they can combine their existing capabilities into novel traces of intermediate steps before task completion and that the traces can sometimes help them to generalize better than past models. As reasoning becomes the next scaling dimension of large language models, careful study of their capabilities in critical tasks is needed. We show that better performance is not always caused by test-time algorithmic improvements or model sizes but also by using impactful benchmarks as curricula for learning. We call this benchmark-driven selection of AI and show its effects on DeepSeek-R1 using our sequential decision-making problem from Humanity's Last Exam. Steering development of AI by impactful benchmarks trades evaluation for learning and makes novelty of test tasks key for measuring generalization capabilities of reasoning models. Consequently, some benchmarks could be seen as curricula for training rather than unseen test sets.

We examine the reasoning and planning capabilities of large language models (LLMs) in solving complex tasks. Recent advances in inference-time techniques demonstrate the potential to enhance LLM reasoning without additional training by exploring intermediate steps during inference. Notably, OpenAI's o1 model shows promising performance through its novel use of multi-step reasoning and verification. Here, we explore how scaling inference-time techniques can improve reasoning and planning, focusing on understanding the tradeoff between computational cost and performance. To this end, we construct a comprehensive benchmark, known as Sys2Bench, and perform extensive experiments evaluating existing inference-time techniques on eleven diverse tasks across five categories, including arithmetic reasoning, logical reasoning, common sense reasoning, algorithmic reasoning, and planning. Our findings indicate that simply scaling inference-time computation has limitations, as no single inference-time technique consistently performs well across all reasoning and planning tasks.

Large Multimodal Models (LMMs) have demonstrated impressive capabilities across a wide range of multimodal tasks, achieving ever-increasing performance on various evaluation benchmarks. However, existing benchmarks are typically static and often overlap with pre-training datasets, leading to fixed complexity constraints and substantial data contamination issues. Meanwhile, manually annotated datasets are labor-intensive, time-consuming, and subject to human bias and inconsistency, leading to reliability and reproducibility issues. To address these problems, we propose a fully dynamic multimodal evaluation framework, named Open-ended Visual Puzzle Generation (OVPG), which aims to generate fresh, diverse, and verifiable evaluation data automatically in puzzle-solving tasks. Specifically, the OVPG pipeline consists of a raw material sampling module, a visual content generation module, and a puzzle rule design module, which ensures that each evaluation instance is primitive, highly randomized, and uniquely solvable, enabling continual adaptation to the evolving capabilities of LMMs. Built upon OVPG, we construct PuzzleBench, a dynamic and scalable benchmark comprising 11,840 VQA samples. It features six carefully designed puzzle tasks targeting three core LMM competencies, visual recognition, logical reasoning, and context understanding. PuzzleBench differs from static benchmarks that quickly become outdated. It enables ongoing dataset refreshing through OVPG and a rich set of open-ended puzzle designs, allowing seamless adaptation to the evolving capabilities of LMMs.

As the mathematical capabilities of large language models (LLMs) improve, it becomes increasingly important to evaluate their performance on research-level tasks at the frontier of mathematical knowledge. However, existing benchmarks are limited, as they focus solely on final-answer questions or high-school competition problems. To address this gap, we introduce IMProofBench, a private benchmark consisting of 39 peer-reviewed problems developed by expert mathematicians. Each problem requires a detailed proof and is paired with subproblems that have final answers, supporting both an evaluation of mathematical reasoning capabilities by human experts and a large-scale quantitative analysis through automated grading. Furthermore, unlike prior benchmarks, the evaluation setup simulates a realistic research environment: models operate in an agentic framework with tools like web search for literature review and mathematical software such as SageMath. Our results show that current LLMs can succeed at the more accessible research-level questions, but still encounter significant difficulties on more challenging problems. Quantitatively, Grok-4 achieves the highest accuracy of 52% on final-answer subproblems, while GPT-5 obtains the best performance for proof generation, achieving a fully correct solution for 22% of problems. IMProofBench will continue to evolve as a dynamic benchmark in collaboration with the mathematical community, ensuring its relevance for evaluating the next generation of LLMs.

Large reasoning models (LRMs) have exhibited the capacity of enhancing reasoning performance via internal test-time scaling. Building upon this, a promising direction is to further scale test-time compute to unlock even greater reasoning capabilities. However, as we push these scaling boundaries, systematically understanding the practical limits and achieving optimal resource allocation becomes a critical challenge. In this paper, we investigate the scaling Pareto of test-time scaling and introduce the Test-Time Scaling Performance Model (TTSPM). We theoretically analyze two fundamental paradigms for such extended scaling, parallel scaling and sequential scaling, from a probabilistic modeling perspective. Our primary contribution is the derivation of the saturation point on the scaling budget for both strategies, identifying thresholds beyond which additional computation yields diminishing returns. Remarkably, despite their distinct mechanisms, both paradigms converge to a unified mathematical structure in their upper bounds. We empirically validate our theoretical findings on challenging reasoning benchmarks, including AIME, MATH-500, and GPQA, demonstrating the practical utility of these bounds for test-time resource allocation. We hope that this work provides insights into the cost-benefit trade-offs of test-time scaling, guiding the development of more resource-efficient inference strategies for large reasoning models.

Commonsense reasoning often involves evaluating multiple plausible interpretations rather than selecting a single atomic answer, yet most benchmarks rely on single-label evaluation, obscuring whether statements are jointly plausible, mutually exclusive, or jointly implausible. We introduce LOGICAL-COMMONSENSEQA, a benchmark that re-frames commonsense reasoning as logical composition over pairs of atomic statements using plausibility-level operators (AND, OR, NEITHER/NOR). Evaluating instruction-tuned, reasoning-specialized, and fine-tuned models under zero-shot, few-shot, and chain-of-thought prompting, we find that while models perform reasonably on conjunctive and moderately on disjunctive reasoning, performance degrades sharply on negation-based questions. LOGICAL-COMMONSENSEQA exposes fundamental reasoning limitations and provides a controlled framework for advancing compositional commonsense reasoning.

Recent advances in large reasoning language models (LRLMs) rely on test-time scaling, which extends long chain-of-thought (CoT) generation to solve complex tasks. However, overthinking in long CoT not only slows down the efficiency of problem solving, but also risks accuracy loss due to the extremely detailed or redundant reasoning steps. We propose a simple yet effective method that allows LLMs to self-truncate CoT sequences by early exit during generation. Instead of relying on fixed heuristics, the proposed method monitors model behavior at potential reasoning transition points (e.g.,"Wait" tokens) and dynamically terminates the next reasoning chain's generation when the model exhibits high confidence in a trial answer. Our method requires no additional training and can be seamlessly integrated into existing o1-like reasoning LLMs. Experiments on 10 reasoning benchmarks (e.g., GSM8K, MATH-500, AMC, GPQA, AIME and LiveCodeBench) show that the proposed method is consistently effective on 11 cutting-edge reasoning LLMs of varying series and sizes, reducing the length of CoT sequences by an average of 19.1% to 80.1% while improving accuracy by 0.3% to 5.0%.

Large language models (LLMs) have transformed code generation, yet their application in hardware design produces gate counts 38\%--1075\% higher than human designs. We present CircuitMind, a multi-agent framework that achieves human-competitive efficiency through three key innovations: syntax locking (constraining generation to basic logic gates), retrieval-augmented generation (enabling knowledge-driven design), and dual-reward optimization (balancing correctness with efficiency). To evaluate our approach, we introduce TC-Bench, the first gate-level benchmark harnessing collective intelligence from the TuringComplete ecosystem -- a competitive circuit design platform with hundreds of thousands of players. Experiments show CircuitMind enables 55.6\% of model implementations to match or exceed top-tier human experts in composite efficiency metrics. Most remarkably, our framework elevates the 14B Phi-4 model to outperform both GPT-4o mini and Gemini 2.0 Flash, achieving efficiency comparable to the top 25\% of human experts without requiring specialized training. These innovations establish a new paradigm for hardware optimization where collaborative AI systems leverage collective human expertise to achieve optimal circuit designs. Our model, data, and code are open-source at https://github.com/BUAA-CLab/CircuitMind.

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.

Recent Large Reasoning Models (LRMs) have achieved remarkable progress on task-specific benchmarks, yet their evaluation methods remain constrained by isolated problem-solving paradigms. Existing benchmarks predominantly assess single-question reasoning through sequential testing, resulting critical limitations: (1) vulnerability to data contamination and less challenging (e.g., DeepSeek-R1 achieves 97.0% on MATH500), forcing costly and perpetual creation of new questions with large human efforts, (2) failure to evaluate models under multi-context pressure, a key requirement for real-world deployment. To bridge this gap, we present REST (Reasoning Evaluation through Simultaneous Testing), a stress-testing framework that concurrently exposes LRMs to multiple problems simultaneously. Beyond basic reasoning, REST specifically evaluates several under-tested capabilities: contextual priority allocation, cross-problem interference resistance, and dynamic cognitive load management. Our evaluation reveals several striking findings: Even state-of-the-art (SOTA) models like DeepSeek-R1 exhibit substantial performance degradation under stress testing. Crucially, REST demonstrates stronger discriminative power than existing benchmarks, revealing pronounced performance differences among models that exhibit similar, near-ceiling performance under single-question evaluations. Some key mechanistic insights emerge from our analysis: (1) the "overthinking trap" is a critical factor contributing to the performance degradation; (2) the models trained with "long2short" technique preserve more accuracy of their single-problem performance under REST, outperforming standard-trained counterparts. These results establish REST as a cost-efficient, future-proof evaluation paradigm that better reflects real-world reasoning demands while reducing reliance on continuous human annotation.

Recent advancements in large language models (LLMs) have led to significant breakthroughs in mathematical reasoning capabilities. However, existing benchmarks like GSM8K or MATH are now being solved with high accuracy (e.g., OpenAI o1 achieves 94.8% on MATH dataset), indicating their inadequacy for truly challenging these models. To bridge this gap, we propose a comprehensive and challenging benchmark specifically designed to assess LLMs' mathematical reasoning at the Olympiad level. Unlike existing Olympiad-related benchmarks, our dataset focuses exclusively on mathematics and comprises a vast collection of 4428 competition-level problems with rigorous human annotation. These problems are meticulously categorized into over 33 sub-domains and span more than 10 distinct difficulty levels, enabling a holistic assessment of model performance in Olympiad-mathematical reasoning. Furthermore, we conducted an in-depth analysis based on this benchmark. Our experimental results show that even the most advanced models, OpenAI o1-mini and OpenAI o1-preview, struggle with highly challenging Olympiad-level problems, with 60.54% and 52.55% accuracy, highlighting significant challenges in Olympiad-level mathematical reasoning.

With the advancement of powerful large-scale reasoning models, effectively evaluating the reasoning capabilities of these models has become increasingly important. However, existing benchmarks designed to assess the reasoning abilities of large models tend to be limited in scope and lack the flexibility to adapt their difficulty according to the evolving reasoning capacities of the models. To address this, we propose MorphoBench, a benchmark that incorporates multidisciplinary questions to evaluate the reasoning capabilities of large models and can adjust and update question difficulty based on the reasoning abilities of advanced models. Specifically, we curate the benchmark by selecting and collecting complex reasoning questions from existing benchmarks and sources such as Olympiad-level competitions. Additionally, MorphoBench adaptively modifies the analytical challenge of questions by leveraging key statements generated during the model's reasoning process. Furthermore, it includes questions generated using simulation software, enabling dynamic adjustment of benchmark difficulty with minimal resource consumption. We have gathered over 1,300 test questions and iteratively adjusted the difficulty of MorphoBench based on the reasoning capabilities of models such as o3 and GPT-5. MorphoBench enhances the comprehensiveness and validity of model reasoning evaluation, providing reliable guidance for improving both the reasoning abilities and scientific robustness of large models. The code has been released in https://github.com/OpenDCAI/MorphoBench.

Achieving human-level intelligence requires refining the transition from the fast, intuitive System 1 to the slower, more deliberate System 2 reasoning. While System 1 excels in quick, heuristic decisions, System 2 relies on logical reasoning for more accurate judgments and reduced biases. Foundational Large Language Models (LLMs) excel at fast decision-making but lack the depth for complex reasoning, as they have not yet fully embraced the step-by-step analysis characteristic of true System 2 thinking. Recently, reasoning LLMs like OpenAI's o1/o3 and DeepSeek's R1 have demonstrated expert-level performance in fields such as mathematics and coding, closely mimicking the deliberate reasoning of System 2 and showcasing human-like cognitive abilities. This survey begins with a brief overview of the progress in foundational LLMs and the early development of System 2 technologies, exploring how their combination has paved the way for reasoning LLMs. Next, we discuss how to construct reasoning LLMs, analyzing their features, the core methods enabling advanced reasoning, and the evolution of various reasoning LLMs. Additionally, we provide an overview of reasoning benchmarks, offering an in-depth comparison of the performance of representative reasoning LLMs. Finally, we explore promising directions for advancing reasoning LLMs and maintain a real-time https://github.com/zzli2022/Awesome-Slow-Reason-System{GitHub Repository} to track the latest developments. We hope this survey will serve as a valuable resource to inspire innovation and drive progress in this rapidly evolving field.

Creative problem-solving requires combining multiple cognitive abilities, including logical reasoning, lateral thinking, analogy-making, and commonsense knowledge, to discover insights that connect seemingly unrelated pieces of information. However, most existing benchmarks for large language models (LLMs) evaluate only specific components of this process. Moreover, many creativity-oriented benchmarks rely on artificially constructed brainteasers or contrived scenarios that do not reflect how creative problem-solving occurs in real-world settings. To address this gap, we introduce CresOWLve, a benchmark for evaluating creative problem-solving using puzzles grounded in real-world knowledge. Problems in CresOWLve require employing multiple creative thinking strategies, retrieving facts from diverse domains, and creatively combining them to arrive at a solution. Evaluating several frontier non-thinking and thinking LLMs, we show that CresOWLve remains highly challenging. Our analysis reveals a consistent performance gap: models perform substantially better on factual questions than on creative ones (up to a -17% drop). While models can often retrieve the relevant knowledge, they struggle to form the non-obvious creative connections required to integrate this information and arrive at the correct answer.

Code benchmarks such as HumanEval are widely adopted to evaluate Large Language Models' (LLMs) coding capabilities. However, there is an unignorable programming language bias in existing code benchmarks -- over 95% code generation benchmarks are dominated by Python, leaving the LLMs' capabilities in other programming languages such as Java and C/C++ unknown. Moreover, coding task bias is also crucial. Most benchmarks focus on code generation capability, while benchmarks for code reasoning (given input, reasoning output; and given output, reasoning input), an essential coding capability, are insufficient. Yet, constructing multi-lingual benchmarks can be expensive and labor-intensive, and codes in contest websites such as Leetcode suffer from data contamination during training. To fill this gap, we propose CRUXEVAL-X, a multi-lingual code reasoning benchmark that contains 19 programming languages. It comprises at least 600 subjects for each language, along with 19K content-consistent tests in total. In particular, the construction pipeline of CRUXEVAL-X works in a fully automated and test-guided manner, which iteratively generates and repairs based on execution feedback. Also, to cross language barriers (e.g., dynamic/static type systems in Python/C++), we formulated various transition rules between language pairs to facilitate translation. Our intensive evaluation of 24 representative LLMs reveals the correlation between language pairs. For example, TypeScript and JavaScript show a significant positive correlation, while Racket has less correlation with other languages. More interestingly, even a model trained solely on Python can achieve at most 34.4% Pass@1 in other languages, revealing the cross-language generalization of LLMs.

Among the hardest tasks for humans are those found in competitive programming where problems require sophisticated algorithmic thinking, puzzle solving, and the creation of effective code. As a domain to assess language models (LMs), it has not received enough attention, though. This study presents the ICPC benchmark, which consists of 254 international collegiate programming contest (ICPC) tasks. Each problem includes official analysis, reference code, and sample, high-quality unit, and hidden tests. We are able to develop and evaluate a variety of LM inference techniques for competitive programming with these resources. With zero-shot chain-of-thought prompting, we find that o1 only achieves a 19.1\% pass@1 solve rate. With our best inference technique, which combines multi-turn self-judge with reflection and retrieval over episodic information, raises this to 42.2\%. Furthermore, we conduct a new human-in-the-loop investigation to gain a deeper understanding of the remaining difficulties. Surprisingly, we discover that o1 can solve 17 out of 18 problems that were previously unsolvable by any model or technique with just a few specific instructions. A footstep toward LMs with grounded, imaginative, and algorithmic thinking is provided by our quantitative findings and qualitative research. We open-source our code and data at https://github.com/kraritt/zolve.

Large reasoning models such as OpenAI o1 and DeepSeek-R1 have achieved remarkable performance in the domain of reasoning. A key component of their training is the incorporation of verifiable rewards within reinforcement learning (RL). However, existing reward benchmarks do not evaluate reference-based reward systems, leaving researchers with limited understanding of the accuracy of verifiers used in RL. In this paper, we introduce two benchmarks, VerifyBench and VerifyBench-Hard, designed to assess the performance of reference-based reward systems. These benchmarks are constructed through meticulous data collection and curation, followed by careful human annotation to ensure high quality. Current models still show considerable room for improvement on both VerifyBench and VerifyBench-Hard, especially smaller-scale models. Furthermore, we conduct a thorough and comprehensive analysis of evaluation results, offering insights for understanding and developing reference-based reward systems. Our proposed benchmarks serve as effective tools for guiding the development of verifier accuracy and the reasoning capabilities of models trained via RL in reasoning tasks.

First-order logic (FOL) reasoning, which involves sequential deduction, is pivotal for intelligent systems and serves as a valuable task for evaluating reasoning capabilities, particularly in chain-of-thought (CoT) contexts. Existing benchmarks often rely on extensive human annotation or handcrafted templates, making it difficult to achieve the necessary complexity, scalability, and diversity for robust evaluation. To address these limitations, we propose a novel framework called ProverGen that synergizes the generative strengths of Large Language Models (LLMs) with the rigor and precision of symbolic provers, enabling the creation of a scalable, diverse, and high-quality FOL reasoning dataset, ProverQA. ProverQA is also distinguished by its inclusion of accessible and logically coherent intermediate reasoning steps for each problem. Our evaluation shows that state-of-the-art LLMs struggle to solve ProverQA problems, even with CoT prompting, highlighting the dataset's challenging nature. We also finetune Llama3.1-8B-Instruct on a separate training set generated by our framework. The finetuned model demonstrates consistent improvements on both in-distribution and out-of-distribution test sets, suggesting the value of our proposed data generation framework. Code available at: https://github.com/opendatalab/ProverGen

Automated theorem proving (ATP) benchmarks largely consist of problems formalized in MathLib, so current ATP training and evaluation are heavily biased toward MathLib's definitional framework. However, frontier mathematics is often exploratory and prototype-heavy, relying on bespoke constructions that deviate from standard libraries. In this work, we evaluate the robustness of current ATP systems when applied to a novel definitional framework, specifically examining the performance gap between standard library problems and bespoke mathematical constructions. We introduce TaoBench, an undergraduate-level benchmark derived from Terence Tao's Analysis I, which formalizes analysis by constructing core mathematical concepts from scratch, without relying on standard Mathlib definitions, as well as by mixing from-scratch and MathLib constructions. For fair evaluation, we build an agentic pipeline that automatically extracts a compilable, self-contained local environment for each problem. To isolate the effect of definitional frameworks, we additionally translate every problem into a mathematically equivalent Mathlib formulation, yielding paired TaoBench-Mathlib statements for direct comparison. While state-of-the-art ATP models perform capably within the MathLib framework, performance drops by an average of roughly 26% on the definitionally equivalent Tao formulation. This indicates that the main bottleneck is limited generalization across definitional frameworks rather than task difficulty. TaoBench thus highlights a gap between benchmark performance and applicability, and provides a concrete foundation for developing and testing provers better aligned with research mathematics.

Reasoning stands as a cornerstone of intelligence, enabling the synthesis of existing knowledge to solve complex problems. Despite remarkable progress, existing reasoning benchmarks often fail to rigorously evaluate the nuanced reasoning capabilities required for complex, real-world problemsolving, particularly in multi-disciplinary and multimodal contexts. In this paper, we introduce a graduate-level, multi-disciplinary, EnglishChinese benchmark, dubbed as Reasoning Bench (R-Bench), for assessing the reasoning capability of both language and multimodal models. RBench spans 1,094 questions across 108 subjects for language model evaluation and 665 questions across 83 subjects for multimodal model testing in both English and Chinese. These questions are meticulously curated to ensure rigorous difficulty calibration, subject balance, and crosslinguistic alignment, enabling the assessment to be an Olympiad-level multi-disciplinary benchmark. We evaluate widely used models, including OpenAI o1, GPT-4o, DeepSeek-R1, etc. Experimental results indicate that advanced models perform poorly on complex reasoning, especially multimodal reasoning. Even the top-performing model OpenAI o1 achieves only 53.2% accuracy on our multimodal evaluation. Data and code are made publicly available at here.

Imagine observing someone scratching their arm; to understand why, additional context would be necessary. However, spotting a mosquito nearby would immediately offer a likely explanation for the person's discomfort, thereby alleviating the need for further information. This example illustrates how subtle visual cues can challenge our cognitive skills and demonstrates the complexity of interpreting visual scenarios. To study these skills, we present Visual Riddles, a benchmark aimed to test vision and language models on visual riddles requiring commonsense and world knowledge. The benchmark comprises 400 visual riddles, each featuring a unique image created by a variety of text-to-image models, question, ground-truth answer, textual hint, and attribution. Human evaluation reveals that existing models lag significantly behind human performance, which is at 82\% accuracy, with Gemini-Pro-1.5 leading with 40\% accuracy. Our benchmark comes with automatic evaluation tasks to make assessment scalable. These findings underscore the potential of Visual Riddles as a valuable resource for enhancing vision and language models' capabilities in interpreting complex visual scenarios.

We introduce MathSticks, a benchmark for Visual Symbolic Compositional Reasoning (VSCR), which unifies visual perception, symbolic manipulation, and arithmetic consistency. Each task presents an incorrect matchstick equation that must be corrected by moving one or two sticks under strict conservation rules. The benchmark includes both text-guided and purely visual settings, systematically covering digit scale, move complexity, solution multiplicity, and operator variation, with 1.4M generated instances and a curated test set. Evaluations of 14 vision--language models reveal substantial limitations: closed-source models succeed only on simple cases, open-source models fail in the visual regime, while humans exceed 90\% accuracy. These findings establish MathSticks as a rigorous testbed for advancing compositional reasoning across vision and symbols. Our code and dataset are publicly available at https://github.com/Yuheng2000/MathSticks.

Grasping the concept of time is a fundamental facet of human cognition, indispensable for truly comprehending the intricacies of the world. Previous studies typically focus on specific aspects of time, lacking a comprehensive temporal reasoning benchmark. To address this, we propose TimeBench, a comprehensive hierarchical temporal reasoning benchmark that covers a broad spectrum of temporal reasoning phenomena. TimeBench provides a thorough evaluation for investigating the temporal reasoning capabilities of large language models. We conduct extensive experiments on GPT-4, LLaMA2, and other popular LLMs under various settings. Our experimental results indicate a significant performance gap between the state-of-the-art LLMs and humans, highlighting that there is still a considerable distance to cover in temporal reasoning. Besides, LLMs exhibit capability discrepancies across different reasoning categories. Furthermore, we thoroughly analyze the impact of multiple aspects on temporal reasoning and emphasize the associated challenges. We aspire for TimeBench to serve as a comprehensive benchmark, fostering research in temporal reasoning. Resources are available at: https://github.com/zchuz/TimeBench

We present miniF2F, a dataset of formal Olympiad-level mathematics problems statements intended to provide a unified cross-system benchmark for neural theorem proving. The miniF2F benchmark currently targets Metamath, Lean, Isabelle (partially) and HOL Light (partially) and consists of 488 problem statements drawn from the AIME, AMC, and the International Mathematical Olympiad (IMO), as well as material from high-school and undergraduate mathematics courses. We report baseline results using GPT-f, a neural theorem prover based on GPT-3 and provide an analysis of its performance. We intend for miniF2F to be a community-driven effort and hope that our benchmark will help spur advances in neural theorem proving.

How well do AI systems perform in algorithm engineering for hard optimization problems in domains such as package-delivery routing, crew scheduling, factory production planning, and power-grid balancing? We introduce ALE-Bench, a new benchmark for evaluating AI systems on score-based algorithmic programming contests. Drawing on real tasks from the AtCoder Heuristic Contests, ALE-Bench presents optimization problems that are computationally hard and admit no known exact solution. Unlike short-duration, pass/fail coding benchmarks, ALE-Bench encourages iterative solution refinement over long time horizons. Our software framework supports interactive agent architectures that leverage test-run feedback and visualizations. Our evaluation of frontier LLMs revealed that while they demonstrate high performance on specific problems, a notable gap remains compared to humans in terms of consistency across problems and long-horizon problem-solving capabilities. This highlights the need for this benchmark to foster future AI advancements.

Large reasoning models (LRMs) have achieved impressive performance in complex tasks, often outperforming conventional large language models (LLMs). However, the prevalent issue of overthinking severely limits their computational efficiency. Overthinking occurs when models generate excessive and redundant tokens that contribute little to accurate outcomes, especially in simple tasks, resulting in a significant waste of computational resources. To systematically investigate this issue, we introduce Think-Bench, a benchmark designed to evaluate the reasoning efficiency of LRMs. We also propose novel efficiency metrics and conduct a comprehensive evaluation of various LRMs across multiple dimensions, including the reasoning process, outcome quality, and chain-of-thought (CoT) characteristics. Our analysis reveals that most LRMs exhibit overthinking in handling easy questions, generating unnecessarily lengthy reasoning chains. While many LRMs demonstrate high CoT quality, several suffer from low efficiency. We hope that Think-Bench can serve as a robust foundation for advancing research into LRMs.

Recent progress in o1-like models has significantly enhanced the reasoning abilities of Large Language Models (LLMs), empowering them to tackle increasingly complex tasks through reflection capabilities, such as making assumptions, backtracking, and self-refinement. However, effectively evaluating such reflection capabilities remains challenging due to the lack of appropriate benchmarks. To bridge this gap, we introduce LR^2Bench, a novel benchmark designed to evaluate the Long-chain Reflective Reasoning capabilities of LLMs. LR^2Bench comprises 850 samples across six Constraint Satisfaction Problems (CSPs) where reflective reasoning is crucial for deriving solutions that meet all given constraints. Each type of task focuses on distinct constraint patterns, such as knowledge-based, logical, and spatial constraints, providing a comprehensive evaluation of diverse problem-solving scenarios. We conduct extensive evaluation on both conventional models and o1-like models. Our experimental results reveal that even the most advanced reasoning-specific models, such as DeepSeek-R1 and OpenAI o1-preview, struggle with tasks in LR^2Bench, achieving an average Exact Match score of only 20.0% and 23.6%, respectively. These findings underscore the significant room for improvement in the reflective reasoning capabilities of current LLMs. The leaderboard of our benchmark is available at https://huggingface.co/spaces/UltraRonin/LR2Bench

The rapid escalation from elementary school-level to frontier problems of the difficulty for LLM benchmarks in recent years have weaved a miracle for researchers that we are only inches away from surpassing human intelligence. However, is the LLMs' remarkable reasoning ability indeed comes from true intelligence by human standards, or are they simply reciting solutions witnessed during training at an Internet level? To study this problem, we propose RoR-Bench, a novel, multi-modal benchmark for detecting LLM's recitation behavior when asked simple reasoning problems but with conditions subtly shifted, and conduct empirical analysis on our benchmark. Surprisingly, we found existing cutting-edge LLMs unanimously exhibits extremely severe recitation behavior; by changing one phrase in the condition, top models such as OpenAI-o1 and DeepSeek-R1 can suffer 60% performance loss on elementary school-level arithmetic and reasoning problems. Such findings are a wake-up call to the LLM community that compels us to re-evaluate the true intelligence level of cutting-edge LLMs.

While Large Language Models (LLMs) have demonstrated significant advancements in reasoning and agent-based problem-solving, current evaluation methodologies fail to adequately assess their capabilities: existing benchmarks either rely on closed-ended questions prone to saturation and memorization, or subjective comparisons that lack consistency and rigor. In this work, we introduce HeuriGym, an agentic framework designed for evaluating heuristic algorithms generated by LLMs for combinatorial optimization problems, characterized by clearly defined objectives and expansive solution spaces. HeuriGym empowers LLMs to propose heuristics, receive evaluative feedback via code execution, and iteratively refine their solutions. We evaluate nine state-of-the-art models on nine problems across domains such as computer systems, logistics, and biology, exposing persistent limitations in tool use, planning, and adaptive reasoning. To quantify performance, we propose the Quality-Yield Index (QYI), a metric that captures both solution pass rate and quality. Even top models like GPT-o4-mini-high and Gemini-2.5-Pro attain QYI scores of only 0.6, well below the expert baseline of 1. Our open-source benchmark aims to guide the development of LLMs toward more effective and realistic problem-solving in scientific and engineering domains.

In this paper, we introduce a combination of novel and exciting tasks: the solution and generation of linguistic puzzles. We focus on puzzles used in Linguistic Olympiads for high school students. We first extend the existing benchmark for the task of solving linguistic puzzles. We explore the use of Large Language Models (LLMs), including recent state-of-the-art models such as OpenAI's o1, for solving linguistic puzzles, analyzing their performance across various linguistic topics. We demonstrate that LLMs outperform humans on most puzzles types, except for those centered on writing systems, and for the understudied languages. We use the insights from puzzle-solving experiments to direct the novel task of puzzle generation. We believe that automating puzzle generation, even for relatively simple puzzles, holds promise for expanding interest in linguistics and introducing the field to a broader audience. This finding highlights the importance of linguistic puzzle generation as a research task: such puzzles can not only promote linguistics but also support the dissemination of knowledge about rare and understudied languages.

In this paper, we aim to establish a simple, effective, and theoretically grounded benchmark for rigorously probing abstract reasoning in Large Language Models (LLMs). To achieve this, we first develop a mathematic framework that defines abstract reasoning as the ability to: (i) extract essential patterns independent of surface representations, and (ii) apply consistent rules to these abstract patterns. Based on this framework, we introduce two novel complementary metrics: \(\scoreGamma\) measures basic reasoning accuracy, while \(\scoreDelta\) quantifies a model's reliance on specific symbols rather than underlying patterns - a key indicator of true abstraction versus mere memorization. To implement this measurement, we design a benchmark: systematic symbol remapping in rule-based tasks, which forces models to demonstrate genuine pattern recognition beyond superficial token matching. Extensive LLM evaluations using this benchmark (commercial API models, 7B-70B, multi-agent) reveal:1) critical limitations in non-decimal arithmetic and symbolic reasoning; 2) persistent abstraction gaps despite chain-of-thought prompting; and 3) \(\scoreDelta\)'s effectiveness in robustly measuring memory dependence by quantifying performance degradation under symbol remapping, particularly highlighting operand-specific memorization. These findings underscore that current LLMs, despite domain-specific strengths, still lack robust abstract reasoning, highlighting key areas for future improvement.

Neurosymbolic approaches integrating large language models with formal reasoning have recently achieved human-level performance on mathematics competition problems in algebra, geometry and number theory. In comparison, combinatorics remains a challenging domain, characterized by a lack of appropriate benchmarks and theorem libraries. To address this gap, we introduce CombiBench, a comprehensive benchmark comprising 100 combinatorial problems, each formalized in Lean~4 and paired with its corresponding informal statement. The problem set covers a wide spectrum of difficulty levels, ranging from middle school to IMO and university level, and span over ten combinatorial topics. CombiBench is suitable for testing IMO solving capabilities since it includes all IMO combinatorial problems since 2000 (except IMO 2004 P3 as its statement contain an images). Furthermore, we provide a comprehensive and standardized evaluation framework, dubbed Fine-Eval (for Fill-in-the-blank in Lean Evaluation), for formal mathematics. It accommodates not only proof-based problems but also, for the first time, the evaluation of fill-in-the-blank questions. Using Fine-Eval as the evaluation method and Kimina Lean Server as the backend, we benchmark several LLMs on CombiBench and observe that their capabilities for formally solving combinatorial problems remain limited. Among all models tested (none of which has been trained for this particular task), Kimina-Prover attains the best results, solving 7 problems (out of 100) under both ``with solution'' and ``without solution'' scenarios. We open source the benchmark dataset alongside with the code of the proposed evaluation method at https://github.com/MoonshotAI/CombiBench/.

Large language models (LLMs) have achieved impressive success on many benchmarks for mathematical reasoning. However, there is growing concern that some of this performance actually reflects dataset contamination, where data closely resembling benchmark questions leaks into the training data, instead of true reasoning ability. To investigate this claim rigorously, we commission Grade School Math 1000 (GSM1k). GSM1k is designed to mirror the style and complexity of the established GSM8k benchmark, the gold standard for measuring elementary mathematical reasoning. We ensure that the two benchmarks are comparable across important metrics such as human solve rates, number of steps in solution, answer magnitude, and more. When evaluating leading open- and closed-source LLMs on GSM1k, we observe accuracy drops of up to 13%, with several families of models (e.g., Phi and Mistral) showing evidence of systematic overfitting across almost all model sizes. At the same time, many models, especially those on the frontier, (e.g., Gemini/GPT/Claude) show minimal signs of overfitting. Further analysis suggests a positive relationship (Spearman's r^2=0.32) between a model's probability of generating an example from GSM8k and its performance gap between GSM8k and GSM1k, suggesting that many models may have partially memorized GSM8k.

While Large Language Models (LLMs) have demonstrated proficiency in handling complex queries, much of the past work has depended on extensively annotated datasets by human experts. However, this reliance on fully-supervised annotations poses scalability challenges, particularly as models and data requirements grow. To mitigate this, we explore the potential of enhancing LLMs' reasoning abilities with minimal human supervision. In this work, we introduce self-reinforcement, which begins with Supervised Fine-Tuning (SFT) of the model using a small collection of annotated questions. Then it iteratively improves LLMs by learning from the differences in responses from the SFT and unfinetuned models on unlabeled questions. Our approach provides an efficient approach without relying heavily on extensive human-annotated explanations. However, current reasoning benchmarks typically only include golden-reference answers or rationales. Therefore, we present PuzzleBen, a weakly supervised benchmark that comprises 25,147 complex questions, answers, and human-generated rationales across various domains, such as brainteasers, puzzles, riddles, parajumbles, and critical reasoning tasks. A unique aspect of our dataset is the inclusion of 10,000 unannotated questions, enabling us to explore utilizing fewer supersized data to boost LLMs' inference capabilities. Our experiments underscore the significance of PuzzleBen, as well as the effectiveness of our methodology as a promising direction in future endeavors. Our dataset and code will be published soon on Anonymity Link.

Large language models demonstrate remarkable capabilities across various domains, especially mathematics and logic reasoning. However, current evaluations overlook physics-based reasoning - a complex task requiring physics theorems and constraints. We present PhysReason, a 1,200-problem benchmark comprising knowledge-based (25%) and reasoning-based (75%) problems, where the latter are divided into three difficulty levels (easy, medium, hard). Notably, problems require an average of 8.1 solution steps, with hard requiring 15.6, reflecting the complexity of physics-based reasoning. We propose the Physics Solution Auto Scoring Framework, incorporating efficient answer-level and comprehensive step-level evaluations. Top-performing models like Deepseek-R1, Gemini-2.0-Flash-Thinking, and o3-mini-high achieve less than 60% on answer-level evaluation, with performance dropping from knowledge questions (75.11%) to hard problems (31.95%). Through step-level evaluation, we identified four key bottlenecks: Physics Theorem Application, Physics Process Understanding, Calculation, and Physics Condition Analysis. These findings position PhysReason as a novel and comprehensive benchmark for evaluating physics-based reasoning capabilities in large language models. Our code and data will be published at https:/dxzxy12138.github.io/PhysReason.

We introduce FloorplanQA, a diagnostic benchmark for evaluating spatial reasoning in large-language models (LLMs). FloorplanQA is grounded in structured representations of indoor scenes, such as (e.g., kitchens, living rooms, bedrooms, bathrooms, and others), encoded symbolically in JSON or XML layouts. The benchmark covers core spatial tasks, including distance measurement, visibility, path finding, and object placement within constrained spaces. Our results across a variety of frontier open-source and commercial LLMs reveal that while models may succeed in shallow queries, they often fail to respect physical constraints, preserve spatial coherence, though they remain mostly robust to small spatial perturbations. FloorplanQA uncovers a blind spot in today's LLMs: inconsistent reasoning about indoor layouts. We hope this benchmark inspires new work on language models that can accurately infer and manipulate spatial and geometric properties in practical settings.

Large Language Models (LLMs) trained via Reinforcement Learning (RL) have recently achieved impressive results on reasoning benchmarks. Yet, growing evidence shows that these models often generate longer but ineffective chains of thought (CoTs), calling into question whether benchmark gains reflect real reasoning improvements. We present new evidence of overthinking, where models disregard correct solutions even when explicitly provided, instead continuing to generate unnecessary reasoning steps that often lead to incorrect conclusions. Experiments on three state-of-the-art models using the AIME2024 math benchmark reveal critical limitations in these models ability to integrate corrective information, posing new challenges for achieving robust and interpretable reasoning.

Code verification has recently found great success as a critical component in training large scale reasoning models for coding. Synthetic techniques such as self-generated test cases and reward models provide a way to enhance code capabilities beyond predefined tests. Building on these advancements, we propose new benchmarks designed to systematically evaluate the impact of synthetic verification methods on assessing solution correctness. We introduce HE-R, HE-R+, MBPP-R, and MBPP-R+, which transform existing coding benchmarks into scoring and ranking datasets to evaluate the effectiveness of synthetic verifiers. Using these benchmarks, we analyze synthetic verification methods in standard, reasoning-based, and reward-based LLMs. Our results show that recent reasoning models significantly improve test case generation and that scaling test cases enhances verification accuracy.

We conduct a systematic audit of three widely used reasoning benchmarks, SocialIQa, FauxPas-EAI, and ToMi, and uncover pervasive flaws in both benchmark items and evaluation methodology. Using five LLMs (GPT-{3, 3.5, 4, o1}, and LLaMA 3.1) as diagnostic tools, we identify structural, semantic, and pragmatic issues in benchmark design (e.g., duplicated items, ambiguous wording, and implausible answers), as well as scoring procedures that prioritize output form over reasoning process. Through systematic human annotation and re-evaluation on cleaned benchmark subsets, we find that model scores often improve not due to due to erratic surface wording variations and not to improved reasoning. Infact, further analyses show that model performance is highly sensitive to minor input variations such as context availability and phrasing, revealing that high scores may reflect alignment with format-specific cues rather than consistent inference based on the input. These findings challenge the validity of current benchmark-based claims about reasoning in LLMs, and highlight the need for evaluation protocols that assess reasoning as a process of drawing inference from available information, rather than as static output selection. We release audited data and evaluation tools to support more interpretable and diagnostic assessments of model reasoning.

LLMs and Agents have achieved impressive progress in code generation, mathematical reasoning, and scientific discovery. However, existing benchmarks primarily measure correctness, overlooking the diversity of methods behind solutions. True innovation depends not only on producing correct answers but also on the originality of the approach. We present InnoGym, the first benchmark and framework designed to systematically evaluate the innovation potential of AI agents. InnoGym introduces two complementary metrics: performance gain, which measures improvement over the best-known solutions, and novelty, which captures methodological differences from prior approaches. The benchmark includes 18 carefully curated tasks from real-world engineering and scientific domains, each standardized through resource filtering, evaluator validation, and solution collection. In addition, we provide iGym, a unified execution environment for reproducible and long-horizon evaluations. Extensive experiments show that while some agents produce novel approaches, their lack of robustness limits performance gains. These results highlight a key gap between creativity and effectiveness, underscoring the need for benchmarks that evaluate both.

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.

Investigating the reasoning abilities of transformer models, and discovering new challenging tasks for them, has been a topic of much interest. Recent studies have found these models to be surprisingly strong at performing deductive reasoning over formal logical theories expressed in natural language. A shortcoming of these studies, however, is that they do not take into account that logical theories, when sampled uniformly at random, do not necessarily lead to hard instances. We propose a new methodology for creating challenging algorithmic reasoning datasets that focus on natural language satisfiability (NLSat) problems. The key idea is to draw insights from empirical sampling of hard propositional SAT problems and from complexity-theoretic studies of language. This methodology allows us to distinguish easy from hard instances, and to systematically increase the complexity of existing reasoning benchmarks such as RuleTaker. We find that current transformers, given sufficient training data, are surprisingly robust at solving the resulting NLSat problems of substantially increased difficulty. They also exhibit some degree of scale-invariance - the ability to generalize to problems of larger size and scope. Our results, however, reveal important limitations too: a careful sampling of training data is crucial for building models that generalize to larger problems, and transformer models' limited scale-invariance suggests they are far from learning robust deductive reasoning algorithms.

Automated Theorem Proving (ATP) in formal languages is a foundational challenge for AI. While Large Language Models (LLMs) have driven remarkable progress, a significant gap remains between their powerful informal reasoning capabilities and their weak formal proving performance. Recent studies show that the informal accuracy exceeds 80% while formal success remains below 8% on benchmarks like PutnamBench. We argue this gap persists because current state-of-the-art provers, by tightly coupling reasoning and proving, are trained with paradigms that inadvertently punish deep reasoning in favor of shallow, tactic-based strategies. To bridge this fundamental gap, we propose a novel framework that decouples high-level reasoning from low-level proof generation. Our approach utilizes two distinct, specialized models: a powerful, general-purpose Reasoner to generate diverse, strategic subgoal lemmas, and an efficient Prover to rigorously verify them. This modular design liberates the model's full reasoning potential and bypasses the pitfalls of end-to-end training. We evaluate our method on a challenging set of post-2000 IMO problems, a problem set on which no prior open-source prover has reported success. Our decoupled framework successfully solves 5 of these problems, demonstrating a significant step towards automated reasoning on exceptionally difficult mathematical challenges. To foster future research, we release our full dataset of generated and verified lemmas for a wide range of IMO problems, available at https://tencent-imo.github.io/ .