Daily Papers

Measuring the full abilities of large language models (LLMs) requires benchmarks representing multiple tasks. We aim to create large, high-quality datasets for comparison of logical reasoning skills across several languages and of suitable difficulty for LLMs of various reasoning ability. We explore multiple ways of increasing difficulty. We generate zebra puzzles in multiple languages, themes, sizes and including 14 different clue types and 8 red herring types (uninformative clues). We find puzzle sizes 2x3 and 4x5 are sufficiently challenging for GPT-4o mini (a non-reasoning model) and o3-mini (a reasoning model), respectively. Including 5 red herrings decreases o3-mini puzzle-level accuracy on 4x5 puzzles by 15pm7 %. Scores of o3-mini on 4x5 puzzles are not significantly affected by use of English vs. Danish or the common houses theme vs. the country-specific smoerrebroed theme. We find no correlation between difficulty and the selected clue types. Datasets of 128+1024 puzzles are published as MultiZebraLogic in each of nine Germanic languages for sizes 2x3 and 4x5. We publish code for puzzle generation, designed for adaptablity into more languages and themes.

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.

We explore the ability of large language models to solve and generate puzzles from the NPR Sunday Puzzle game show using PUZZLEQA, a dataset comprising 15 years of on-air puzzles. We evaluate four large language models using PUZZLEQA, in both multiple choice and free response formats, and explore two prompt engineering techniques to improve free response performance: chain-of-thought reasoning and prompt summarization. We find that state-of-the-art large language models can solve many PUZZLEQA puzzles: the best model, GPT-3.5, achieves 50.2% loose accuracy. However, in our few-shot puzzle generation experiment, we find no evidence that models can generate puzzles: GPT-3.5 generates puzzles with answers that do not conform to the generated rules. Puzzle generation remains a challenging task for future work.

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.

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.

Solving grid puzzles involves a significant amount of logical reasoning. Hence, it is a good domain to evaluate the reasoning capability of a model which can then guide us to improve the reasoning ability of models. However, most existing works evaluate only the final predicted answer of a puzzle, without delving into an in-depth analysis of the LLMs' reasoning chains (such as where they falter) or providing any finer metrics to evaluate them. Since LLMs may rely on simple heuristics or artifacts to predict the final answer, it is crucial to evaluate the generated reasoning chain beyond overall correctness measures, for accurately evaluating the reasoning abilities of LLMs. To this end, we first develop GridPuzzle, an evaluation dataset comprising 274 grid-based puzzles with different complexities. Second, we propose a new error taxonomy derived from manual analysis of reasoning chains from LLMs including GPT-4, Claude-3, Gemini, Mistral, and Llama-2. Then, we develop an LLM-based framework for large-scale subjective evaluation (i.e., identifying errors) and an objective metric, PuzzleEval, to evaluate the correctness of reasoning chains. Evaluating reasoning chains from LLMs leads to several interesting findings. We further show that existing prompting methods used for enhancing models' reasoning abilities do not improve performance on GridPuzzle. This highlights the importance of understanding fine-grained errors and presents a challenge for future research to enhance LLMs' puzzle-solving abilities by developing methods that address these errors. Data and source code are available at https://github.com/Mihir3009/GridPuzzle.

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.

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.

Cell type annotation is a key task in analyzing the heterogeneity of single-cell RNA sequencing data. Although recent foundation models automate this process, they typically annotate cells independently, without considering batch-level cellular context or providing explanatory reasoning. In contrast, human experts often annotate distinct cell types for different cell clusters based on their domain knowledge. To mimic this workflow, we introduce the CellPuzzles task, where the objective is to assign unique cell types to a batch of cells. This benchmark spans diverse tissues, diseases, and donor conditions, and requires reasoning across the batch-level cellular context to ensure label uniqueness. We find that off-the-shelf large language models (LLMs) struggle on CellPuzzles, with the best baseline (OpenAI's o1) achieving only 19.0% batch-level accuracy. To fill this gap, we propose Cell-o1, a 7B LLM trained via supervised fine-tuning on distilled reasoning traces, followed by reinforcement learning with batch-level rewards. Cell-o1 achieves state-of-the-art performance, outperforming o1 by over 73% and generalizing well across contexts. Further analysis of training dynamics and reasoning behaviors provides insights into batch-level annotation performance and emergent expert-like reasoning. Code and data are available at https://github.com/ncbi-nlp/cell-o1.

We propose a new benchmark evaluating the performance of multimodal large language models on rebus puzzles. The dataset covers 333 original examples of image-based wordplay, cluing 13 categories such as movies, composers, major cities, and food. To achieve good performance on the benchmark of identifying the clued word or phrase, models must combine image recognition and string manipulation with hypothesis testing, multi-step reasoning, and an understanding of human cognition, making for a complex, multimodal evaluation of capabilities. We find that proprietary models such as GPT-4V and Gemini Pro significantly outperform all other tested models. However, even the best model has a final accuracy of just 24%, highlighting the need for substantial improvements in reasoning. Further, models rarely understand all parts of a puzzle, and are almost always incapable of retroactively explaining the correct answer. Our benchmark can therefore be used to identify major shortcomings in the knowledge and reasoning of multimodal large language models.

This paper introduces the novel task of multimodal puzzle solving, framed within the context of visual question-answering. We present a new dataset, AlgoPuzzleVQA designed to challenge and evaluate the capabilities of multimodal language models in solving algorithmic puzzles that necessitate both visual understanding, language understanding, and complex algorithmic reasoning. We create the puzzles to encompass a diverse array of mathematical and algorithmic topics such as boolean logic, combinatorics, graph theory, optimization, search, etc., aiming to evaluate the gap between visual data interpretation and algorithmic problem-solving skills. The dataset is generated automatically from code authored by humans. All our puzzles have exact solutions that can be found from the algorithm without tedious human calculations. It ensures that our dataset can be scaled up arbitrarily in terms of reasoning complexity and dataset size. Our investigation reveals that large language models (LLMs) such as GPT4V and Gemini exhibit limited performance in puzzle-solving tasks. We find that their performance is near random in a multi-choice question-answering setup for a significant number of puzzles. The findings emphasize the challenges of integrating visual, language, and algorithmic knowledge for solving complex reasoning problems.

Crosswords are a form of word puzzle that require a solver to demonstrate a high degree of proficiency in natural language understanding, wordplay, reasoning, and world knowledge, along with adherence to character and length constraints. In this paper we tackle the challenge of solving crosswords with Large Language Models (LLMs). We demonstrate that the current generation of state-of-the art (SoTA) language models show significant competence at deciphering cryptic crossword clues, and outperform previously reported SoTA results by a factor of 2-3 in relevant benchmarks. We also develop a search algorithm that builds off this performance to tackle the problem of solving full crossword grids with LLMs for the very first time, achieving an accuracy of 93\% on New York Times crossword puzzles. Contrary to previous work in this area which concluded that LLMs lag human expert performance significantly, our research suggests this gap is a lot narrower.

We introduce a new type of programming challenge called programming puzzles, as an objective and comprehensive evaluation of program synthesis, and release an open-source dataset of Python Programming Puzzles (P3). Each puzzle is defined by a short Python program f, and the goal is to find an input which makes f return True. The puzzles are objective in that each one is specified entirely by the source code of its verifier f, so evaluating f is all that is needed to test a candidate solution. They do not require an answer key or input/output examples, nor do they depend on natural language understanding. The dataset is comprehensive in that it spans problems of a range of difficulties and domains, ranging from trivial string manipulation problems, to classic programming puzzles (e.g., Tower of Hanoi), to interview/competitive-programming problems (e.g., dynamic programming), to longstanding open problems in algorithms and mathematics (e.g., factoring). We develop baseline enumerative program synthesis, GPT-3 and Codex solvers that are capable of solving puzzles -- even without access to any reference solutions -- by learning from their own past solutions. Codex performs best, solving up to 18% of 397 test problems with a single try and 80% of the problems with 1,000 tries per problem. In a small user study, we find a positive correlation between puzzle-solving performance and coding experience, and between the puzzle difficulty for humans and AI solvers. Therefore, further improvements on P3 could have a significant impact on many program synthesis areas.

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.

Existing reasoning datasets saturate and fail to test abstract, multi-step problems, especially pathfinding and complex rule constraint satisfaction. We introduce SPaRC (Spatial Pathfinding Reasoning Challenge), a dataset of 1,000 2D grid pathfinding puzzles to evaluate spatial and symbolic reasoning, requiring step-by-step planning with arithmetic and geometric rules. Humans achieve near-perfect accuracy (98.0%; 94.5% on hard puzzles), while the best reasoning models, such as o4-mini, struggle (15.8%; 1.1% on hard puzzles). Models often generate invalid paths (>50% of puzzles for o4-mini), and reasoning tokens reveal they make errors in navigation and spatial logic. Unlike humans, who take longer on hard puzzles, models fail to scale test-time compute with difficulty. Allowing models to make multiple solution attempts improves accuracy, suggesting potential for better spatial reasoning with improved training and efficient test-time scaling methods. SPaRC can be used as a window into models' spatial reasoning limitations and drive research toward new methods that excel in abstract, multi-step problem-solving.

We provide here a dataset for tasks related to natural language understanding and natural language inference. The dataset contains logical puzzles in natural language from three domains: comparing puzzles, knighs and knaves, and zebra puzzles. Each puzzle is associated with the entire set of atomic questions that can be generated based on the relations and individuals occurring in the text. For each question we provide the correct answer: entailment, contradiction or ambiguity. The answer's correctness is verified against theorem provers. Good puzzles have two properties: (i) each piece of information is necessary and (ii) no unnecessary information is provided. These properties make puzzles interesting candidates for machine comprehension tasks.

We introduce "Method Actors" as a mental model for guiding LLM prompt engineering and prompt architecture. Under this mental model, LLMs should be thought of as actors; prompts as scripts and cues; and LLM responses as performances. We apply this mental model to the task of improving LLM performance at playing Connections, a New York Times word puzzle game that prior research identified as a challenging benchmark for evaluating LLM reasoning. Our experiments with GPT-4o show that a "Method Actors" approach can significantly improve LLM performance over both a vanilla and "Chain of Thoughts" approach. A vanilla approach solves 27% of Connections puzzles in our dataset and a "Chain of Thoughts" approach solves 41% of puzzles, whereas our strongest "Method Actor" approach solves 86% of puzzles. We also test OpenAI's newest model designed specifically for complex reasoning tasks, o1-preview. When asked to solve a puzzle all at once, o1-preview solves 79% of Connections puzzles in our dataset, and when allowed to build puzzle solutions one guess at a time over multiple API calls, o1-preview solves 100% of the puzzles. Incorporating a "Method Actor" prompt architecture increases the percentage of puzzles that o1-preview solves perfectly from 76% to 87%.

Understanding Rebus Puzzles (Rebus Puzzles use pictures, symbols, and letters to represent words or phrases creatively) requires a variety of skills such as image recognition, cognitive skills, commonsense reasoning, multi-step reasoning, image-based wordplay, etc., making this a challenging task for even current Vision-Language Models. In this paper, we present left|,circlearrowright,text{BUS},right|, a large and diverse benchmark of 1,333 English Rebus Puzzles containing different artistic styles and levels of difficulty, spread across 18 categories such as food, idioms, sports, finance, entertainment, etc. We also propose RebusDescProgICE, a model-agnostic framework which uses a combination of an unstructured description and code-based, structured reasoning, along with better, reasoning-based in-context example selection, improving the performance of Vision-Language Models on left|,circlearrowright,text{BUS},right| by 2.1-4.1% and 20-30% using closed-source and open-source models respectively compared to Chain-of-Thought Reasoning.

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

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/.

Reasoning LLMs such as OpenAI o1, o3 and DeepSeek R1 have made significant progress in mathematics and coding, yet find challenging advanced tasks such as International Mathematical Olympiad (IMO) combinatorics problems, Abstraction and Reasoning Corpus (ARC) puzzles, and Humanity's Last Exam (HLE) questions. We use a diverse inference approach that combines multiple models and methods at test time. We find that verifying mathematics and code problems, and rejection sampling on other problems is simple and effective. We automatically verify correctness of solutions to IMO problems by Lean, and ARC puzzles by code, and find that best-of-N effectively answers HLE questions. Our approach increases answer accuracy on IMO combinatorics problems from 33.3% to 77.8%, accuracy on HLE questions from 8% to 37%, and solves 80% of ARC puzzles that 948 humans could not and 26.5% of ARC puzzles that o3 high compute does not. Test-time simulations, reinforcement learning, and meta-learning with inference feedback improve generalization by adapting agent graph representations and varying prompts, code, and datasets. Our approach is reliable, robust, and scalable, and in the spirit of reproducible research, we will make it publicly available upon publication.

Existing reasoning evaluation frameworks for Large Language Models (LLMs) and Large Vision-Language Models (LVLMs) predominantly either assess text-based reasoning or vision-language understanding capabilities, with limited dynamic interplay between textual and visual constraints. To address this limitation, we introduce CrossWordBench, a benchmark designed to evaluate the reasoning capabilities of both LLMs and LVLMs through the medium of crossword puzzles-a task requiring multimodal adherence to semantic constraints from text-based clues and intersectional constraints from visual grid structures. CrossWordBench leverages a controllable puzzle generation framework that produces puzzles in multiple formats (text and image) and offers different evaluation strategies ranging from direct puzzle solving to interactive modes. Our extensive evaluation of over 20 models reveals that reasoning LLMs outperform non-reasoning models substantially by effectively leveraging crossing-letter constraints. We further demonstrate that LVLMs struggle with the task, showing a strong correlation between their puzzle-solving performance and grid-parsing accuracy. Our findings offer insights into the limitations of the reasoning capabilities of current LLMs and LVLMs, and provide an effective approach for creating multimodal constrained tasks for future evaluations.

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 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.

Crossword puzzles are popular linguistic games often used as tools to engage students in learning. Educational crosswords are characterized by less cryptic and more factual clues that distinguish them from traditional crossword puzzles. Despite there exist several publicly available clue-answer pair databases for traditional crosswords, educational clue-answer pairs datasets are missing. In this article, we propose a methodology to build educational clue generation datasets that can be used to instruct Large Language Models (LLMs). By gathering from Wikipedia pages informative content associated with relevant keywords, we use Large Language Models to automatically generate pedagogical clues related to the given input keyword and its context. With such an approach, we created clue-instruct, a dataset containing 44,075 unique examples with text-keyword pairs associated with three distinct crossword clues. We used clue-instruct to instruct different LLMs to generate educational clues from a given input content and keyword. Both human and automatic evaluations confirmed the quality of the generated clues, thus validating the effectiveness of our approach.

While visual question-answering (VQA) benchmarks have catalyzed the development of reasoning techniques, they have focused on vertical thinking. Effective problem-solving also necessitates lateral thinking, which remains understudied in AI and has not been used to test visual perception systems. To bridge this gap, we formulate visual lateral thinking as a multiple-choice question-answering task and describe a three-step taxonomy-driven methodology for instantiating task examples. Then, we develop COLUMBUS, a synthetic benchmark that applies the task pipeline to create QA sets with text and icon rebus puzzles based on publicly available collections of compounds and common phrases. COLUMBUS comprises over 1,000 puzzles, each with four answer candidates. While the SotA vision-language models (VLMs) achieve decent performance, our evaluation demonstrates a substantial gap between humans and models. VLMs benefit from human-curated descriptions but struggle to self-generate such representations at the right level of abstraction.

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.

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.

The releases of OpenAI's o1 and o3 mark a significant paradigm shift in Large Language Models towards advanced reasoning capabilities. Notably, o3 outperformed humans in novel problem-solving and skill acquisition on the Abstraction and Reasoning Corpus for Artificial General Intelligence (ARC-AGI). However, this benchmark is limited to symbolic patterns, whereas humans often perceive and reason about multimodal scenarios involving both vision and language data. Thus, there is an urgent need to investigate advanced reasoning capabilities in multimodal tasks. To this end, we track the evolution of the GPT-[n] and o-[n] series models on challenging multimodal puzzles, requiring fine-grained visual perception with abstract or algorithmic reasoning. The superior performance of o1 comes at nearly 750 times the computational cost of GPT-4o, raising concerns about its efficiency. Our results reveal a clear upward trend in reasoning capabilities across model iterations, with notable performance jumps across GPT-series models and subsequently to o1. Nonetheless, we observe that the o1 model still struggles with simple multimodal puzzles requiring abstract reasoning. Furthermore, its performance in algorithmic puzzles remains poor. We plan to continuously track new models in the series and update our results in this paper accordingly. All resources used in this evaluation are openly available https://github.com/declare-lab/LLM-PuzzleTest.

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.

Prompt sensitivity, referring to the phenomenon where paraphrasing (i.e., repeating something written or spoken using different words) leads to significant changes in large language model (LLM) performance, has been widely accepted as a core limitation of LLMs. In this work, we revisit this issue and ask: Is the widely reported high prompt sensitivity truly an inherent weakness of LLMs, or is it largely an artifact of evaluation processes? To answer this question, we systematically evaluate 7 LLMs (e.g., GPT and Gemini family) across 6 benchmarks, including both multiple-choice and open-ended tasks on 12 diverse prompt templates. We find that much of the prompt sensitivity stems from heuristic evaluation methods, including log-likelihood scoring and rigid answer matching, which often overlook semantically correct responses expressed through alternative phrasings, such as synonyms or paraphrases. When we adopt LLM-as-a-Judge evaluations, we observe a substantial reduction in performance variance and a consistently higher correlation in model rankings across prompts. Our findings suggest that modern LLMs are more robust to prompt templates than previously believed, and that prompt sensitivity may be more an artifact of evaluation than a flaw in the models.

Interestingly, LLMs yet struggle with some basic tasks that humans find trivial to handle, e.g., counting the number of character r's in the word "strawberry". There are several popular conjectures (e.g., tokenization, architecture and training data) regarding the reason for deficiency of LLMs in simple word-based counting problems, sharing the similar belief that such failure stems from model pretraining hence probably inevitable during deployment. In this paper, we carefully design multiple evaluation settings to investigate validity of prevalent conjectures. Meanwhile, we measure transferability of advanced mathematical and coding reasoning capabilities from specialized LLMs to simple counting tasks. Although specialized LLMs suffer from counting problems as well, we find conjectures about inherent deficiency of LLMs invalid and further seek opportunities to elicit knowledge and capabilities from LLMs that are beneficial to counting tasks. Compared with strategies such as finetuning and in-context learning that are commonly adopted to enhance performance on new or challenging tasks, we show that engaging reasoning is the most robust and efficient way to help LLMs better perceive tasks with more accurate responses. We hope our conjecture validation design could provide insights into the study of future critical failure modes of LLMs. Based on challenges in transferring advanced capabilities to much simpler tasks, we call for more attention to model capability acquisition and evaluation. We also highlight the importance of cultivating consciousness of "reasoning before responding" during model pretraining.

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.

The task of predicting time and location from images is challenging and requires complex human-like puzzle-solving ability over different clues. In this work, we formalize this ability into core skills and implement them using different modules in an expert pipeline called PuzzleGPT. PuzzleGPT consists of a perceiver to identify visual clues, a reasoner to deduce prediction candidates, a combiner to combinatorially combine information from different clues, a web retriever to get external knowledge if the task can't be solved locally, and a noise filter for robustness. This results in a zero-shot, interpretable, and robust approach that records state-of-the-art performance on two datasets -- TARA and WikiTilo. PuzzleGPT outperforms large VLMs such as BLIP-2, InstructBLIP, LLaVA, and even GPT-4V, as well as automatically generated reasoning pipelines like VisProg, by at least 32% and 38%, respectively. It even rivals or surpasses finetuned models.

Large multimodal models extend the impressive capabilities of large language models by integrating multimodal understanding abilities. However, it is not clear how they can emulate the general intelligence and reasoning ability of humans. As recognizing patterns and abstracting concepts are key to general intelligence, we introduce PuzzleVQA, a collection of puzzles based on abstract patterns. With this dataset, we evaluate large multimodal models with abstract patterns based on fundamental concepts, including colors, numbers, sizes, and shapes. Through our experiments on state-of-the-art large multimodal models, we find that they are not able to generalize well to simple abstract patterns. Notably, even GPT-4V cannot solve more than half of the puzzles. To diagnose the reasoning challenges in large multimodal models, we progressively guide the models with our ground truth reasoning explanations for visual perception, inductive reasoning, and deductive reasoning. Our systematic analysis finds that the main bottlenecks of GPT-4V are weaker visual perception and inductive reasoning abilities. Through this work, we hope to shed light on the limitations of large multimodal models and how they can better emulate human cognitive processes in the future (Our data and code will be released publicly at https://github.com/declare-lab/LLM-PuzzleTest).

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.

Reasoning models have demonstrated impressive performance on difficult tasks that traditional language models struggle at. However, many are plagued with the problem of overthinking--generating large amounts of unnecessary tokens which don't improve accuracy on a question. We introduce approximate measures of problem-level difficulty and demonstrate that a clear relationship between problem difficulty and optimal token spend exists, and evaluate how well calibrated a variety of reasoning models are in terms of efficiently allocating the optimal token count. We find that in general, reasoning models are poorly calibrated, particularly on easy problems. To evaluate calibration on easy questions we introduce DUMB500, a dataset of extremely easy math, reasoning, code, and task problems, and jointly evaluate reasoning model on these simple examples and extremely difficult examples from existing frontier benchmarks on the same task domain. Finally, we introduce THOUGHTTERMINATOR, a training-free black box decoding technique that significantly improves reasoning model calibration.

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.

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

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.

This paper investigates the mathematical reasoning capabilities of large language models (LLMs) using 50 newly constructed high-school-level word problems. Unlike prior studies that focus solely on answer correctness, we rigorously analyze both final answers and solution steps to identify reasoning failures. Evaluating eight state-of-the-art models - including Mixtral, Llama, Gemini, GPT-4o, and OpenAI's o1 variants - we find that while newer models (e.g., o3-mini, deepseek-r1) achieve higher accuracy, all models exhibit errors in spatial reasoning, strategic planning, and arithmetic, sometimes producing correct answers through flawed logic. Common failure modes include unwarranted assumptions, over-reliance on numerical patterns, and difficulty translating physical intuition into mathematical steps. Manual analysis reveals that models struggle with problems requiring multi-step deduction or real-world knowledge, despite possessing broad mathematical knowledge. Our results underscore the importance of evaluating reasoning processes, not just answers, and caution against overestimating LLMs' problem-solving proficiency. The study highlights persistent gaps in LLMs' generalization abilities, emphasizing the need for targeted improvements in structured reasoning and constraint handling.

Vision-Language Models (VLMs) excel at many multimodal tasks, yet their cognitive processes remain opaque on complex lateral thinking challenges like rebus puzzles. While recent work has demonstrated these models struggle significantly with rebus puzzle solving, the underlying reasoning processes and failure patterns remain largely unexplored. We address this gap through a comprehensive explainability analysis that moves beyond performance metrics to understand how VLMs approach these complex lateral thinking challenges. Our study contributes a systematically annotated dataset of 221 rebus puzzles across six cognitive categories, paired with an evaluation framework that separates reasoning quality from answer correctness. We investigate three prompting strategies designed to elicit different types of explanatory processes and reveal critical insights into VLM cognitive processes. Our findings demonstrate that reasoning quality varies dramatically across puzzle categories, with models showing systematic strengths in visual composition while exhibiting fundamental limitations in absence interpretation and cultural symbolism. We also discover that prompting strategy substantially influences both cognitive approach and problem-solving effectiveness, establishing explainability as an integral component of model performance rather than a post-hoc consideration.

The New York Times Connections game has emerged as a popular and challenging pursuit for word puzzle enthusiasts. We collect 438 Connections games to evaluate the performance of state-of-the-art large language models (LLMs) against expert and novice human players. Our results show that even the best performing LLM, Claude 3.5 Sonnet, which has otherwise shown impressive reasoning abilities on a wide variety of benchmarks, can only fully solve 18% of the games. Novice and expert players perform better than Claude 3.5 Sonnet, with expert human players significantly outperforming it. We create a taxonomy of the knowledge types required to successfully cluster and categorize words in the Connections game. We find that while LLMs perform relatively well on categorizing words based on semantic relations they struggle with other types of knowledge such as Encyclopedic Knowledge, Multiword Expressions or knowledge that combines both Word Form and Meaning. Our results establish the New York Times Connections game as a challenging benchmark for evaluating abstract reasoning capabilities in AI systems.

While recent success of large reasoning models (LRMs) significantly advanced LLMs' reasoning capability by optimizing the final answer accuracy using reinforcement learning, they may also drastically increase the output length due to overthinking, characterized by unnecessarily complex reasoning paths that waste computation and potentially degrade the performance. We hypothesize that such inefficiencies stem from LRMs' limited capability to dynamically select the proper modular reasoning strategies, termed thinking patterns at the right position. To investigate this hypothesis, we propose a dynamic optimization framework that segments model-generated reasoning paths into distinct thinking patterns, systematically identifying and promoting beneficial patterns that improve the answer while removing detrimental ones. Empirical analysis confirms that our optimized thinking paths yield more concise yet sufficiently informative trajectories, enhancing reasoning efficiency by reducing attention FLOPs by up to 47% while maintaining accuracy for originally correct responses. Moreover, a non-trivial portion of originally incorrect responses are transformed into correct ones, achieving a 15.6% accuracy improvement with reduced length. Motivated by the improvement brought by the optimized thinking paths, we apply a preference optimization technique supported by a pairwise dataset contrasting suboptimal and optimal reasoning paths. Experimental evaluations across multiple mathematical reasoning benchmarks reveal that our method notably reduces computational overhead while simultaneously improving reasoning accuracy, achieving up to a 12% accuracy improvement and reducing token usage from approximately 5,000 to 3,000 tokens.

Shojaee et al. (2025) report that Large Reasoning Models (LRMs) exhibit "accuracy collapse" on planning puzzles beyond certain complexity thresholds. We demonstrate that their findings primarily reflect experimental design limitations rather than fundamental reasoning failures. Our analysis reveals three critical issues: (1) Tower of Hanoi experiments systematically exceed model output token limits at reported failure points, with models explicitly acknowledging these constraints in their outputs; (2) The authors' automated evaluation framework fails to distinguish between reasoning failures and practical constraints, leading to misclassification of model capabilities; (3) Most concerningly, their River Crossing benchmarks include mathematically impossible instances for N > 5 due to insufficient boat capacity, yet models are scored as failures for not solving these unsolvable problems. When we control for these experimental artifacts, by requesting generating functions instead of exhaustive move lists, preliminary experiments across multiple models indicate high accuracy on Tower of Hanoi instances previously reported as complete failures. These findings highlight the importance of careful experimental design when evaluating AI reasoning capabilities.

In this paper we look at the ability of recent large language models (LLMs) at solving mathematical problems in combinatorics. We compare models LLaMA-2, LLaMA-3.1, GPT-4, and Mixtral against each other and against human pupils and undergraduates with prior experience in mathematical olympiads. To facilitate these comparisons we introduce the Combi-Puzzles dataset, which contains 125 problem variants based on 25 combinatorial reasoning problems. Each problem is presented in one of five distinct forms, created by systematically manipulating the problem statements through adversarial additions, numeric parameter changes, and linguistic obfuscation. Our variations preserve the mathematical core and are designed to measure the generalisability of LLM problem-solving abilities, while also increasing confidence that problems are submitted to LLMs in forms that have not been seen as training instances. We found that a model based on GPT-4 outperformed all other models in producing correct responses, and performed significantly better in the mathematical variation of the problems than humans. We also found that modifications to problem statements significantly impact the LLM's performance, while human performance remains unaffected.

Accuracy remains a standard metric for evaluating AI systems, but it offers limited insight into how models arrive at their solutions. In this work, we introduce a benchmark based on brainteasers written in long narrative form to probe more deeply into the types of reasoning strategies that models use. Brainteasers are well-suited for this goal because they can be solved with multiple approaches, such as a few-step solution that uses a creative insight or a longer solution that uses more brute force. We investigate large language models (LLMs) across multiple layers of reasoning, focusing not only on correctness but also on the quality and creativity of their solutions. We investigate many aspects of the reasoning process: (1) semantic parsing of the brainteasers into precise mathematical competition style formats; (2) generating solutions from these mathematical forms; (3) self-correcting solutions based on gold solutions; (4) producing step-by-step sketches of solutions; and (5) making use of hints. We find that LLMs are in many cases able to find creative, insightful solutions to brainteasers, suggesting that they capture some of the capacities needed to solve novel problems in creative ways. Nonetheless, there also remain situations where they rely on brute force despite the availability of more efficient, creative solutions, highlighting a potential direction for improvement in the reasoning abilities of LLMs.

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.

Causal language modeling using the Transformer architecture has yielded remarkable capabilities in Large Language Models (LLMs) over the last few years. However, the extent to which fundamental search and reasoning capabilities emerged within LLMs remains a topic of ongoing debate. In this work, we study if causal language modeling can learn a complex task such as solving Sudoku puzzles. To solve a Sudoku, the model is first required to search over all empty cells of the puzzle to decide on a cell to fill and then apply an appropriate strategy to fill the decided cell. Sometimes, the application of a strategy only results in thinning down the possible values in a cell rather than concluding the exact value of the cell. In such cases, multiple strategies are applied one after the other to fill a single cell. We observe that Transformer models trained on this synthetic task can indeed learn to solve Sudokus (our model solves 94.21% of the puzzles fully correctly) when trained on a logical sequence of steps taken by a solver. We find that training Transformers with the logical sequence of steps is necessary and without such training, they fail to learn Sudoku. We also extend our analysis to Zebra puzzles (known as Einstein puzzles) and show that the model solves 92.04 % of the puzzles fully correctly. In addition, we study the internal representations of the trained Transformer and find that through linear probing, we can decode information about the set of possible values in any given cell from them, pointing to the presence of a strong reasoning engine implicit in the Transformer weights.

Recent years have witnessed a surge in the number of large language models (LLMs), yet efficiently managing and utilizing these vast resources remains a significant challenge. In this work, we explore how to learn compact representations of LLM abilities that can facilitate downstream tasks, such as model routing and performance prediction on new benchmarks. We frame this problem as estimating the probability that a given model will correctly answer a specific query. Inspired by the item response theory (IRT) in psychometrics, we model this probability as a function of three key factors: (i) the model's multi-skill ability vector, (2) the query's discrimination vector that separates models of differing skills, and (3) the query's difficulty scalar. To learn these parameters jointly, we introduce a Mixture-of-Experts (MoE) network that couples model- and query-level embeddings. Extensive experiments demonstrate that our approach leads to state-of-the-art performance in both model routing and benchmark accuracy prediction. Moreover, analysis validates that the learned parameters encode meaningful, interpretable information about model capabilities and query characteristics.

Large language models (LLMs) can correctly answer "When was Einstein born?" yet fail to provide the same date when writing about Einstein's life revealing a fundamental inconsistency in how models access factual knowledge across task complexities. While models display impressive accuracy on factual question-answering benchmarks, the reliability gap between simple and complex queries remains poorly understood, eroding their trustworthiness. In this work, we introduce Short-Long Form Alignment for Factual Question Answering (SLAQ), a controlled evaluation framework that compares LLMs' answers to the same factual questions asked (a) in isolation (short) vs. (b) integrated into complex queries (long). Looking at 16 LLMs across 600 queries, we find a systematic misalignment of answers to the corresponding short and long queries. We further uncover position-dependent accuracy loss and momentum effects where consecutive correct or incorrect answers create self-reinforcing patterns. Through mechanistic analysis, we find that aligned facts activate overlapping model internals, and that metrics based on mechanistic similarity can predict short-long answer alignment with up to 78% accuracy. Our work establishes factual consistency over query complexity as an important aspect of LLMs' trustworthiness and challenges current evaluation practices, which implicitly assume that good performance for simple factual queries implies reliability in more complex knowledge-seeking tasks too.

We introduce KiloGram, a resource for studying abstract visual reasoning in humans and machines. Drawing on the history of tangram puzzles as stimuli in cognitive science, we build a richly annotated dataset that, with >1k distinct stimuli, is orders of magnitude larger and more diverse than prior resources. It is both visually and linguistically richer, moving beyond whole shape descriptions to include segmentation maps and part labels. We use this resource to evaluate the abstract visual reasoning capacities of recent multi-modal models. We observe that pre-trained weights demonstrate limited abstract reasoning, which dramatically improves with fine-tuning. We also observe that explicitly describing parts aids abstract reasoning for both humans and models, especially when jointly encoding the linguistic and visual inputs. KiloGram is available at https://lil.nlp.cornell.edu/kilogram .

Among the most important properties of algorithms investigated in computer science are soundness, completeness, and complexity. These properties, however, are rarely analyzed for the vast collection of recently proposed methods for planning with large language models. In this work, we alleviate this gap. We analyse these properties of using LLMs for planning and highlight that recent trends abandon both soundness and completeness for the sake of inefficiency. We propose a significantly more efficient approach that can, at the same time, maintain both soundness and completeness. We exemplify on four representative search problems, comparing to the LLM-based solutions from the literature that attempt to solve these problems. We show that by using LLMs to produce the code for the search components we can solve the entire datasets with 100\% accuracy with only a few calls to the LLM. We argue for a responsible use of compute resources; urging research community to investigate sound and complete LLM-based approaches that uphold efficiency.

Context-grounded hallucinations are cases where model outputs contain information not verifiable against the source text. We study the applicability of LLMs for localizing such hallucinations, as a more practical alternative to existing complex evaluation pipelines. In the absence of established benchmarks for meta-evaluation of hallucinations localization, we construct one tailored to LLMs, involving a challenging human annotation of over 1,000 examples. We complement the benchmark with an LLM-based evaluation protocol, verifying its quality in a human evaluation. Since existing representations of hallucinations limit the types of errors that can be expressed, we propose a new representation based on free-form textual descriptions, capturing the full range of possible errors. We conduct a comprehensive study, evaluating four large-scale LLMs, which highlights the benchmark's difficulty, as the best model achieves an F1 score of only 0.67. Through careful analysis, we offer insights into optimal prompting strategies for the task and identify the main factors that make it challenging for LLMs: (1) a tendency to incorrectly flag missing details as inconsistent, despite being instructed to check only facts in the output; and (2) difficulty with outputs containing factually correct information absent from the source - and thus not verifiable - due to alignment with the model's parametric knowledge.

Current evaluation of mathematical reasoning in language models relies primarily on answer accuracy, potentially masking fundamental failures in logical computation. We introduce a diagnostic framework that distinguishes genuine mathematical reasoning from superficial pattern matching through four complementary axes: forward-backward consistency, transitivity coverage, counterfactual sensitivity, and perturbation robustness. Through a case study applying this framework to Qwen3-0.6B on the MenatQA dataset, we reveal a striking disconnect between surface performance and reasoning fidelity. While the model achieves reasonable answer accuracy (70%+), it demonstrates poor backward consistency (15%), limited transitivity coverage (32.2%), and brittle sensitivity to perturbations. Our diagnostics expose reasoning failures invisible to traditional accuracy metrics, suggesting that this small model relies heavily on pattern matching rather than genuine logical computation. While our empirical findings are based on a single 600M-parameter model, the diagnostic framework itself is model-agnostic and generalizable. We release our evaluation protocols to enable the research community to assess reasoning fidelity across different model scales and architectures, moving beyond surface-level accuracy toward verifiable mathematical reasoning.

In this work, we unveil a novel tool for generating Italian crossword puzzles from text, utilizing advanced language models such as GPT-4o, Mistral-7B-Instruct-v0.3, and Llama3-8b-Instruct. Crafted specifically for educational applications, this cutting-edge generator makes use of the comprehensive Italian-Clue-Instruct dataset, which comprises over 30,000 entries including diverse text, solutions, and types of clues. This carefully assembled dataset is designed to facilitate the creation of contextually relevant clues in various styles associated with specific texts and keywords. The study delves into four distinctive styles of crossword clues: those without format constraints, those formed as definite determiner phrases, copular sentences, and bare noun phrases. Each style introduces unique linguistic structures to diversify clue presentation. Given the lack of sophisticated educational tools tailored to the Italian language, this project seeks to enhance learning experiences and cognitive development through an engaging, interactive platform. By meshing state-of-the-art AI with contemporary educational strategies, our tool can dynamically generate crossword puzzles from Italian educational materials, thereby providing an enjoyable and interactive learning environment. This technological advancement not only redefines educational paradigms but also sets a new benchmark for interactive and cognitive language learning solutions.

We present the Chinese Elementary School Math Word Problems (CMATH) dataset, comprising 1.7k elementary school-level math word problems with detailed annotations, source from actual Chinese workbooks and exams. This dataset aims to provide a benchmark tool for assessing the following question: to what grade level of elementary school math do the abilities of popular large language models (LLMs) correspond? We evaluate a variety of popular LLMs, including both commercial and open-source options, and discover that only GPT-4 achieves success (accuracy geq 60\%) across all six elementary school grades, while other models falter at different grade levels. Furthermore, we assess the robustness of several top-performing LLMs by augmenting the original problems in the CMATH dataset with distracting information. Our findings reveal that GPT-4 is able to maintains robustness, while other model fail. We anticipate that our study will expose limitations in LLMs' arithmetic and reasoning capabilities, and promote their ongoing development and advancement.

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

Large language models (LLMs) are known to struggle with complicated reasoning tasks such as math word problems (MWPs). In this paper, we present how analogy from similarly structured questions can improve LLMs' problem-solving capabilities for MWPs. Specifically, we rely on the retrieval of problems with similar computational graphs to the given question to serve as exemplars in the prompt, providing the correct reasoning path for the generation model to refer to. Empirical results across six math word problem datasets demonstrate the effectiveness of our proposed method, which achieves a significant improvement of up to 6.7 percent on average in absolute value, compared to baseline methods. These results highlight our method's potential in addressing the reasoning challenges in current LLMs.

In this thesis, I evaluate the performance of Large Language Models (LLMs) on the Law School Admissions Test (LSAT), specifically the Logic Games section of the test. I focus on this section because it presents a complex logical reasoning task and thus is a valuable source of data for evaluating how modern, increasingly capable LLMs can handle hard logical reasoning tasks. I construct a dataset of LSAT logic games and their associated metadata, and extensively evaluate LLMs' performance in a Chain-of-Thought prompting setting. Given the weak performance in this setting, I explore other prompting frameworks on a smaller subset of the dataset, adapting ideas from Reflexion to this task. This results in a substantially improved accuracy of 70 percent for GPT-4 and 46 percent for GPT-3.5 on this data subset, highlighting the capacity of LLMs to revise their logical errors, despite initially weak performance. Finally, I analyze the types of logic games that models perform better or worse on, as well as the types of logical errors I observe from human annotation, providing detailed insights on the logical reasoning capabilities of LLMs.

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

Large Language Models (LLMs) have exhibited exceptional performance across a broad range of tasks and domains. However, they still encounter difficulties in solving mathematical problems due to the rigorous and logical nature of mathematics. Previous studies have employed techniques such as supervised fine-tuning (SFT), prompt engineering, and search-based methods to improve the mathematical problem-solving abilities of LLMs. Despite these efforts, their performance remains suboptimal and demands substantial computational resources. To address this issue, we propose a novel approach, BEATS, to enhance mathematical problem-solving abilities. Our method leverages newly designed prompts that guide the model to iteratively rewrite, advance by one step, and generate answers based on previous steps. Additionally, we introduce a new back-verification technique that uses LLMs to validate the correctness of the generated answers. Furthermore, we employ a pruning tree search to optimize search time while achieving strong performance. Notably, our method improves Qwen2-7b-Instruct's score from 36.94 to 61.52, outperforming GPT4's 42.5 on the MATH benchmark.

Large Language Models (LLMs) leverage step-by-step reasoning to solve complex problems. Standard evaluation practice involves generating a complete reasoning trace and assessing the correctness of the final answer presented at its conclusion. In this paper, we challenge the reliance on the final answer by posing the following two questions: Does the final answer reliably represent the model's optimal conclusion? Can alternative reasoning paths yield different results? To answer these questions, we analyze intermediate reasoning steps, termed subthoughts, and propose a method based on our findings. Our approach involves segmenting a reasoning trace into sequential subthoughts based on linguistic cues. We start by prompting the model to generate continuations from the end-point of each intermediate subthought. We extract a potential answer from every completed continuation originating from different subthoughts. We find that aggregating these answers by selecting the most frequent one (the mode) often yields significantly higher accuracy compared to relying solely on the answer derived from the original complete trace. Analyzing the consistency among the answers derived from different subthoughts reveals characteristics that correlate with the model's confidence and correctness, suggesting potential for identifying less reliable answers. Our experiments across various LLMs and challenging mathematical reasoning datasets (AIME2024 and AIME2025) show consistent accuracy improvements, with gains reaching up to 13\% and 10\% respectively. Implementation is available at: https://github.com/hammoudhasan/SubthoughtReasoner.

Chain-of-thought prompting has demonstrated remarkable performance on various natural language reasoning tasks. However, it tends to perform poorly on tasks which requires solving problems harder than the exemplars shown in the prompts. To overcome this challenge of easy-to-hard generalization, we propose a novel prompting strategy, least-to-most prompting. The key idea in this strategy is to break down a complex problem into a series of simpler subproblems and then solve them in sequence. Solving each subproblem is facilitated by the answers to previously solved subproblems. Our experimental results on tasks related to symbolic manipulation, compositional generalization, and math reasoning reveal that least-to-most prompting is capable of generalizing to more difficult problems than those seen in the prompts. A notable finding is that when the GPT-3 code-davinci-002 model is used with least-to-most prompting, it can solve the compositional generalization benchmark SCAN in any split (including length split) with an accuracy of at least 99% using just 14 exemplars, compared to only 16% accuracy with chain-of-thought prompting. This is particularly noteworthy because neural-symbolic models in the literature that specialize in solving SCAN are trained on the entire training set containing over 15,000 examples. We have included prompts for all the tasks in the Appendix.

We introduce HRMCR (HAE-RAE Multi-Step Commonsense Reasoning), a benchmark designed to evaluate large language models' ability to perform multi-step reasoning in culturally specific contexts, focusing on Korean. The questions are automatically generated via templates and algorithms, requiring LLMs to integrate Korean cultural knowledge into sequential reasoning steps. Consistent with prior observations on emergent abilities, our experiments reveal that models trained on fewer than \(2 \cdot 10^{25}\) training FLOPs struggle to solve any questions, showing near-zero performance. Beyond this threshold, performance improves sharply. State-of-the-art models (e.g., O1) still score under 50\%, underscoring the difficulty of our tasks. Notably, stepwise analysis suggests the observed emergent behavior may stem from compounding errors across multiple steps rather than reflecting a genuinely new capability. We publicly release the benchmark and commit to regularly updating the dataset to prevent contamination.

Large Language Models (LLMs) have shown excellent performance in language understanding, text generation, code synthesis, and many other tasks, while they still struggle in complex multi-step reasoning problems, such as mathematical reasoning. In this paper, through a newly proposed arithmetical puzzle problem, we show that the model can perform well on multi-step reasoning tasks via fine-tuning on high-quality synthetic data. Experimental results with the open-llama-3B model on three different test datasets show that not only the model can reach a zero-shot pass@1 at 0.44 on the in-domain dataset, it also demonstrates certain generalization capabilities on the out-of-domain datasets. Specifically, this paper has designed two out-of-domain datasets in the form of extending the numerical range and the composing components of the arithmetical puzzle problem separately. The fine-tuned models have shown encouraging performance on these two far more difficult tasks with the zero-shot pass@1 at 0.33 and 0.35, respectively.

Search-augmented large language models (LLMs) excel at knowledge-intensive tasks by integrating external retrieval. However, they often over-search -- unnecessarily invoking search tool even when it does not improve response quality, which leads to computational inefficiency and hallucinations by incorporating irrelevant context. In this work, we conduct a systematic evaluation of over-searching across multiple dimensions, including query types, model categories, retrieval conditions, and multi-turn conversations. Our finding shows: (i) search generally improves answer accuracy on answerable queries but harms abstention on unanswerable ones; (ii) over-searching is more pronounced in complex reasoning models and deep research systems, is exacerbated by noisy retrieval, and compounds across turns in multi-turn conversations; and (iii) the composition of retrieved evidence is crucial, as the presence of negative evidence improves abstention. To quantify over-searching, we introduce Tokens Per Correctness (TPC), an evaluation metric that captures the performance-cost trade-off for search-augmented LLMs. Lastly, we investigate mitigation approaches at both the query and retrieval levels and release the OverSearchQA to foster continued research into efficient search-augmented LLMs.

Recent supervised fine-tuning (SFT) approaches have significantly improved language models' performance on mathematical reasoning tasks, even when models are trained at a small scale. However, the specific capabilities enhanced through such fine-tuning remain poorly understood. In this paper, we conduct a detailed analysis of model performance on the AIME24 dataset to understand how reasoning capabilities evolve. We discover a ladder-like structure in problem difficulty, categorize questions into four tiers (Easy, Medium, Hard, and Extremely Hard (Exh)), and identify the specific requirements for advancing between tiers. We find that progression from Easy to Medium tier requires adopting an R1 reasoning style with minimal SFT (500-1K instances), while Hard-level questions suffer from frequent model's errors at each step of the reasoning chain, with accuracy plateauing at around 65% despite logarithmic scaling. Exh-level questions present a fundamentally different challenge; they require unconventional problem-solving skills that current models uniformly struggle with. Additional findings reveal that carefully curated small-scale datasets offer limited advantage-scaling dataset size proves far more effective. Our analysis provides a clearer roadmap for advancing language model capabilities in mathematical reasoning.

Retriever-augmented instruction-following models are attractive alternatives to fine-tuned approaches for information-seeking tasks such as question answering (QA). By simply prepending retrieved documents in its input along with an instruction, these models can be adapted to various information domains and tasks without additional fine-tuning. While the model responses tend to be natural and fluent, the additional verbosity makes traditional QA evaluation metrics such as exact match (EM) and F1 unreliable for accurately quantifying model performance. In this work, we investigate the performance of instruction-following models across three information-seeking QA tasks. We use both automatic and human evaluation to evaluate these models along two dimensions: 1) how well they satisfy the user's information need (correctness), and 2) whether they produce a response based on the provided knowledge (faithfulness). Guided by human evaluation and analysis, we highlight the shortcomings of traditional metrics for both correctness and faithfulness. We then propose simple token-overlap based and model-based metrics that reflect the true performance of these models. Our analysis reveals that instruction-following models are competitive, and sometimes even outperform fine-tuned models for correctness. However, these models struggle to stick to the provided knowledge and often hallucinate in their responses. We hope our work encourages a more holistic evaluation of instruction-following models for QA. Our code and data is available at https://github.com/McGill-NLP/instruct-qa

Assessing the quality of Large Language Model (LLM) outputs presents a critical challenge. Previous methods either rely on text-level information (e.g., reward models, majority voting), which can overfit to superficial cues, or on calibrated confidence from token probabilities, which would fail on less-calibrated models. Yet both of these signals are, in fact, partial projections of a richer source of information: the model's internal hidden states. Early layers, closer to token embeddings, preserve semantic and lexical features that underpin text-based judgments, while later layers increasingly align with output logits, embedding confidence-related information. This paper explores hidden states directly as a unified foundation for verification. We show that the correctness of a solution is encoded as a geometrically separable signature within the trajectory of hidden activations. To validate this, we present Clue (Clustering and Experience-based Verification), a deliberately minimalist, non-parametric verifier. With no trainable parameters, CLUE only summarizes each reasoning trace by an hidden state delta and classifies correctness via nearest-centroid distance to ``success'' and ``failure'' clusters formed from past experience. The simplicity of this method highlights the strength of the underlying signal. Empirically, CLUE consistently outperforms LLM-as-a-judge baselines and matches or exceeds modern confidence-based methods in reranking candidates, improving both top-1 and majority-vote accuracy across AIME 24/25 and GPQA. As a highlight, on AIME 24 with a 1.5B model, CLUE boosts accuracy from 56.7% (majority@64) to 70.0% (top-maj@16).

While multi-modal large language models (MLLMs) have shown significant progress on many popular visual reasoning benchmarks, whether they possess abstract visual reasoning abilities remains an open question. Similar to the Sudoku puzzles, abstract visual reasoning (AVR) problems require finding high-level patterns (e.g., repetition constraints) that control the input shapes (e.g., digits) in a specific task configuration (e.g., matrix). However, existing AVR benchmarks only considered a limited set of patterns (addition, conjunction), input shapes (rectangle, square), and task configurations (3 by 3 matrices). To evaluate MLLMs' reasoning abilities comprehensively, we introduce MARVEL, a multidimensional AVR benchmark with 770 puzzles composed of six core knowledge patterns, geometric and abstract shapes, and five different task configurations. To inspect whether the model accuracy is grounded in perception and reasoning, MARVEL complements the general AVR question with perception questions in a hierarchical evaluation framework. We conduct comprehensive experiments on MARVEL with nine representative MLLMs in zero-shot and few-shot settings. Our experiments reveal that all models show near-random performance on the AVR question, with significant performance gaps (40%) compared to humans across all patterns and task configurations. Further analysis of perception questions reveals that MLLMs struggle to comprehend the visual features (near-random performance) and even count the panels in the puzzle ( <45%), hindering their ability for abstract reasoning. We release our entire code and dataset.

While Generative AI rapidly advances in various domains, generating truly creative, aesthetic, and counter-intuitive outputs remains a challenge. This paper presents an approach to tackle these difficulties in the domain of chess puzzles. We start by benchmarking Generative AI architectures, and then introduce an RL framework with novel rewards based on chess engine search statistics to overcome some of those shortcomings. The rewards are designed to enhance a puzzle's uniqueness, counter-intuitiveness, diversity, and realism. Our RL approach dramatically increases counter-intuitive puzzle generation by 10x, from 0.22\% (supervised) to 2.5\%, surpassing existing dataset rates (2.1\%) and the best Lichess-trained model (0.4\%). Our puzzles meet novelty and diversity benchmarks, retain aesthetic themes, and are rated by human experts as more creative, enjoyable, and counter-intuitive than composed book puzzles, even approaching classic compositions. Our final outcome is a curated booklet of these AI-generated puzzles, which is acknowledged for creativity by three world-renowned experts.

Recent works have shown the benefits to LLMs from fine-tuning golden-standard Chain-of-Thought (CoT) rationales or using them as correct examples in few-shot prompting. While humans can indeed imitate correct examples, learning from our mistakes is another vital aspect of human cognition. Hence, a question naturally arises: can LLMs learn and benefit from their mistakes, especially for their reasoning? This study investigates this problem from both the prompting and model-tuning perspectives. We begin by introducing CoTErrorSet, a new benchmark with 609,432 questions, each designed with both correct and error references, and demonstrating the types and reasons for making such mistakes. To explore the effectiveness of those mistakes, we design two methods: (1) Self-rethinking prompting guides LLMs to rethink whether they have made similar previous mistakes; and (2) Mistake tuning involves finetuning models in both correct and incorrect reasoning domains, rather than only tuning models to learn ground truth in traditional methodology. We conduct a series of experiments to prove LLMs can obtain benefits from mistakes in both directions. Our two methods offer potentially cost-effective strategies by leveraging errors to enhance reasoning capabilities, which costs significantly less than creating meticulously hand-crafted golden references. We ultimately make a thorough analysis of the reasons behind LLMs' errors, which provides directions that future research needs to overcome. CoTErrorSet will be published soon on \url{https://github.com/YookiTong/Learn-from-Mistakes-CotErrorSet}.

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

While recent works (e.g. o1, DeepSeek R1) have demonstrated great promise of using long Chain-of-Thought (CoT) to improve reasoning capabilities of language models, scaling it up during test-time is challenging due to inefficient memory usage -- intermediate computations accumulate indefinitely in context even no longer needed for future thoughts. We propose PENCIL, which incorporates a reduction mechanism into the autoregressive generation process, allowing the model to recursively clean up intermediate thoughts based on patterns learned from training. With this reduction mechanism, PENCIL significantly reduces the maximal context length required during generation, and thus can generate longer thoughts with limited memory, solving larger-scale problems given more thinking time. For example, we demonstrate PENCIL achieves 97\% accuracy on the challenging Einstein's puzzle -- a task even large models like GPT-4 struggle with -- using only a small 25M-parameter transformer with 2048 context length. Theoretically, we prove PENCIL can perform universal space-efficient computation by simulating Turing machines with optimal time and space complexity, and thus can solve arbitrary computational tasks that would otherwise be intractable given context window constraints.

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.

Recent advances in Large Language Models (LLMs) have demonstrated remarkable general reasoning capabilities. However, systematically evaluating and enhancing these reasoning capabilities is challenging due to the lack of controllable and scalable tools for fine-grained analysis. Existing benchmarks and datasets often lack the necessary variable control for multi-dimensional, systematic analysis and training, or have narrow problem types and formats. To address these limitations, we introduce SATQuest, a systematic verifier designed to evaluate and enhance logical reasoning in LLMs by generating diverse, Satisfiability-based logical reasoning problems directly from Conjunctive Normal Form (CNF) instances. SATQuest structures these problems along three orthogonal dimensions: instance scale, problem type, and question format, employing randomized, SAT-based problem generation and objective answer verification via PySAT. This design mitigates memorization issues, allows for nuanced insights into reasoning performance, and enables effective reinforcement fine-tuning. Our extensive evaluation of various LLMs using SATQuest identified significant limitations in their logical reasoning, particularly in generalizing beyond familiar mathematical formats. Furthermore, we show that reinforcement fine-tuning with SATQuest rewards substantially improves targeted task performance and generalizes to more complex instances, while highlighting remaining challenges in cross-format adaptation. Through these demonstrations, we showcase SATQuest's potential as a foundational tool and a valuable starting point for advancing LLM logical reasoning.

Large language models have demonstrated impressive performance on challenging mathematical reasoning tasks, which has triggered the discussion of whether the performance is achieved by true reasoning capability or memorization. To investigate this question, prior work has constructed mathematical benchmarks when questions undergo simple perturbations -- modifications that still preserve the underlying reasoning patterns of the solutions. However, no work has explored hard perturbations, which fundamentally change the nature of the problem so that the original solution steps do not apply. To bridge the gap, we construct MATH-P-Simple and MATH-P-Hard via simple perturbation and hard perturbation, respectively. Each consists of 279 perturbed math problems derived from level-5 (hardest) problems in the MATH dataset (Hendrycksmath et. al., 2021). We observe significant performance drops on MATH-P-Hard across various models, including o1-mini (-16.49%) and gemini-2.0-flash-thinking (-12.9%). We also raise concerns about a novel form of memorization where models blindly apply learned problem-solving skills without assessing their applicability to modified contexts. This issue is amplified when using original problems for in-context learning. We call for research efforts to address this challenge, which is critical for developing more robust and reliable reasoning models.

The hallucination of non-existent facts by LLMs is an important problem given its widespread adoption across various applications. Previous research addresses this problem by analyzing the internal parameterized knowledge boundaries to estimate confidence. However, these studies focus on the single-problem setting and have not explored the more challenging multi-problem setting, which requires accurately answering multiple questions simultaneously. We introduce a novel method for the multi-problem setting, Multiple Answers and Confidence Stepwise Tuning (MAC-Tuning), that separates the learning of answer prediction and confidence estimation during fine-tuning on instruction data. Extensive experiments demonstrate that our method outperforms baselines by up to 25\% in average precision.

Reinforcement learning (RL) is often credited with improving language model reasoning and generalization at the expense of degrading memorized knowledge. We challenge this narrative by observing that RL-enhanced models consistently outperform their base and supervised fine-tuned (SFT) counterparts on pure knowledge recall tasks, particularly those requiring traversal of hierarchical, structured knowledge (e.g., medical codes). We hypothesize these gains stem not from newly acquired data, but from improved procedural skills in navigating and searching existing knowledge hierarchies within the model parameters. To support this hypothesis, we show that structured prompting, which explicitly guides SFTed models through hierarchical traversal, recovers most of the performance gap (reducing 24pp to 7pp on MedConceptsQA for DeepSeek-V3/R1). We further find that while prompting improves final-answer accuracy, RL-enhanced models retain superior ability to recall correct procedural paths on deep-retrieval tasks. Finally our layer-wise internal activation analysis reveals that while factual representations (e.g., activations for the statement "code 57.95 refers to urinary infection") maintain high cosine similarity between SFT and RL models, query representations (e.g., "what is code 57.95") diverge noticeably, indicating that RL primarily transforms how models traverse knowledge rather than the knowledge representation itself.

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

In this paper, we investigate which questions are challenging for retrieval-based Question Answering (QA). We (i) propose retrieval complexity (RC), a novel metric conditioned on the completeness of retrieved documents, which measures the difficulty of answering questions, and (ii) propose an unsupervised pipeline to measure RC given an arbitrary retrieval system. Our proposed pipeline measures RC more accurately than alternative estimators, including LLMs, on six challenging QA benchmarks. Further investigation reveals that RC scores strongly correlate with both QA performance and expert judgment across five of the six studied benchmarks, indicating that RC is an effective measure of question difficulty. Subsequent categorization of high-RC questions shows that they span a broad set of question shapes, including multi-hop, compositional, and temporal QA, indicating that RC scores can categorize a new subset of complex questions. Our system can also have a major impact on retrieval-based systems by helping to identify more challenging questions on existing datasets.

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."

This paper presents an end-to-end neural architecture based on Diffusion Models for spatial puzzle solving, particularly jigsaw puzzle and room arrangement tasks. In the latter task, for instance, the proposed system "PuzzleFusion" takes a set of room layouts as polygonal curves in the top-down view and aligns the room layout pieces by estimating their 2D translations and rotations, akin to solving the jigsaw puzzle of room layouts. A surprising discovery of the paper is that the simple use of a Diffusion Model effectively solves these challenging spatial puzzle tasks as a conditional generation process. To enable learning of an end-to-end neural system, the paper introduces new datasets with ground-truth arrangements: 1) 2D Voronoi jigsaw dataset, a synthetic one where pieces are generated by Voronoi diagram of 2D pointset; and 2) MagicPlan dataset, a real one offered by MagicPlan from its production pipeline, where pieces are room layouts constructed by augmented reality App by real-estate consumers. The qualitative and quantitative evaluations demonstrate that our approach outperforms the competing methods by significant margins in all the tasks.

Large language models (LLMs) have achieved striking successes on many benchmarks, yet recent studies continue to expose fundamental weaknesses. In particular, tasks that require abstract reasoning remain challenging, often because they use representations such as grids, symbols, or visual patterns that differ from the natural language data LLMs are trained on. In this paper, we introduce Concept, a simple word-guessing board game, as a benchmark for probing abductive reasoning in a representation that is much closer to LLM pre-training data: natural language. Our results show that this game, easily solved by humans (with a success rate of over 90\%), is still very challenging for state-of-the-art LLMs (no model exceeds 40\% success rate). Specifically, we observe that LLMs struggle with interpreting other players' strategic intents, and with correcting initial hypotheses given sequential information updates. In addition, we extend the evaluation across multiple languages, and find that the LLM performance drops further in lower-resource languages (Dutch, French, and Spanish) compared to English.

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.

The application of rule-based reinforcement learning (RL) to multimodal large language models (MLLMs) introduces unique challenges and potential deviations from findings in text-only domains, particularly for perception-heavy tasks. This paper provides a comprehensive study of rule-based visual RL, using jigsaw puzzles as a structured experimental framework. Jigsaw puzzles offer inherent ground truth, adjustable difficulty, and demand complex decision-making, making them ideal for this study. Our research reveals several key findings: Firstly, we find that MLLMs, initially performing near to random guessing on the simplest jigsaw puzzles, achieve near-perfect accuracy and generalize to complex, unseen configurations through fine-tuning. Secondly, training on jigsaw puzzles can induce generalization to other visual tasks, with effectiveness tied to specific task configurations. Thirdly, MLLMs can learn and generalize with or without explicit reasoning, though open-source models often favor direct answering. Consequently, even when trained for step-by-step reasoning, they can ignore the thinking process in deriving the final answer. Fourthly, we observe that complex reasoning patterns appear to be pre-existing rather than emergent, with their frequency increasing alongside training and task difficulty. Finally, our results demonstrate that RL exhibits more effective generalization than Supervised Fine-Tuning (SFT), and an initial SFT cold start phase can hinder subsequent RL optimization. Although these observations are based on jigsaw puzzles and may vary across other visual tasks, this research contributes a valuable piece of jigsaw to the larger puzzle of collective understanding rule-based visual RL and its potential in multimodal learning. The code is available at: https://github.com/zifuwanggg/Jigsaw-R1.

Recent large language models have shown promising capabilities in long-form reasoning, following structured chains of thought before arriving at a final answer. However, we observe that these reasoning paths tend to include substantial redundancy; analyzing attention patterns reveals that attention scores are widely scattered, particularly incorrect answers exhibit greater attention sparsity. In this paper, we demonstrate that deliberately removing this redundancy in the reasoning process significantly improves performance through clear thinking, i.e., removing distraction. Specifically, we systematically identify reasoning redundancy by measuring token-level attention scores to a special end-of-thinking token, which is appended to an explicit instruction inserted to conclude each intermediate reasoning step. Furthermore, we propose structure-aware pruning that prioritizes removing tokens in low-contributing reasoning chunks over individual tokens. After evicting redundant tokens, we remove the injected end-of-thinking instruction, then resume the reasoning generation. We demonstrate that our method significantly improves overall accuracy across reasoning-intensive benchmarks without any training involved. In particular, our method shows strong performance on challenging mathematical competition benchmarks such as AIME and AMC, where reasoning redundancy is more prevalent.

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

A primary concern regarding training large language models (LLMs) is whether they abuse copyrighted online text. With the increasing training data scale and the prevalence of LLMs in daily lives, two problems arise: 1) false positive membership inference results misled by similar examples; 2) membership inference methods are usually too complex for end users to understand and use. To address these issues, we propose an alternative insert-and-detect methodology, advocating that web users and content platforms employ \textit{unique identifiers} for reliable and independent membership inference. Users and platforms can create their identifiers, embed them in copyrighted text, and independently detect them in future LLMs. As an initial demonstration, we introduce \textbf{ghost sentences} and a user-friendly last-k words test, allowing end users to chat with LLMs for membership inference. Ghost sentences consist primarily of unique passphrases of random natural words, which can come with customized elements to bypass possible filter rules. The last-k words test requires a significant repetition time of ghost sentences~(ge10). For cases with fewer repetitions, we designed an extra perplexity test, as LLMs exhibit high perplexity when encountering unnatural passphrases. We also conduct a comprehensive study on the memorization and membership inference of ghost sentences, examining factors such as training data scales, model sizes, repetition times, insertion positions, wordlist of passphrases, alignment, etc. Our study shows the possibility of applying ghost sentences in real scenarios and provides instructions for the potential application.

Large language models have demonstrated remarkable proficiency in long and complex reasoning tasks. However, they frequently exhibit a problematic reliance on familiar reasoning patterns, a phenomenon we term reasoning rigidity. Despite explicit instructions from users, these models often override clearly stated conditions and default to habitual reasoning trajectories, leading to incorrect conclusions. This behavior presents significant challenges, particularly in domains such as mathematics and logic puzzle, where precise adherence to specified constraints is critical. To systematically investigate reasoning rigidity, a behavior largely unexplored in prior work, we introduce a expert-curated diagnostic set, . Our dataset includes specially modified variants of existing mathematical benchmarks, namely AIME and MATH500, as well as well-known puzzles deliberately redesigned to require deviation from familiar reasoning strategies. Using this dataset, we identify recurring contamination patterns that occur when models default to ingrained reasoning. Specifically, we categorize this contamination into three distinctive modes: (i) Interpretation Overload, (ii) Input Distrust, and (iii) Partial Instruction Attention, each causing models to ignore or distort provided instructions. We publicly release our diagnostic set to facilitate future research on mitigating reasoning rigidity in language models.

We introduce a new problem KTRL+F, a knowledge-augmented in-document search task that necessitates real-time identification of all semantic targets within a document with the awareness of external sources through a single natural query. This task addresses following unique challenges for in-document search: 1) utilizing knowledge outside the document for extended use of additional information about targets to bridge the semantic gap between the query and the targets, and 2) balancing between real-time applicability with the performance. We analyze various baselines in KTRL+F and find there are limitations of existing models, such as hallucinations, low latency, or difficulties in leveraging external knowledge. Therefore we propose a Knowledge-Augmented Phrase Retrieval model that shows a promising balance between speed and performance by simply augmenting external knowledge embedding in phrase embedding. Additionally, we conduct a user study to verify whether solving KTRL+F can enhance search experience of users. It demonstrates that even with our simple model users can reduce the time for searching with less queries and reduced extra visits to other sources for collecting evidence. We encourage the research community to work on KTRL+F to enhance more efficient in-document information access.

Although large Vision-Language Models (VLMs) have demonstrated remarkable performance in a wide range of multimodal tasks, their true reasoning capabilities on human IQ tests remain underexplored. To advance research on the fluid intelligence of VLMs, we introduce **IQBench**, a new benchmark designed to evaluate VLMs on standardized visual IQ tests. We focus on evaluating the reasoning capabilities of VLMs, which we argue are more important than the accuracy of the final prediction. **Our benchmark is visually centric, minimizing the dependence on unnecessary textual content**, thus encouraging models to derive answers primarily from image-based information rather than learned textual knowledge. To this end, we manually collected and annotated 500 visual IQ questions to **prevent unintentional data leakage during training**. Unlike prior work that focuses primarily on the accuracy of the final answer, we evaluate the reasoning ability of the models by assessing their explanations and the patterns used to solve each problem, along with the accuracy of the final prediction and human evaluation. Our experiments show that there are substantial performance disparities between tasks, with models such as `o4-mini`, `gemini-2.5-flash`, and `claude-3.7-sonnet` achieving the highest average accuracies of 0.615, 0.578, and 0.548, respectively. However, all models struggle with 3D spatial and anagram reasoning tasks, highlighting significant limitations in current VLMs' general reasoning abilities. In terms of reasoning scores, `o4-mini`, `gemini-2.5-flash`, and `claude-3.7-sonnet` achieved top averages of 0.696, 0.586, and 0.516, respectively. These results highlight inconsistencies between the reasoning processes of the models and their final answers, emphasizing the importance of evaluating the accuracy of the reasoning in addition to the final predictions.

Motivated by reducing the computational and storage costs of LLMs, model compression and KV cache compression have attracted much attention from researchers. However, current methods predominantly emphasize maintaining the performance of compressed LLMs, as measured by perplexity or simple accuracy on tasks of common sense knowledge QA and basic arithmetic reasoning. In this blog, we present a brief review of recent advancements in LLMs related to retrieval-augmented generation, multi-step reasoning, external tools, and computational expressivity, all of which substantially enhance LLM performance. Then, we propose a lottery LLM hypothesis suggesting that for a given LLM and task, there exists a smaller lottery LLM capable of producing the same performance as the original LLM with the assistance of multi-step reasoning and external tools. Based on the review of current progress in LLMs, we discuss and summarize the essential capabilities that the lottery LLM and KV cache compression must possess, which are currently overlooked in existing methods.

The widespread adoption of large language models (LLMs) makes it important to recognize their strengths and limitations. We argue that in order to develop a holistic understanding of these systems we need to consider the problem that they were trained to solve: next-word prediction over Internet text. By recognizing the pressures that this task exerts we can make predictions about the strategies that LLMs will adopt, allowing us to reason about when they will succeed or fail. This approach - which we call the teleological approach - leads us to identify three factors that we hypothesize will influence LLM accuracy: the probability of the task to be performed, the probability of the target output, and the probability of the provided input. We predict that LLMs will achieve higher accuracy when these probabilities are high than when they are low - even in deterministic settings where probability should not matter. To test our predictions, we evaluate two LLMs (GPT-3.5 and GPT-4) on eleven tasks, and we find robust evidence that LLMs are influenced by probability in the ways that we have hypothesized. In many cases, the experiments reveal surprising failure modes. For instance, GPT-4's accuracy at decoding a simple cipher is 51% when the output is a high-probability word sequence but only 13% when it is low-probability. These results show that AI practitioners should be careful about using LLMs in low-probability situations. More broadly, we conclude that we should not evaluate LLMs as if they are humans but should instead treat them as a distinct type of system - one that has been shaped by its own particular set of pressures.

There has been considerable divergence of opinion on the reasoning abilities of Large Language Models (LLMs). While the initial optimism that reasoning might emerge automatically with scale has been tempered thanks to a slew of counterexamples, a wide spread belief in their iterative self-critique capabilities persists. In this paper, we set out to systematically investigate the effectiveness of iterative prompting of LLMs in the context of Graph Coloring, a canonical NP-complete reasoning problem that is related to propositional satisfiability as well as practical problems like scheduling and allocation. We present a principled empirical study of the performance of GPT4 in solving graph coloring instances or verifying the correctness of candidate colorings. In iterative modes, we experiment with the model critiquing its own answers and an external correct reasoner verifying proposed solutions. In both cases, we analyze whether the content of the criticisms actually affects bottom line performance. The study seems to indicate that (i) LLMs are bad at solving graph coloring instances (ii) they are no better at verifying a solution--and thus are not effective in iterative modes with LLMs critiquing LLM-generated solutions (iii) the correctness and content of the criticisms--whether by LLMs or external solvers--seems largely irrelevant to the performance of iterative prompting. We show that the observed increase in effectiveness is largely due to the correct solution being fortuitously present in the top-k completions of the prompt (and being recognized as such by an external verifier). Our results thus call into question claims about the self-critiquing capabilities of state of the art LLMs.

A key component of successfully reading a passage of text is the ability to apply knowledge gained from the passage to a new situation. In order to facilitate progress on this kind of reading, we present ROPES, a challenging benchmark for reading comprehension targeting Reasoning Over Paragraph Effects in Situations. We target expository language describing causes and effects (e.g., "animal pollinators increase efficiency of fertilization in flowers"), as they have clear implications for new situations. A system is presented a background passage containing at least one of these relations, a novel situation that uses this background, and questions that require reasoning about effects of the relationships in the background passage in the context of the situation. We collect background passages from science textbooks and Wikipedia that contain such phenomena, and ask crowd workers to author situations, questions, and answers, resulting in a 14,322 question dataset. We analyze the challenges of this task and evaluate the performance of state-of-the-art reading comprehension models. The best model performs only slightly better than randomly guessing an answer of the correct type, at 61.6% F1, well below the human performance of 89.0%.

When deploying large language models (LLMs), it is important to ensure that these models are not only capable, but also reliable. Many benchmarks have been created to track LLMs' growing capabilities, however there has been no similar focus on measuring their reliability. To understand the potential ramifications of this gap, we investigate how well current benchmarks quantify model reliability. We find that pervasive label errors can compromise these evaluations, obscuring lingering model failures and hiding unreliable behavior. Motivated by this gap in the evaluation of reliability, we then propose the concept of so-called platinum benchmarks, i.e., benchmarks carefully curated to minimize label errors and ambiguity. As a first attempt at constructing such benchmarks, we revise examples from fifteen existing popular benchmarks. We evaluate a wide range of models on these platinum benchmarks and find that, indeed, frontier LLMs still exhibit failures on simple tasks such as elementary-level math word problems. Analyzing these failures further reveals previously unidentified patterns of problems on which frontier models consistently struggle. We provide code at https://github.com/MadryLab/platinum-benchmarks

Recent progress in large language models (LLMs) highlights the power of scaling test-time compute to achieve strong performance on complex tasks, such as mathematical reasoning and code generation. This raises a critical question: how should model training be modified to optimize performance under a subsequent test-time compute strategy and budget? To explore this, we focus on pass@N, a simple test-time strategy that searches for a correct answer in N independent samples. We show, surprisingly, that training with cross-entropy (CE) loss can be {it misaligned} with pass@N in that pass@N accuracy {it decreases} with longer training. We explain the origins of this misalignment in terms of model overconfidence induced by CE, and experimentally verify our prediction of overconfidence as an impediment to scaling test-time compute via pass@N. Furthermore we suggest a principled, modified training loss that is better aligned to pass@N by limiting model confidence and rescuing pass@N test performance. Our algorithm demonstrates improved mathematical reasoning on MATH and MiniF2F benchmarks under several scenarios: (1) providing answers to math questions; and (2) proving theorems by searching over proof trees of varying shapes. Overall our work underscores the importance of co-designing two traditionally separate phases of LLM development: training-time protocols and test-time search and reasoning strategies.

Reasoning models have achieved remarkable performance on tasks like math and logical reasoning thanks to their ability to search during reasoning. However, they still suffer from overthinking, often performing unnecessary reasoning steps even after reaching the correct answer. This raises the question: can models evaluate the correctness of their intermediate answers during reasoning? In this work, we study whether reasoning models encode information about answer correctness through probing the model's hidden states. The resulting probe can verify intermediate answers with high accuracy and produces highly calibrated scores. Additionally, we find models' hidden states encode correctness of future answers, enabling early prediction of the correctness before the intermediate answer is fully formulated. We then use the probe as a verifier to decide whether to exit reasoning at intermediate answers during inference, reducing the number of inference tokens by 24\% without compromising performance. These findings confirm that reasoning models do encode a notion of correctness yet fail to exploit it, revealing substantial untapped potential to enhance their efficiency.

Recent work on open domain question answering (QA) assumes strong supervision of the supporting evidence and/or assumes a blackbox information retrieval (IR) system to retrieve evidence candidates. We argue that both are suboptimal, since gold evidence is not always available, and QA is fundamentally different from IR. We show for the first time that it is possible to jointly learn the retriever and reader from question-answer string pairs and without any IR system. In this setting, evidence retrieval from all of Wikipedia is treated as a latent variable. Since this is impractical to learn from scratch, we pre-train the retriever with an Inverse Cloze Task. We evaluate on open versions of five QA datasets. On datasets where the questioner already knows the answer, a traditional IR system such as BM25 is sufficient. On datasets where a user is genuinely seeking an answer, we show that learned retrieval is crucial, outperforming BM25 by up to 19 points in exact match.

We propose a new benchmark to measure a language model's linguistic reasoning skills without relying on pre-existing language-specific knowledge. The test covers 894 questions grouped in 160 problems across 75 (mostly) extremely low-resource languages, extracted from the International Linguistic Olympiad corpus. To attain high accuracy on this benchmark, models don't need previous knowledge of the tested language, as all the information needed to solve the linguistic puzzle is presented in the context. We find that, while all analyzed models rank below 25% accuracy, there is a significant gap between open and closed models, with the best-performing proprietary model at 24.05% and the best-performing open model at 8.84%.

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.

The current evaluation of mathematical skills in LLMs is limited, as existing benchmarks are either relatively small, primarily focus on elementary and high-school problems, or lack diversity in topics. Additionally, the inclusion of visual elements in tasks remains largely under-explored. To address these gaps, we introduce U-MATH, a novel benchmark of 1,100 unpublished open-ended university-level problems sourced from teaching materials. It is balanced across six core subjects, with 20% of multimodal problems. Given the open-ended nature of U-MATH problems, we employ an LLM to judge the correctness of generated solutions. To this end, we release mu-MATH, a dataset to evaluate the LLMs' capabilities in judging solutions. The evaluation of general domain, math-specific, and multimodal LLMs highlights the challenges presented by U-MATH. Our findings reveal that LLMs achieve a maximum accuracy of only 63% on text-based tasks, with even lower 45% on visual problems. The solution assessment proves challenging for LLMs, with the best LLM judge having an F1-score of 80% on mu-MATH.

Educational crosswords offer numerous benefits for students, including increased engagement, improved understanding, critical thinking, and memory retention. Creating high-quality educational crosswords can be challenging, but recent advances in natural language processing and machine learning have made it possible to use language models to generate nice wordplays. The exploitation of cutting-edge language models like GPT3-DaVinci, GPT3-Curie, GPT3-Babbage, GPT3-Ada, and BERT-uncased has led to the development of a comprehensive system for generating and verifying crossword clues. A large dataset of clue-answer pairs was compiled to fine-tune the models in a supervised manner to generate original and challenging clues from a given keyword. On the other hand, for generating crossword clues from a given text, Zero/Few-shot learning techniques were used to extract clues from the input text, adding variety and creativity to the puzzles. We employed the fine-tuned model to generate data and labeled the acceptability of clue-answer parts with human supervision. To ensure quality, we developed a classifier by fine-tuning existing language models on the labeled dataset. Conversely, to assess the quality of clues generated from the given text using zero/few-shot learning, we employed a zero-shot learning approach to check the quality of generated clues. The results of the evaluation have been very promising, demonstrating the effectiveness of the approach in creating high-standard educational crosswords that offer students engaging and rewarding learning experiences.

Recent breakthroughs in large language models (LLMs) have effectively improved their reasoning abilities, particularly on mathematical and logical problems that have verifiable answers, through techniques such as supervised finetuning (SFT) and reinforcement learning (RL). Prior research indicates that RL effectively internalizes search strategies, enabling long chain-of-thought (CoT) reasoning, with backtracking emerging naturally as a learned capability. However, the precise benefits of backtracking, specifically, how significantly it contributes to reasoning improvements and the optimal extent of its use, remain poorly understood. In this work, we systematically investigate the dynamics between SFT and RL on eight reasoning tasks: Countdown, Sudoku, Arc 1D, Geometry, Color Cube Rotation, List Functions, Zebra Puzzles, and Self Reference. Our findings highlight that short CoT sequences used in SFT as a warm-up do have moderate contribution to RL training, compared with cold-start RL; however such contribution diminishes when tasks become increasingly difficult. Motivated by this observation, we construct synthetic datasets varying systematically in the number of backtracking steps and conduct controlled experiments to isolate the influence of either the correctness (content) or the structure (i.e., backtrack frequency). We find that (1) longer CoT with backtracks generally induce better and more stable RL training, (2) more challenging problems with larger search space tend to need higher numbers of backtracks during the SFT stage. Additionally, we demonstrate through experiments on distilled data that RL training is largely unaffected by the correctness of long CoT sequences, suggesting that RL prioritizes structural patterns over content correctness. Collectively, our results offer practical insights into designing optimal training strategies to effectively scale reasoning in LLMs.

Large Language Models (LLMs) have demonstrated promising capabilities in solving mathematical reasoning tasks, leveraging Chain-of-Thought (CoT) data as a vital component in guiding answer generation. Current paradigms typically generate CoT and answers directly for a given problem, diverging from human problem-solving strategies to some extent. Humans often solve problems by recalling analogous cases and leveraging their solutions to reason about the current task. Inspired by this cognitive process, we propose MetaLadder, a novel framework that explicitly prompts LLMs to recall and reflect on meta-problems, those structurally or semantically analogous problems, alongside their CoT solutions before addressing the target problem. Additionally, we introduce a problem-restating mechanism to enhance the model's comprehension of the target problem by regenerating the original question, which further improves reasoning accuracy. Therefore, the model can achieve reasoning transfer from analogical problems, mimicking human-like "learning from examples" and generalization abilities. Extensive experiments on mathematical benchmarks demonstrate that our MetaLadder significantly boosts LLMs' problem-solving accuracy, largely outperforming standard CoT-based methods (10.3\% accuracy gain) and other methods. Our code and data has been released at https://github.com/LHL3341/MetaLadder.

As language models regularly make mistakes when solving math problems, automated identification of errors in the reasoning process becomes increasingly significant for their scalable oversight. In this paper, we introduce ProcessBench for measuring the ability to identify erroneous steps in mathematical reasoning. It consists of 3,400 test cases, primarily focused on competition- and Olympiad-level math problems. Each test case contains a step-by-step solution with error location annotated by human experts. Models are required to identify the earliest step that contains an error, or conclude that all steps are correct. We conduct extensive evaluation on ProcessBench, involving two types of models: process reward models (PRMs) and critic models, where for the latter we prompt general language models to critique each solution step by step. We draw two main observations: (1) Existing PRMs typically fail to generalize to more challenging math problems beyond GSM8K and MATH. They underperform both critic models (i.e., prompted general language models) and our own trained PRM that is straightforwardly fine-tuned on the PRM800K dataset. (2) The best open-source model, QwQ-32B-Preview, has demonstrated the critique capability competitive with the proprietary model GPT-4o, despite that it still lags behind the reasoning-specialized o1-mini. We hope ProcessBench can foster future research in reasoning process assessment, paving the way toward scalable oversight of language models.

Recent Language Models (LMs) achieve breakthrough performance in code generation when trained on human-authored problems, even solving some competitive-programming problems. Self-play has proven useful in games such as Go, and thus it is natural to ask whether LMs can generate their own instructive programming problems to improve their performance. We show that it is possible for an LM to synthesize programming problems and solutions, which are filtered for correctness by a Python interpreter. The LM's performance is then seen to improve when it is fine-tuned on its own synthetic problems and verified solutions; thus the model 'improves itself' using the Python interpreter. Problems are specified formally as programming puzzles [Schuster et al., 2021], a code-based problem format where solutions can easily be verified for correctness by execution. In experiments on publicly-available LMs, test accuracy more than doubles. This work demonstrates the potential for code LMs, with an interpreter, to generate instructive problems and improve their own performance.

A standard way to evaluate the abilities of LLM involves presenting a multiple-choice question and selecting the option with the highest logit as the model's predicted answer. However, such a format for evaluating LLMs has limitations, since even if the model knows the correct answer, it may struggle to select the corresponding letter simply due to difficulties in following this rigid format. To address this, we introduce new scores that better capture and reveal model's underlying knowledge: the Query-Key Score (QK-score), derived from the interaction between query and key representations in attention heads, and the Attention Score, based on attention weights. These scores are extracted from specific select-and-copy heads, which show consistent performance across popular Multi-Choice Question Answering (MCQA) datasets. Based on these scores, our method improves knowledge extraction, yielding up to 16\% gain for LLaMA2-7B and up to 10\% for larger models on popular MCQA benchmarks. At the same time, the accuracy on a simple synthetic dataset, where the model explicitly knows the right answer, increases by almost 60\%, achieving nearly perfect accuracy, therefore demonstrating the method's efficiency in mitigating MCQA format limitations. To support our claims, we conduct experiments on models ranging from 7 billion to 70 billion parameters in both zero- and few-shot setups.

Large language models (LLMs) are regularly evaluated using benchmark datasets. But what justifies making inferences about an LLM's capabilities based on its answers to a curated set of questions? This paper first introduces a formal framework to address this question. The key is to note that the benchmarks used to test LLMs -- such as AP exams -- are also those used to test people. However, this raises an implication: these benchmarks are only valid tests if LLMs misunderstand concepts in ways that mirror human misunderstandings. Otherwise, success on benchmarks only demonstrates potemkin understanding: the illusion of understanding driven by answers irreconcilable with how any human would interpret a concept. We present two procedures for quantifying the existence of potemkins: one using a specially designed benchmark in three domains, the other using a general procedure that provides a lower-bound on their prevalence. We find that potemkins are ubiquitous across models, tasks, and domains. We also find that these failures reflect not just incorrect understanding, but deeper internal incoherence in concept representations.

We present Hermes 4, a family of hybrid reasoning models that combine structured, multi-turn reasoning with broad instruction-following ability. We describe the challenges encountered during data curation, synthesis, training, and evaluation, and outline the solutions employed to address these challenges at scale. We comprehensively evaluate across mathematical reasoning, coding, knowledge, comprehension, and alignment benchmarks, and we report both quantitative performance and qualitative behavioral analysis. To support open research, all model weights are published publicly at https://huggingface.co/collections/NousResearch/hermes-4-collection-68a731bfd452e20816725728

Recent studies on large language model (LLM) reasoning capabilities have demonstrated promising improvements in model performance by leveraging a lengthy thinking process and additional computational resources during inference, primarily in tasks involving mathematical reasoning (Muennighoff et al., 2025). However, it remains uncertain if longer reasoning chains inherently enhance factual accuracy, particularly beyond mathematical contexts. In this work, we thoroughly examine LLM reasoning within complex open-domain question-answering (QA) scenarios. We initially distill reasoning traces from advanced, large-scale reasoning models (QwQ-32B and DeepSeek-R1-671B), then fine-tune a variety of models ranging from smaller, instruction-tuned variants to larger architectures based on Qwen2.5. To enrich reasoning traces, we introduce factual information from knowledge graphs in the form of paths into our reasoning traces. Our experimental setup includes four baseline approaches and six different instruction-tuned models evaluated across a benchmark of six datasets, encompassing over 22.6K questions. Overall, we carry out 168 experimental runs and analyze approximately 1.7 million reasoning traces. Our findings indicate that, within a single run, smaller reasoning models achieve noticeable improvements in factual accuracy compared to their original instruction-tuned counterparts. Moreover, our analysis demonstrates that adding test-time compute and token budgets factual accuracy consistently improves by 2-8%, further confirming the effectiveness of test-time scaling for enhancing performance and consequently improving reasoning accuracy in open-domain QA tasks. We release all the experimental artifacts for further research.

There is a growing literature on reasoning by large language models (LLMs), but the discussion on the uncertainty in their responses is still lacking. Our aim is to assess the extent of confidence that LLMs have in their answers and how it correlates with accuracy. Confidence is measured (i) qualitatively in terms of persistence in keeping their answer when prompted to reconsider, and (ii) quantitatively in terms of self-reported confidence score. We investigate the performance of three LLMs -- GPT4o, GPT4-turbo and Mistral -- on two benchmark sets of questions on causal judgement and formal fallacies and a set of probability and statistical puzzles and paradoxes. Although the LLMs show significantly better performance than random guessing, there is a wide variability in their tendency to change their initial answers. There is a positive correlation between qualitative confidence and accuracy, but the overall accuracy for the second answer is often worse than for the first answer. There is a strong tendency to overstate the self-reported confidence score. Confidence is only partially explained by the underlying token-level probability. The material effects of prompting on qualitative confidence and the strong tendency for overconfidence indicate that current LLMs do not have any internally coherent sense of confidence.

Large reasoning models (LRMs) show strong capabilities in complex reasoning, yet their marginal gains on evidence-dependent factual questions are limited. We find this limitation is partially attributable to a reasoning-answer hit gap, where the model identifies the correct facts during reasoning but fails to incorporate them into the final response, thereby reducing factual fidelity. To address this issue, we propose MR-ALIGN, a Meta-Reasoning informed alignment framework that enhances factuality without relying on external verifiers. MR-ALIGN quantifies state transition probabilities along the model's thinking process and constructs a transition-aware implicit reward that reinforces beneficial reasoning patterns while suppressing defective ones at the atomic thinking segments. This re-weighting reshapes token-level signals into probability-aware segment scores, encouraging coherent reasoning trajectories that are more conducive to factual correctness. Empirical evaluations across four factual QA datasets and one long-form factuality benchmark show that MR-ALIGN consistently improves accuracy and truthfulness while reducing misleading reasoning. These results highlight that aligning the reasoning process itself, rather than merely the outputs, is pivotal for advancing factuality in LRMs.

The advent of natural language understanding (NLU) benchmarks for English, such as GLUE and SuperGLUE allows new NLU models to be evaluated across a diverse set of tasks. These comprehensive benchmarks have facilitated a broad range of research and applications in natural language processing (NLP). The problem, however, is that most such benchmarks are limited to English, which has made it difficult to replicate many of the successes in English NLU for other languages. To help remedy this issue, we introduce the first large-scale Chinese Language Understanding Evaluation (CLUE) benchmark. CLUE is an open-ended, community-driven project that brings together 9 tasks spanning several well-established single-sentence/sentence-pair classification tasks, as well as machine reading comprehension, all on original Chinese text. To establish results on these tasks, we report scores using an exhaustive set of current state-of-the-art pre-trained Chinese models (9 in total). We also introduce a number of supplementary datasets and additional tools to help facilitate further progress on Chinese NLU. Our benchmark is released at https://www.CLUEbenchmarks.com

Current NLP datasets targeting ambiguity can be solved by a native speaker with relative ease. We present Cryptonite, a large-scale dataset based on cryptic crosswords, which is both linguistically complex and naturally sourced. Each example in Cryptonite is a cryptic clue, a short phrase or sentence with a misleading surface reading, whose solving requires disambiguating semantic, syntactic, and phonetic wordplays, as well as world knowledge. Cryptic clues pose a challenge even for experienced solvers, though top-tier experts can solve them with almost 100% accuracy. Cryptonite is a challenging task for current models; fine-tuning T5-Large on 470k cryptic clues achieves only 7.6% accuracy, on par with the accuracy of a rule-based clue solver (8.6%).

Rebus puzzles, visual riddles that encode language through imagery, spatial arrangement, and symbolic substitution, pose a unique challenge to current vision-language models (VLMs). Unlike traditional image captioning or question answering tasks, rebus solving requires multi-modal abstraction, symbolic reasoning, and a grasp of cultural, phonetic and linguistic puns. In this paper, we investigate the capacity of contemporary VLMs to interpret and solve rebus puzzles by constructing a hand-generated and annotated benchmark of diverse English-language rebus puzzles, ranging from simple pictographic substitutions to spatially-dependent cues ("head" over "heels"). We analyze how different VLMs perform, and our findings reveal that while VLMs exhibit some surprising capabilities in decoding simple visual clues, they struggle significantly with tasks requiring abstract reasoning, lateral thinking, and understanding visual metaphors.

Accurate estimation of item (question or task) difficulty is critical for educational assessment but suffers from the cold start problem. While Large Language Models demonstrate superhuman problem-solving capabilities, it remains an open question whether they can perceive the cognitive struggles of human learners. In this work, we present a large-scale empirical analysis of Human-AI Difficulty Alignment for over 20 models across diverse domains such as medical knowledge and mathematical reasoning. Our findings reveal a systematic misalignment where scaling up model size is not reliably helpful; instead of aligning with humans, models converge toward a shared machine consensus. We observe that high performance often impedes accurate difficulty estimation, as models struggle to simulate the capability limitations of students even when being explicitly prompted to adopt specific proficiency levels. Furthermore, we identify a critical lack of introspection, as models fail to predict their own limitations. These results suggest that general problem-solving capability does not imply an understanding of human cognitive struggles, highlighting the challenge of using current models for automated difficulty prediction.

Large Language Models (LLMs) have shown impressive performance on various benchmarks, yet their ability to engage in deliberate reasoning remains questionable. We present NYT-Connections, a collection of 358 simple word classification puzzles derived from the New York Times Connections game. This benchmark is designed to penalize quick, intuitive "System 1" thinking, isolating fundamental reasoning skills. We evaluated six recent LLMs, a simple machine learning heuristic, and humans across three configurations: single-attempt, multiple attempts without hints, and multiple attempts with contextual hints. Our findings reveal a significant performance gap: even top-performing LLMs like GPT-4 fall short of human performance by nearly 30%. Notably, advanced prompting techniques such as Chain-of-Thought and Self-Consistency show diminishing returns as task difficulty increases. NYT-Connections uniquely combines linguistic isolation, resistance to intuitive shortcuts, and regular updates to mitigate data leakage, offering a novel tool for assessing LLM reasoning capabilities.