Daily Papers

Evaluating the performance of visual language models (VLMs) in graphic reasoning tasks has become an important research topic. However, VLMs still show obvious deficiencies in simulating human-level graphic reasoning capabilities, especially in complex graphic reasoning and abstract problem solving, which are less studied and existing studies only focus on simple graphics. To evaluate the performance of VLMs in complex graphic reasoning, we propose ReasonBench, the first evaluation benchmark focused on structured graphic reasoning tasks, which includes 1,613 questions from real-world intelligence tests. ReasonBench covers reasoning dimensions related to location, attribute, quantity, and multi-element tasks, providing a comprehensive evaluation of the performance of VLMs in spatial, relational, and abstract reasoning capabilities. We benchmark 11 mainstream VLMs (including closed-source and open-source models) and reveal significant limitations of current models. Based on these findings, we propose a dual optimization strategy: Diagrammatic Reasoning Chain (DiaCoT) enhances the interpretability of reasoning by decomposing layers, and ReasonTune enhances the task adaptability of model reasoning through training, all of which improves VLM performance by 33.5\%. All experimental data and code are in the repository: https://huggingface.co/datasets/cistine/ReasonBench.

We provide conceptual and mathematical foundations for near-term quantum natural language processing (QNLP), and do so in quantum computer scientist friendly terms. We opted for an expository presentation style, and provide references for supporting empirical evidence and formal statements concerning mathematical generality. We recall how the quantum model for natural language that we employ canonically combines linguistic meanings with rich linguistic structure, most notably grammar. In particular, the fact that it takes a quantum-like model to combine meaning and structure, establishes QNLP as quantum-native, on par with simulation of quantum systems. Moreover, the now leading Noisy Intermediate-Scale Quantum (NISQ) paradigm for encoding classical data on quantum hardware, variational quantum circuits, makes NISQ exceptionally QNLP-friendly: linguistic structure can be encoded as a free lunch, in contrast to the apparently exponentially expensive classical encoding of grammar. Quantum speed-up for QNLP tasks has already been established in previous work with Will Zeng. Here we provide a broader range of tasks which all enjoy the same advantage. Diagrammatic reasoning is at the heart of QNLP. Firstly, the quantum model interprets language as quantum processes via the diagrammatic formalism of categorical quantum mechanics. Secondly, these diagrams are via ZX-calculus translated into quantum circuits. Parameterisations of meanings then become the circuit variables to be learned. Our encoding of linguistic structure within quantum circuits also embodies a novel approach for establishing word-meanings that goes beyond the current standards in mainstream AI, by placing linguistic structure at the heart of Wittgenstein's meaning-is-context.

Human reasoning relies on constructing and manipulating mental models-simplified internal representations of situations that we use to understand and solve problems. Conceptual diagrams (for example, sketches drawn by humans to aid reasoning) externalize these mental models, abstracting irrelevant details to efficiently capture relational and spatial information. In contrast, Large Language Models (LLMs) and Large Multimodal Models (LMMs) predominantly reason through textual representations, limiting their effectiveness in complex multi-step combinatorial and planning tasks. In this paper, we propose a zero-shot fully automatic framework that enables LMMs to reason through multiple chains of self-generated intermediate conceptual diagrams, significantly enhancing their combinatorial planning capabilities. Our approach does not require any human initialization beyond a natural language description of the task. It integrates both textual and diagrammatic reasoning within an optimized graph-of-thought inference framework, enhanced by beam search and depth-wise backtracking. Evaluated on multiple challenging PDDL planning domains, our method substantially improves GPT-4o's performance (for example, from 35.5% to 90.2% in Blocksworld). On more difficult planning domains with solution depths up to 40, our approach outperforms even the o1-preview reasoning model (for example, over 13% improvement in Parking). These results highlight the value of conceptual diagrams as a complementary reasoning medium in LMMs.

Geometry problem solving (GPS) represents a critical frontier in artificial intelligence, with profound applications in education, computer-aided design, and computational graphics. Despite its significance, automating GPS remains challenging due to the dual demands of spatial understanding and rigorous logical reasoning. Recent advances in large models have enabled notable breakthroughs, particularly for SAT-level problems, yet the field remains fragmented across methodologies, benchmarks, and evaluation frameworks. This survey systematically synthesizes GPS advancements through three core dimensions: (1) benchmark construction, (2) textual and diagrammatic parsing, and (3) reasoning paradigms. We further propose a unified analytical paradigm, assess current limitations, and identify emerging opportunities to guide future research toward human-level geometric reasoning, including automated benchmark generation and interpretable neuro-symbolic integration.

We introduce Diagram of Thought (DoT), a framework that models iterative reasoning in large language models (LLMs) as the construction of a directed acyclic graph (DAG) within a single model. Unlike traditional approaches that represent reasoning as linear chains or trees, DoT organizes propositions, critiques, refinements, and verifications into a cohesive DAG structure, allowing the model to explore complex reasoning pathways while maintaining logical consistency. Each node in the diagram corresponds to a proposition that has been proposed, critiqued, refined, or verified, enabling the LLM to iteratively improve its reasoning through natural language feedback. By leveraging auto-regressive next-token prediction with role-specific tokens, DoT facilitates seamless transitions between proposing ideas and critically evaluating them, providing richer feedback than binary signals. Furthermore, we formalize the DoT framework using Topos Theory, providing a mathematical foundation that ensures logical consistency and soundness in the reasoning process. This approach enhances both the training and inference processes within a single LLM, eliminating the need for multiple models or external control mechanisms. DoT offers a conceptual framework for designing next-generation reasoning-specialized models, emphasizing training efficiency, robust reasoning capabilities, and theoretical grounding. The code is available at https://github.com/diagram-of-thought/diagram-of-thought.

Visual language is a system of communication that conveys information through symbols, shapes, and spatial arrangements. Diagrams are a typical example of a visual language depicting complex concepts and their relationships in the form of an image. The symbolic nature of diagrams presents significant challenges for building models capable of understanding them. Yet, recent studies seem to suggest that Large Vision-Language Models (LVLMs) can even tackle complex reasoning tasks involving diagrams. In this paper, we investigate this phenomenon by developing a comprehensive test suite to evaluate the diagram comprehension capability of LVLMs. Our test suite uses a variety of questions focused on concept entities and their relationships over a set of synthetic as well as real diagrams across several domains to evaluate the recognition and reasoning abilities of models. Our evaluation of three LVLMs (GPT-4V, GPT-4o, and Gemini) shows that while these models can accurately identify and reason about entities, their ability to understand relationships is notably limited. Further testing reveals that the decent performance on diagram understanding largely stems from leveraging their background knowledge as shortcuts to identify and reason about the relational information. Thus, we conclude that LVLMs have a limited capability for genuine diagram understanding, and their impressive performance in diagram reasoning is an illusion emanating from other confounding factors, such as the background knowledge in the models.

Chain-of-thought traces have been shown to improve performance of large language models in a plethora of reasoning tasks, yet there is no consensus on the mechanism through which this performance boost is achieved. To shed more light on this, we introduce Causal CoT Graphs (CCGs), which are directed acyclic graphs automatically extracted from reasoning traces that model fine-grained causal dependencies in the language model output. A collection of 1671 mathematical reasoning problems from MATH500, GSM8K and AIME, and their associated CCGs are compiled into our dataset -- KisMATH. Our detailed empirical analysis with 15 open-weight LLMs shows that (i) reasoning nodes in the CCG are mediators for the final answer, a condition necessary for reasoning; and (ii) LLMs emphasise reasoning paths given by the CCG, indicating that models internally realise structures akin to our graphs. KisMATH enables controlled, graph-aligned interventions and opens up avenues for further investigation into the role of chain-of-thought in LLM reasoning.

Large language models have shown impressive results for multi-hop mathematical reasoning when the input question is only textual. Many mathematical reasoning problems, however, contain both text and image. With the ever-increasing adoption of vision language models (VLMs), understanding their reasoning abilities for such problems is crucial. In this paper, we evaluate the reasoning capabilities of VLMs along various axes through the lens of geometry problems. We procedurally create a synthetic dataset of geometry questions with controllable difficulty levels along multiple axes, thus enabling a systematic evaluation. The empirical results obtained using our benchmark for state-of-the-art VLMs indicate that these models are not as capable in subjects like geometry (and, by generalization, other topics requiring similar reasoning) as suggested by previous benchmarks. This is made especially clear by the construction of our benchmark at various depth levels, since solving higher-depth problems requires long chains of reasoning rather than additional memorized knowledge. We release the dataset for further research in this area.

Text-to-image (T2I) generation has seen significant growth over the past few years. Despite this, there has been little work on generating diagrams with T2I models. A diagram is a symbolic/schematic representation that explains information using structurally rich and spatially complex visualizations (e.g., a dense combination of related objects, text labels, directional arrows, connection lines, etc.). Existing state-of-the-art T2I models often fail at diagram generation because they lack fine-grained object layout control when many objects are densely connected via complex relations such as arrows/lines and also often fail to render comprehensible text labels. To address this gap, we present DiagrammerGPT, a novel two-stage text-to-diagram generation framework that leverages the layout guidance capabilities of LLMs (e.g., GPT-4) to generate more accurate open-domain, open-platform diagrams. In the first stage, we use LLMs to generate and iteratively refine 'diagram plans' (in a planner-auditor feedback loop) which describe all the entities (objects and text labels), their relationships (arrows or lines), and their bounding box layouts. In the second stage, we use a diagram generator, DiagramGLIGEN, and a text label rendering module to generate diagrams following the diagram plans. To benchmark the text-to-diagram generation task, we introduce AI2D-Caption, a densely annotated diagram dataset built on top of the AI2D dataset. We show quantitatively and qualitatively that our DiagrammerGPT framework produces more accurate diagrams, outperforming existing T2I models. We also provide comprehensive analysis including open-domain diagram generation, vector graphic diagram generation in different platforms, human-in-the-loop diagram plan editing, and multimodal planner/auditor LLMs (e.g., GPT-4Vision). We hope our work can inspire further research on diagram generation via T2I models and LLMs.

Large Language Models (LLMs) have showcased impressive reasoning capabilities, particularly when guided by specifically designed prompts in complex reasoning tasks such as math word problems. These models typically solve tasks using a chain-of-thought approach, which not only bolsters their reasoning abilities but also provides valuable insights into their problem-solving process. However, there is still significant room for enhancing the reasoning abilities of LLMs. Some studies suggest that the integration of an LLM output verifier can boost reasoning accuracy without necessitating additional model training. In this paper, we follow these studies and introduce a novel graph-based method to further augment the reasoning capabilities of LLMs. We posit that multiple solutions to a reasoning task, generated by an LLM, can be represented as a reasoning graph due to the logical connections between intermediate steps from different reasoning paths. Therefore, we propose the Reasoning Graph Verifier (RGV) to analyze and verify the solutions generated by LLMs. By evaluating these graphs, models can yield more accurate and reliable results.Our experimental results show that our graph-based verification method not only significantly enhances the reasoning abilities of LLMs but also outperforms existing verifier methods in terms of improving these models' reasoning performance.

Exploiting large language models (LLMs) to tackle deductive reasoning has garnered growing attention. It still remains highly challenging to achieve satisfactory results in complex deductive problems, characterized by plenty of premises (i.e., facts or rules) entailing intricate relationships among entities and requiring multi-hop reasoning. One intuitive solution is to decompose the original task into smaller sub-tasks, and then chain the multiple casual reasoning steps together in a forward (e.g., Selection-Inference) or backward (e.g., LAMBADA) direction. However, these techniques inevitably necessitate a large number of overall stages, leading to computationally expensive operations and a higher possibility of making misleading steps. In addition to stage-by-stage decomposition, we draw inspiration from another aspect of human problem-solving. Humans tend to distill the most relevant information and organize their thoughts systematically (e.g., creating mind maps), which assists them in answering questions or drawing conclusions precisely and quickly. In light of this, we propose a novel reasoning approach named Concise and Organized Perception (COP). COP carefully analyzes the given statements to efficiently identify the most pertinent information while eliminating redundancy. It then prompts the LLMs in a more organized form that adapts to the model's inference process. By perceiving concise and organized proofs, the deductive reasoning abilities of LLMs can be better elicited, and the risk of acquiring errors caused by excessive reasoning stages is mitigated. Furthermore, our approach can be combined with the aforementioned ones to further boost their performance. Extensive experimental results on three popular deductive benchmarks (i.e., ProofWriter, PrOntoQA and PrOntoQA-OOD) show that COP significantly outperforms previous state-of-the-art methods.

Reasoning is a fundamental capability for solving complex multi-step problems, particularly in visual contexts where sequential step-wise understanding is essential. Existing approaches lack a comprehensive framework for evaluating visual reasoning and do not emphasize step-wise problem-solving. To this end, we propose a comprehensive framework for advancing step-by-step visual reasoning in large language models (LMMs) through three key contributions. First, we introduce a visual reasoning benchmark specifically designed to evaluate multi-step reasoning tasks. The benchmark presents a diverse set of challenges with eight different categories ranging from complex visual perception to scientific reasoning with over 4k reasoning steps in total, enabling robust evaluation of LLMs' abilities to perform accurate and interpretable visual reasoning across multiple steps. Second, we propose a novel metric that assesses visual reasoning quality at the granularity of individual steps, emphasizing both correctness and logical coherence. The proposed metric offers deeper insights into reasoning performance compared to traditional end-task accuracy metrics. Third, we present a new multimodal visual reasoning model, named LlamaV-o1, trained using a multi-step curriculum learning approach, where tasks are progressively organized to facilitate incremental skill acquisition and problem-solving. The proposed LlamaV-o1 is designed for multi-step reasoning and learns step-by-step through a structured training paradigm. Extensive experiments show that our LlamaV-o1 outperforms existing open-source models and performs favorably against close-source proprietary models. Compared to the recent Llava-CoT, our LlamaV-o1 achieves an average score of 67.3 with an absolute gain of 3.8\% across six benchmarks while being 5 times faster during inference scaling. Our benchmark, model, and code are publicly available.

Understanding and reasoning over diagrams is a fundamental aspect of human intelligence. While Large Multimodal Models (LMMs) have demonstrated impressive capabilities across various tasks, existing benchmarks lack comprehensive evaluation of their diagram interpretation and reasoning abilities, particularly in coding contexts. We present HumanEval-V, a rigorous benchmark of human-annotated coding tasks that spans six task types and evaluates diverse visual reasoning capabilities. Each task features carefully crafted diagrams paired with function signatures and test cases, employing novel code generation tasks to thoroughly assess models' diagram comprehension. Through extensive experiments with 22 LMMs, we find that even top-performing models achieve modest success rates, with Claude 3.5 Sonnet reaching only 36.8% pass@1, highlighting substantial room for improvement. Our analysis reveals that current LMMs struggle with spatial transformations, topological relationships, and dynamic patterns that humans find intuitive. These findings provide valuable insights for advancing LMMs' visual reasoning abilities. We have open-sourced our code and benchmark at https://github.com/HumanEval-V/HumanEval-V-Benchmark.

Despite strong performance on vision-language tasks, Multimodal Large Language Models (MLLMs) struggle with mathematical problem-solving, with both open-source and state-of-the-art models falling short of human performance on visual-math benchmarks. To systematically examine visual-mathematical reasoning in MLLMs, we (1) evaluate their understanding of geometric primitives, (2) test multi-step reasoning, and (3) explore a potential solution to improve visual reasoning capabilities. Our findings reveal fundamental shortcomings in shape recognition, with top models achieving under 50% accuracy in identifying regular polygons. We analyze these failures through the lens of dual-process theory and show that MLLMs rely on System 1 (intuitive, memorized associations) rather than System 2 (deliberate reasoning). Consequently, MLLMs fail to count the sides of both familiar and novel shapes, suggesting they have neither learned the concept of sides nor effectively process visual inputs. Finally, we propose Visually Cued Chain-of-Thought (VC-CoT) prompting, which enhances multi-step mathematical reasoning by explicitly referencing visual annotations in diagrams, boosting GPT-4o's accuracy on an irregular polygon side-counting task from 7% to 93%. Our findings suggest that System 2 reasoning in MLLMs remains an open problem, and visually-guided prompting is essential for successfully engaging visual reasoning. Code available at: https://github.com/rsinghlab/Shape-Blind.

When presented with questions involving visual thinking, humans naturally switch reasoning modalities, often forming mental images or drawing visual aids. Large language models have shown promising results in arithmetic and symbolic reasoning by expressing intermediate reasoning in text as a chain of thought, yet struggle to extend this capability to answer text queries that are easily solved by visual reasoning, even with extensive multimodal pretraining. We introduce a simple method, whiteboard-of-thought prompting, to unlock the visual reasoning capabilities of multimodal large language models across modalities. Whiteboard-of-thought prompting provides multimodal large language models with a metaphorical `whiteboard' to draw out reasoning steps as images, then returns these images back to the model for further processing. We find this can be accomplished with no demonstrations or specialized modules, instead leveraging models' existing ability to write code with libraries such as Matplotlib and Turtle. This simple approach shows state-of-the-art results on four difficult natural language tasks that involve visual and spatial reasoning. We identify multiple settings where GPT-4o using chain-of-thought fails dramatically, including more than one where it achieves 0% accuracy, while whiteboard-of-thought enables up to 92% accuracy in these same settings. We present a detailed exploration of where the technique succeeds as well as its sources of error.

Large Language Models (LLMs) reasoning processes are challenging to analyze due to their complexity and the lack of organized visualization tools. We present ReasonGraph, a web-based platform for visualizing and analyzing LLM reasoning processes. It supports both sequential and tree-based reasoning methods while integrating with major LLM providers and over fifty state-of-the-art models. ReasonGraph incorporates an intuitive UI with meta reasoning method selection, configurable visualization parameters, and a modular framework that facilitates efficient extension. Our evaluation shows high parsing reliability, efficient processing, and strong usability across various downstream applications. By providing a unified visualization framework, ReasonGraph reduces cognitive load in analyzing complex reasoning paths, improves error detection in logical processes, and enables more effective development of LLM-based applications. The platform is open-source, promoting accessibility and reproducibility in LLM reasoning analysis.

Diagrams are common tools for representing complex concepts, relationships and events, often when it would be difficult to portray the same information with natural images. Understanding natural images has been extensively studied in computer vision, while diagram understanding has received little attention. In this paper, we study the problem of diagram interpretation and reasoning, the challenging task of identifying the structure of a diagram and the semantics of its constituents and their relationships. We introduce Diagram Parse Graphs (DPG) as our representation to model the structure of diagrams. We define syntactic parsing of diagrams as learning to infer DPGs for diagrams and study semantic interpretation and reasoning of diagrams in the context of diagram question answering. We devise an LSTM-based method for syntactic parsing of diagrams and introduce a DPG-based attention model for diagram question answering. We compile a new dataset of diagrams with exhaustive annotations of constituents and relationships for over 5,000 diagrams and 15,000 questions and answers. Our results show the significance of our models for syntactic parsing and question answering in diagrams using DPGs.

Reasoning is a fundamental cognitive process that enables logical inference, problem-solving, and decision-making. With the rapid advancement of large language models (LLMs), reasoning has emerged as a key capability that distinguishes advanced AI systems from conventional models that empower chatbots. In this survey, we categorize existing methods along two orthogonal dimensions: (1) Regimes, which define the stage at which reasoning is achieved (either at inference time or through dedicated training); and (2) Architectures, which determine the components involved in the reasoning process, distinguishing between standalone LLMs and agentic compound systems that incorporate external tools, and multi-agent collaborations. Within each dimension, we analyze two key perspectives: (1) Input level, which focuses on techniques that construct high-quality prompts that the LLM condition on; and (2) Output level, which methods that refine multiple sampled candidates to enhance reasoning quality. This categorization provides a systematic understanding of the evolving landscape of LLM reasoning, highlighting emerging trends such as the shift from inference-scaling to learning-to-reason (e.g., DeepSeek-R1), and the transition to agentic workflows (e.g., OpenAI Deep Research, Manus Agent). Additionally, we cover a broad spectrum of learning algorithms, from supervised fine-tuning to reinforcement learning such as PPO and GRPO, and the training of reasoners and verifiers. We also examine key designs of agentic workflows, from established patterns like generator-evaluator and LLM debate to recent innovations. ...

Mathematical reasoning, a core aspect of human cognition, is vital across many domains, from educational problem-solving to scientific advancements. As artificial general intelligence (AGI) progresses, integrating large language models (LLMs) with mathematical reasoning tasks is becoming increasingly significant. This survey provides the first comprehensive analysis of mathematical reasoning in the era of multimodal large language models (MLLMs). We review over 200 studies published since 2021, and examine the state-of-the-art developments in Math-LLMs, with a focus on multimodal settings. We categorize the field into three dimensions: benchmarks, methodologies, and challenges. In particular, we explore multimodal mathematical reasoning pipeline, as well as the role of (M)LLMs and the associated methodologies. Finally, we identify five major challenges hindering the realization of AGI in this domain, offering insights into the future direction for enhancing multimodal reasoning capabilities. This survey serves as a critical resource for the research community in advancing the capabilities of LLMs to tackle complex multimodal reasoning tasks.

Humans often use visual aids, for example diagrams or sketches, when solving complex problems. Training multimodal models to do the same, known as Visual Chain of Thought (Visual CoT), is challenging due to: (1) poor off-the-shelf visual CoT performance, which hinders reinforcement learning, and (2) the lack of high-quality visual CoT training data. We introduce Zebra-CoT, a diverse large-scale dataset with 182,384 samples, containing logically coherent interleaved text-image reasoning traces. We focus on four categories of tasks where sketching or visual reasoning is especially natural, spanning scientific questions such as geometry, physics, and algorithms; 2D visual reasoning tasks like visual search and jigsaw puzzles; 3D reasoning tasks including 3D multi-hop inference, embodied and robot planning; visual logic problems and strategic games like chess. Fine-tuning the Anole-7B model on the Zebra-CoT training corpus results in an improvement of +12% in our test-set accuracy and yields up to +13% performance gain on standard VLM benchmark evaluations. Fine-tuning Bagel-7B yields a model that generates high-quality interleaved visual reasoning chains, underscoring Zebra-CoT's effectiveness for developing multimodal reasoning abilities. We open-source our dataset and models to support development and evaluation of visual CoT.

Reasoning is central to human intelligence, enabling structured problem-solving across diverse tasks. Recent advances in large language models (LLMs) have greatly enhanced their reasoning abilities in arithmetic, commonsense, and symbolic domains. However, effectively extending these capabilities into multimodal contexts-where models must integrate both visual and textual inputs-continues to be a significant challenge. Multimodal reasoning introduces complexities, such as handling conflicting information across modalities, which require models to adopt advanced interpretative strategies. Addressing these challenges involves not only sophisticated algorithms but also robust methodologies for evaluating reasoning accuracy and coherence. This paper offers a concise yet insightful overview of reasoning techniques in both textual and multimodal LLMs. Through a thorough and up-to-date comparison, we clearly formulate core reasoning challenges and opportunities, highlighting practical methods for post-training optimization and test-time inference. Our work provides valuable insights and guidance, bridging theoretical frameworks and practical implementations, and sets clear directions for future research.

Visual mathematical reasoning, as a fundamental visual reasoning ability, has received widespread attention from the Large Multimodal Models (LMMs) community. Existing benchmarks, such as MathVista and MathVerse, focus more on the result-oriented performance but neglect the underlying principles in knowledge acquisition and generalization. Inspired by human-like mathematical reasoning, we introduce WE-MATH, the first benchmark specifically designed to explore the problem-solving principles beyond end-to-end performance. We meticulously collect and categorize 6.5K visual math problems, spanning 67 hierarchical knowledge concepts and five layers of knowledge granularity. We decompose composite problems into sub-problems according to the required knowledge concepts and introduce a novel four-dimensional metric, namely Insufficient Knowledge (IK), Inadequate Generalization (IG), Complete Mastery (CM), and Rote Memorization (RM), to hierarchically assess inherent issues in LMMs' reasoning process. With WE-MATH, we conduct a thorough evaluation of existing LMMs in visual mathematical reasoning and reveal a negative correlation between solving steps and problem-specific performance. We confirm the IK issue of LMMs can be effectively improved via knowledge augmentation strategies. More notably, the primary challenge of GPT-4o has significantly transitioned from IK to IG, establishing it as the first LMM advancing towards the knowledge generalization stage. In contrast, other LMMs exhibit a marked inclination towards Rote Memorization - they correctly solve composite problems involving multiple knowledge concepts yet fail to answer sub-problems. We anticipate that WE-MATH will open new pathways for advancements in visual mathematical reasoning for LMMs. The WE-MATH data and evaluation code are available at https://github.com/We-Math/We-Math.

Cognitive textual and visual reasoning tasks, such as puzzles, series, and analogies, demand the ability to quickly reason, decipher, and evaluate patterns both textually and spatially. While LLMs and VLMs, through extensive training on large amounts of human-curated data, have attained a high level of pseudo-human intelligence in some common sense reasoning tasks, they still struggle with more complex reasoning tasks that require cognitive understanding. In this work, we introduce a new dataset, NTSEBench, designed to evaluate the cognitive multi-modal reasoning and problem-solving skills of large models. The dataset comprises 2,728 multiple-choice questions comprising of a total of 4,642 images across 26 categories sampled from the NTSE examination conducted nationwide in India, featuring both visual and textual general aptitude questions that do not rely on rote learning. We establish baselines on the dataset using state-of-the-art LLMs and VLMs. To facilitate a comparison between open source and propriety models, we propose four distinct modeling strategies to handle different modalities (text and images) in the dataset instances.

Large language models (LLMs) have demonstrated impressive reasoning abilities in complex tasks. However, they lack up-to-date knowledge and experience hallucinations during reasoning, which can lead to incorrect reasoning processes and diminish their performance and trustworthiness. Knowledge graphs (KGs), which capture vast amounts of facts in a structured format, offer a reliable source of knowledge for reasoning. Nevertheless, existing KG-based LLM reasoning methods only treat KGs as factual knowledge bases and overlook the importance of their structural information for reasoning. In this paper, we propose a novel method called reasoning on graphs (RoG) that synergizes LLMs with KGs to enable faithful and interpretable reasoning. Specifically, we present a planning-retrieval-reasoning framework, where RoG first generates relation paths grounded by KGs as faithful plans. These plans are then used to retrieve valid reasoning paths from the KGs for LLMs to conduct faithful reasoning. Furthermore, RoG not only distills knowledge from KGs to improve the reasoning ability of LLMs through training but also allows seamless integration with any arbitrary LLMs during inference. Extensive experiments on two benchmark KGQA datasets demonstrate that RoG achieves state-of-the-art performance on KG reasoning tasks and generates faithful and interpretable reasoning results.

Deductive reasoning plays a pivotal role in the formulation of sound and cohesive arguments. It allows individuals to draw conclusions that logically follow, given the truth value of the information provided. Recent progress in the domain of large language models (LLMs) has showcased their capability in executing deductive reasoning tasks. Nonetheless, a significant portion of research primarily assesses the accuracy of LLMs in solving such tasks, often overlooking a deeper analysis of their reasoning behavior. In this study, we draw upon principles from cognitive psychology to examine inferential strategies employed by LLMs, through a detailed evaluation of their responses to propositional logic problems. Our findings indicate that LLMs display reasoning patterns akin to those observed in humans, including strategies like supposition following or chain construction. Moreover, our research demonstrates that the architecture and scale of the model significantly affect its preferred method of reasoning, with more advanced models tending to adopt strategies more frequently than less sophisticated ones. Importantly, we assert that a model's accuracy, that is the correctness of its final conclusion, does not necessarily reflect the validity of its reasoning process. This distinction underscores the necessity for more nuanced evaluation procedures in the field.

As textual reasoning with large language models (LLMs) has advanced significantly, there has been growing interest in enhancing the multimodal reasoning capabilities of large vision-language models (LVLMs). However, existing methods primarily approach multimodal reasoning in a straightforward, text-centric manner, where both reasoning and answer derivation are conducted purely through text, with the only difference being the presence of multimodal input. As a result, these methods often encounter fundamental limitations in spatial reasoning tasks that demand precise geometric understanding and continuous spatial tracking-capabilities that humans achieve through mental visualization and manipulation. To address the limitations, we propose drawing to reason in space, a novel paradigm that enables LVLMs to reason through elementary drawing operations in the visual space. By equipping models with basic drawing operations, including annotating bounding boxes and drawing auxiliary lines, we empower them to express and analyze spatial relationships through direct visual manipulation, meanwhile avoiding the performance ceiling imposed by specialized perception tools in previous tool-integrated reasoning approaches. To cultivate this capability, we develop a three-stage training framework: cold-start training with synthetic data to establish basic drawing abilities, reflective rejection sampling to enhance self-reflection behaviors, and reinforcement learning to directly optimize for target rewards. Extensive experiments demonstrate that our model, named VILASR, consistently outperforms existing methods across diverse spatial reasoning benchmarks, involving maze navigation, static spatial reasoning, video-based reasoning, and multi-view-based reasoning tasks, with an average improvement of 18.4%.

Reasoning is a fundamental aspect of human intelligence that plays a crucial role in activities such as problem solving, decision making, and critical thinking. In recent years, large language models (LLMs) have made significant progress in natural language processing, and there is observation that these models may exhibit reasoning abilities when they are sufficiently large. However, it is not yet clear to what extent LLMs are capable of reasoning. This paper provides a comprehensive overview of the current state of knowledge on reasoning in LLMs, including techniques for improving and eliciting reasoning in these models, methods and benchmarks for evaluating reasoning abilities, findings and implications of previous research in this field, and suggestions on future directions. Our aim is to provide a detailed and up-to-date review of this topic and stimulate meaningful discussion and future work.

Chain-of-thought prompting~(CoT) and tool augmentation have been validated in recent work as effective practices for improving large language models~(LLMs) to perform step-by-step reasoning on complex math-related tasks. However, most existing math reasoning datasets may be not able to fully evaluate and analyze the ability of LLMs in manipulating tools and performing reasoning, as they may only require very few invocations of tools or miss annotations for evaluating intermediate reasoning steps. To address the issue, we construct CARP, a new Chinese dataset consisting of 4,886 computation-intensive algebra problems with formulated annotations on intermediate steps. In CARP, we test four LLMs with CoT prompting, and find that they are all prone to make mistakes at the early steps of the solution, leading to wrong answers. Based on this finding, we propose a new approach that can deliberate the reasoning steps with tool interfaces, namely DELI. In DELI, we first initialize a step-by-step solution based on retrieved exemplars, then iterate two deliberation procedures that check and refine the intermediate steps of the generated solution, from the perspectives of tool manipulation and natural language reasoning, until obtaining converged solutions or reaching the maximum turn. Experimental results on CARP and six other datasets show that the proposed DELI mostly outperforms competitive baselines, and can further boost the performance of existing CoT methods. Our data and code are available in https://github.com/RUCAIBox/CARP.

Reasoning, as an essential ability for complex problem-solving, can provide back-end support for various real-world applications, such as medical diagnosis, negotiation, etc. This paper provides a comprehensive survey of cutting-edge research on reasoning with language model prompting. We introduce research works with comparisons and summaries and provide systematic resources to help beginners. We also discuss the potential reasons for emerging such reasoning abilities and highlight future research directions. Resources are available at https://github.com/zjunlp/Prompt4ReasoningPapers (updated periodically).

Humans draw to facilitate reasoning: we draw auxiliary lines when solving geometry problems; we mark and circle when reasoning on maps; we use sketches to amplify our ideas and relieve our limited-capacity working memory. However, such actions are missing in current multimodal language models (LMs). Current chain-of-thought and tool-use paradigms only use text as intermediate reasoning steps. In this work, we introduce Sketchpad, a framework that gives multimodal LMs a visual sketchpad and tools to draw on the sketchpad. The LM conducts planning and reasoning according to the visual artifacts it has drawn. Different from prior work, which uses text-to-image models to enable LMs to draw, Sketchpad enables LMs to draw with lines, boxes, marks, etc., which is closer to human sketching and better facilitates reasoning. Sketchpad can also use specialist vision models during the sketching process (e.g., draw bounding boxes with object detection models, draw masks with segmentation models), to further enhance visual perception and reasoning. We experiment with a wide range of math tasks (including geometry, functions, graphs, and chess) and complex visual reasoning tasks. Sketchpad substantially improves performance on all tasks over strong base models with no sketching, yielding an average gain of 12.7% on math tasks, and 8.6% on vision tasks. GPT-4o with Sketchpad sets a new state of the art on all tasks, including V*Bench (80.3%), BLINK spatial reasoning (83.9%), and visual correspondence (80.8%). All codes and data are in https://visualsketchpad.github.io/.

We introduce FigureQA, a visual reasoning corpus of over one million question-answer pairs grounded in over 100,000 images. The images are synthetic, scientific-style figures from five classes: line plots, dot-line plots, vertical and horizontal bar graphs, and pie charts. We formulate our reasoning task by generating questions from 15 templates; questions concern various relationships between plot elements and examine characteristics like the maximum, the minimum, area-under-the-curve, smoothness, and intersection. To resolve, such questions often require reference to multiple plot elements and synthesis of information distributed spatially throughout a figure. To facilitate the training of machine learning systems, the corpus also includes side data that can be used to formulate auxiliary objectives. In particular, we provide the numerical data used to generate each figure as well as bounding-box annotations for all plot elements. We study the proposed visual reasoning task by training several models, including the recently proposed Relation Network as a strong baseline. Preliminary results indicate that the task poses a significant machine learning challenge. We envision FigureQA as a first step towards developing models that can intuitively recognize patterns from visual representations of data.

Studies have underscored how, regardless of the recent breakthrough and swift advances in AI research, even state-of-the-art Large Language models (LLMs) continue to struggle when performing logical and mathematical reasoning. The results seem to suggest that LLMs still work as (highly advanced) data pattern identifiers, scoring poorly when attempting to generalise and solve reasoning problems the models have never previously seen or that are not close to samples presented in their training data. To address this compelling concern, this paper makes use of the notion of critical questions from the literature on argumentation theory, focusing in particular on Toulmin's model of argumentation. We show that employing these critical questions can improve the reasoning capabilities of LLMs. By probing the rationale behind the models' reasoning process, the LLM can assess whether some logical mistake is occurring and correct it before providing the final reply to the user prompt. The underlying idea is drawn from the gold standard of any valid argumentative procedure: the conclusion is valid if it is entailed by accepted premises. Or, to paraphrase such Aristotelian principle in a real-world approximation, characterised by incomplete information and presumptive logic, the conclusion is valid if not proved otherwise. This approach successfully steers the models' output through a reasoning pipeline, resulting in better performance against the baseline and its Chain-of-Thought (CoT) implementation. To this end, an extensive evaluation of the proposed approach on the MT-Bench Reasoning and Math tasks across a range of LLMs is provided.

Chain-of-Thought (CoT) prompting can dramatically improve the multi-step reasoning abilities of large language models (LLMs). CoT explicitly encourages the LLM to generate intermediate rationales for solving a problem, by providing a series of reasoning steps in the demonstrations. Despite its success, there is still little understanding of what makes CoT prompting effective and which aspects of the demonstrated reasoning steps contribute to its performance. In this paper, we show that CoT reasoning is possible even with invalid demonstrations - prompting with invalid reasoning steps can achieve over 80-90% of the performance obtained using CoT under various metrics, while still generating coherent lines of reasoning during inference. Further experiments show that other aspects of the rationales, such as being relevant to the query and correctly ordering the reasoning steps, are much more important for effective CoT reasoning. Overall, these findings both deepen our understanding of CoT prompting, and open up new questions regarding LLMs' capability to learn to reason in context.

Large language models (LLMs) have made remarkable strides in various natural language processing tasks, but their performance on complex reasoning problems remains hindered by a lack of explainability and trustworthiness. This issue, often manifesting as hallucinations or unattributable reasoning processes, limits their applicability in complex reasoning scenarios. To address this, we propose Knowledge Graph-constrained Trajectory Reasoning Attribution and Chain Explanation Supervision (KG-TRACES), a novel framework that enhances the reasoning ability of LLMs through explicit supervision over reasoning paths and processes. KG-TRACES jointly supervises the model to: (1) predict symbolic relation paths, (2) predict full triple-level reasoning paths, and (3) generate attribution-aware reasoning processes grounded in the reasoning paths. At inference phase, the model adapts to both KG-available and KG-unavailable scenarios, retrieving reasoning paths from a KG when possible or predicting plausible reasoning paths with only intrinsic knowledge when not. This design enables the model to reason in an explainable and source-attributable pattern. Through extensive experiments on complex reasoning tasks, we demonstrate that KG-TRACES significantly outperforms existing SOTA: it improves Hits@1 by 1.6% and F1 by 4.7% on WebQSP, and achieves improvements of 4.8% in Hits@1 and 2.1% in F1 on CWQ. Moreover, we show its transferability to specialized domains such as medicine. By visualizing the intermediate steps of reasoning processes, we further show that the explicit supervision introduced by KG-TRACES leads to more stable and goal-directed reasoning processes, aligning closely with correct answers. Code is available at https://github.com/Edaizi/KG-TRACES.

Multi-modal Large Language Models (MLLMs) exhibit impressive problem-solving abilities in various domains, but their visual comprehension and abstract reasoning skills remain under-evaluated. To this end, we present PolyMATH, a challenging benchmark aimed at evaluating the general cognitive reasoning abilities of MLLMs. PolyMATH comprises 5,000 manually collected high-quality images of cognitive textual and visual challenges across 10 distinct categories, including pattern recognition, spatial reasoning, and relative reasoning. We conducted a comprehensive, and quantitative evaluation of 15 MLLMs using four diverse prompting strategies, including Chain-of-Thought and Step-Back. The best scores achieved on PolyMATH are ~41%, ~36%, and ~27%, obtained by Claude-3.5 Sonnet, GPT-4o and Gemini-1.5 Pro respectively - highlighting the logical and visual complexity of these questions. A further fine-grained error analysis reveals that these models struggle to understand spatial relations and perform drawn-out, high-level reasoning. This is further strengthened by our ablation study estimating MLLM performance when given textual descriptions in place of diagrams. As evidenced by ~4% improvement over textual descriptions as opposed to actual images, we discover that models do not truly comprehend visual diagrams and the spatial information therein, and are thus prone to logical errors. Finally, we evaluate the OpenAI o1 models and find that their performance only matches the human baseline, highlighting the difficulty of the benchmark. The results on PolyMATH highlight the room for improvement in multi-modal reasoning and provide unique insights to guide the development of future MLLMs.

Large language models (LLMs) have demonstrated remarkable success across a wide range of tasks; however, they still encounter challenges in reasoning tasks that require understanding and inferring relationships between distinct pieces of information within text sequences. This challenge is particularly pronounced in tasks involving multi-step processes, such as logical reasoning and multi-hop question answering, where understanding implicit relationships between entities and leveraging multi-hop connections in the given context are crucial. Graphs, as fundamental data structures, explicitly represent pairwise relationships between entities, thereby offering the potential to enhance LLMs' reasoning capabilities. External graphs have proven effective in supporting LLMs across multiple tasks. However, in many reasoning tasks, no pre-existing graph structure is provided. Can we structure implicit knowledge derived from context into graphs to assist LLMs in reasoning? In this paper, we propose Reasoning with Graphs (RwG) by first constructing explicit graphs from the context and then leveraging these graphs to enhance LLM reasoning performance on reasoning tasks. Extensive experiments demonstrate the effectiveness of the proposed method in improving both logical reasoning and multi-hop question answering tasks.

Solving complex chart Q&A tasks requires advanced visual reasoning abilities in multimodal large language models (MLLMs). Recent studies highlight that these abilities consist of two main parts: recognizing key information from visual inputs and conducting reasoning over it. Thus, a promising approach to enhance MLLMs is to construct relevant training data focusing on the two aspects. However, collecting and annotating complex charts and questions is costly and time-consuming, and ensuring the quality of annotated answers remains a challenge. In this paper, we propose Code-as-Intermediary Translation (CIT), a cost-effective, efficient and easily scalable data synthesis method for distilling visual reasoning abilities from LLMs to MLLMs. The code serves as an intermediary that translates visual chart representations into textual representations, enabling LLMs to understand cross-modal information. Specifically, we employ text-based synthesizing techniques to construct chart-plotting code and produce ReachQA, a dataset containing 3k reasoning-intensive charts and 20k Q&A pairs to enhance both recognition and reasoning abilities. Experiments show that when fine-tuned with our data, models not only perform well on chart-related benchmarks, but also demonstrate improved multimodal reasoning abilities on general mathematical benchmarks like MathVista. The code and dataset are publicly available at https://github.com/hewei2001/ReachQA.

Mathematical reasoning has been challenging for large language models (LLMs). However, the introduction of step-by-step Chain-of-Thought (CoT) inference has significantly advanced the mathematical capabilities of LLMs. Despite this progress, current approaches either necessitate extensive inference datasets for training or depend on few-shot methods that frequently compromise computational accuracy. To address these bottlenecks in mathematical reasoning, we propose a novel method called Step Guidied Reasoning, which is more stable and generalizable than few-shot methods and does not involve further fine-tuning of the model. In this approach, LLMs reflect on small reasoning steps, similar to how humans deliberate and focus attention on what to do next. By incorporating this reflective process into the inference stage, LLMs can effectively guide their reasoning from one step to the next. Through extensive experiments, we demonstrate the significant effect of Step Guidied Reasoning in augmenting mathematical performance in state-of-the-art language models. Qwen2-72B-Instruct outperforms its math-specific counterpart, Qwen2.5-72B-Math-Instruct, on MMLU- STEM with a score of 90.9%, compared to 87.3%. The average scores of Qwen2-7B-Instruct and Qwen2-72B-Instruct increase from 27.1% to 36.3% and from 36.5% to 47.4% on the mathematics domain, respectively.

Large language models (LLMs) have dramatically enhanced the field of language intelligence, as demonstrably evidenced by their formidable empirical performance across a spectrum of complex reasoning tasks. Additionally, theoretical proofs have illuminated their emergent reasoning capabilities, providing a compelling showcase of their advanced cognitive abilities in linguistic contexts. Critical to their remarkable efficacy in handling complex reasoning tasks, LLMs leverage the intriguing chain-of-thought (CoT) reasoning techniques, obliging them to formulate intermediate steps en route to deriving an answer. The CoT reasoning approach has not only exhibited proficiency in amplifying reasoning performance but also in enhancing interpretability, controllability, and flexibility. In light of these merits, recent research endeavors have extended CoT reasoning methodologies to nurture the development of autonomous language agents, which adeptly adhere to language instructions and execute actions within varied environments. This survey paper orchestrates a thorough discourse, penetrating vital research dimensions, encompassing: (i) the foundational mechanics of CoT techniques, with a focus on elucidating the circumstances and justification behind its efficacy; (ii) the paradigm shift in CoT; and (iii) the burgeoning of language agents fortified by CoT approaches. Prospective research avenues envelop explorations into generalization, efficiency, customization, scaling, and safety. This paper caters to a wide audience, including beginners seeking comprehensive knowledge of CoT reasoning and language agents, as well as experienced researchers interested in foundational mechanics and engaging in cutting-edge discussions on these topics. A repository for the related papers is available at https://github.com/Zoeyyao27/CoT-Igniting-Agent.

Modern large language models (LLMs) employ various forms of logical inference, both implicitly and explicitly, when addressing reasoning tasks. Understanding how to optimally leverage these inference paradigms is critical for advancing LLMs' reasoning capabilities. This paper adopts an exploratory approach by introducing a controlled evaluation environment for analogical reasoning -- a fundamental cognitive task -- that is systematically parameterized across three dimensions: modality (textual, visual, symbolic), difficulty (easy, medium, hard), and task format (multiple-choice or free-text generation). We analyze the comparative dynamics of inductive, abductive, and deductive inference pipelines across these dimensions, and demonstrate that our findings generalize to broader in-context learning tasks. Additionally, we investigate advanced paradigms such as hypothesis selection, verification, and refinement, revealing their potential to scale up logical inference in LLM reasoning. This exploratory study provides a foundation for future research in enhancing LLM reasoning through systematic logical inference strategies.

Analogical reasoning is fundamental to human cognition and holds an important place in various fields. However, previous studies mainly focus on single-modal analogical reasoning and ignore taking advantage of structure knowledge. Notably, the research in cognitive psychology has demonstrated that information from multimodal sources always brings more powerful cognitive transfer than single modality sources. To this end, we introduce the new task of multimodal analogical reasoning over knowledge graphs, which requires multimodal reasoning ability with the help of background knowledge. Specifically, we construct a Multimodal Analogical Reasoning dataSet (MARS) and a multimodal knowledge graph MarKG. We evaluate with multimodal knowledge graph embedding and pre-trained Transformer baselines, illustrating the potential challenges of the proposed task. We further propose a novel model-agnostic Multimodal analogical reasoning framework with Transformer (MarT) motivated by the structure mapping theory, which can obtain better performance. Code and datasets are available in https://github.com/zjunlp/MKG_Analogy.

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

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

Visual language such as charts and plots is ubiquitous in the human world. Comprehending plots and charts requires strong reasoning skills. Prior state-of-the-art (SOTA) models require at least tens of thousands of training examples and their reasoning capabilities are still much limited, especially on complex human-written queries. This paper presents the first one-shot solution to visual language reasoning. We decompose the challenge of visual language reasoning into two steps: (1) plot-to-text translation, and (2) reasoning over the translated text. The key in this method is a modality conversion module, named as DePlot, which translates the image of a plot or chart to a linearized table. The output of DePlot can then be directly used to prompt a pretrained large language model (LLM), exploiting the few-shot reasoning capabilities of LLMs. To obtain DePlot, we standardize the plot-to-table task by establishing unified task formats and metrics, and train DePlot end-to-end on this task. DePlot can then be used off-the-shelf together with LLMs in a plug-and-play fashion. Compared with a SOTA model finetuned on more than >28k data points, DePlot+LLM with just one-shot prompting achieves a 24.0% improvement over finetuned SOTA on human-written queries from the task of chart QA.

Logical reasoning is a fundamental aspect of human intelligence and an essential capability for multimodal large language models (MLLMs). Despite the significant advancement in multimodal reasoning, existing benchmarks fail to comprehensively evaluate their reasoning abilities due to the lack of explicit categorization for logical reasoning types and an unclear understanding of reasoning. To address these issues, we introduce MME-Reasoning, a comprehensive benchmark designed to evaluate the reasoning ability of MLLMs, which covers all three types of reasoning (i.e., inductive, deductive, and abductive) in its questions. We carefully curate the data to ensure that each question effectively evaluates reasoning ability rather than perceptual skills or knowledge breadth, and extend the evaluation protocols to cover the evaluation of diverse questions. Our evaluation reveals substantial limitations of state-of-the-art MLLMs when subjected to holistic assessments of logical reasoning capabilities. Even the most advanced MLLMs show limited performance in comprehensive logical reasoning, with notable performance imbalances across reasoning types. In addition, we conducted an in-depth analysis of approaches such as ``thinking mode'' and Rule-based RL, which are commonly believed to enhance reasoning abilities. These findings highlight the critical limitations and performance imbalances of current MLLMs in diverse logical reasoning scenarios, providing comprehensive and systematic insights into the understanding and evaluation of reasoning capabilities.

Mathematical reasoning---a core ability within human intelligence---presents some unique challenges as a domain: we do not come to understand and solve mathematical problems primarily on the back of experience and evidence, but on the basis of inferring, learning, and exploiting laws, axioms, and symbol manipulation rules. In this paper, we present a new challenge for the evaluation (and eventually the design) of neural architectures and similar system, developing a task suite of mathematics problems involving sequential questions and answers in a free-form textual input/output format. The structured nature of the mathematics domain, covering arithmetic, algebra, probability and calculus, enables the construction of training and test splits designed to clearly illuminate the capabilities and failure-modes of different architectures, as well as evaluate their ability to compose and relate knowledge and learned processes. Having described the data generation process and its potential future expansions, we conduct a comprehensive analysis of models from two broad classes of the most powerful sequence-to-sequence architectures and find notable differences in their ability to resolve mathematical problems and generalize their knowledge.

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).

With the emergence of advanced reasoning models like OpenAI o3 and DeepSeek-R1, large language models (LLMs) have demonstrated remarkable reasoning capabilities. However, their ability to perform rigorous logical reasoning remains an open question. This survey synthesizes recent advancements in logical reasoning within LLMs, a critical area of AI research. It outlines the scope of logical reasoning in LLMs, its theoretical foundations, and the benchmarks used to evaluate reasoning proficiency. We analyze existing capabilities across different reasoning paradigms - deductive, inductive, abductive, and analogical - and assess strategies to enhance reasoning performance, including data-centric tuning, reinforcement learning, decoding strategies, and neuro-symbolic approaches. The review concludes with future directions, emphasizing the need for further exploration to strengthen logical reasoning in AI systems.

Vision-language models (VLMs) are achieving increasingly strong performance on multimodal tasks. However, reasoning capabilities remain limited particularly for smaller VLMs, while those of large-language models (LLMs) have seen numerous improvements. We propose a technique to transfer capabilities from LLMs to VLMs. On the recently introduced ChartQA, our method obtains state-of-the-art performance when applied on the PaLI3-5B VLM by chen2023pali3, while also enabling much better performance on PlotQA and FigureQA. We first improve the chart representation by continuing the pre-training stage using an improved version of the chart-to-table translation task by liu2023deplot. We then propose constructing a 20x larger dataset than the original training set. To improve general reasoning capabilities and improve numerical operations, we synthesize reasoning traces using the table representation of charts. Lastly, our model is fine-tuned using the multitask loss introduced by hsieh2023distilling. Our variant ChartPaLI-5B outperforms even 10x larger models such as PaLIX-55B without using an upstream OCR system, while keeping inference time constant compared to the PaLI3-5B baseline. When rationales are further refined with a simple program-of-thought prompt chen2023program, our model outperforms the recently introduced Gemini Ultra and GPT-4V.

Chain-of-Thought (CoT) prompting has become the de facto method to elicit reasoning capabilities from large language models (LLMs). However, to mitigate hallucinations in CoT that are notoriously difficult to detect, current methods such as process reward models (PRMs) or self-consistency operate as opaque boxes and do not provide checkable evidence for their judgments, possibly limiting their effectiveness. To address this issue, we draw inspiration from the idea that "the gold standard for supporting a mathematical claim is to provide a proof". We propose a retrospective, step-aware formal verification framework Safe. Rather than assigning arbitrary scores, we strive to articulate mathematical claims in formal mathematical language Lean 4 at each reasoning step and provide formal proofs to identify hallucinations. We evaluate our framework Safe across multiple language models and various mathematical datasets, demonstrating a significant performance improvement while offering interpretable and verifiable evidence. We also propose FormalStep as a benchmark for step correctness theorem proving with 30,809 formal statements. To the best of our knowledge, our work represents the first endeavor to utilize formal mathematical language Lean 4 for verifying natural language content generated by LLMs, aligning with the reason why formal mathematical languages were created in the first place: to provide a robust foundation for hallucination-prone human-written proofs.

Mathematical reasoning is a cornerstone of artificial general intelligence and a primary benchmark for evaluating the capabilities of Large Language Models (LLMs). While state-of-the-art models show promise, they often falter when faced with complex problems that demand deep conceptual understanding and intricate, multi-step deliberation. To address this challenge, we introduce JT-Math-8B, a series of open-source models comprising base, instruct, and thinking versions, built upon a systematic, multi-stage optimization framework. Our pre-training corpus is a high-quality, 210B-token dataset curated through a dedicated data pipeline that uses model-based validation to ensure quality and diversity. The Instruct Model is optimized for direct, concise answers through Supervised Fine-Tuning (SFT) and a GRPO-based reinforcement learning (RL) method. The Thinking Model is trained for complex problem-solving using a Long Chain-of-Thought (Long CoT) approach, combining SFT with a novel, multi-stage RL curriculum that progressively increases task difficulty and context length up to 32K tokens. JT-Math-8B achieves state-of-the-art results among open-source models of similar size, surpassing prominent models like OpenAI's O1-mini and GPT-4o , and demonstrating superior performance on competition-level mathematics.

Recent advancements in Large Language Models (LLMs) have demonstrated enhanced reasoning capabilities, evolving from Chain-of-Thought (CoT) prompting to advanced, product-oriented solutions like OpenAI o1. During our re-implementation of this model, we noticed that in multimodal tasks requiring visual input (e.g., geometry problems), Multimodal LLMs (MLLMs) struggle to maintain focus on the visual information, in other words, MLLMs suffer from a gradual decline in attention to visual information as reasoning progresses, causing text-over-relied outputs. To investigate this, we ablate image inputs during long-chain reasoning. Concretely, we truncate the reasoning process midway, then re-complete the reasoning process with the input image removed. We observe only a ~2% accuracy drop on MathVista's test-hard subset, revealing the model's textual outputs dominate the following reasoning process. Motivated by this, we propose Take-along Visual Conditioning (TVC), a strategy that shifts image input to critical reasoning stages and compresses redundant visual tokens via dynamic pruning. This methodology helps the model retain attention to the visual components throughout the reasoning. Our approach achieves state-of-the-art performance on average across five mathematical reasoning benchmarks (+3.4% vs previous sota), demonstrating the effectiveness of TVC in enhancing multimodal reasoning systems.

A long-standing goal of AI systems is to perform complex multimodal reasoning like humans. Recently, large language models (LLMs) have made remarkable strides in such multi-step reasoning on the language modality solely by leveraging the chain of thought (CoT) to mimic human thinking. However, the transfer of these advancements to multimodal contexts introduces heightened challenges, including but not limited to the impractical need for labor-intensive annotation and the limitations in terms of flexibility, generalizability, and explainability. To evoke CoT reasoning in multimodality, this work first conducts an in-depth analysis of these challenges posed by multimodality and presents two key insights: "keeping critical thinking" and "letting everyone do their jobs" in multimodal CoT reasoning. Furthermore, this study proposes a novel DDCoT prompting that maintains a critical attitude through negative-space prompting and incorporates multimodality into reasoning by first dividing the reasoning responsibility of LLMs into reasoning and recognition and then integrating the visual recognition capability of visual models into the joint reasoning process. The rationales generated by DDCoT not only improve the reasoning abilities of both large and small language models in zero-shot prompting and fine-tuning learning, significantly outperforming state-of-the-art methods but also exhibit impressive generalizability and explainability.

Recent years have witnessed significant progress in large language models' (LLMs) reasoning, which is largely due to the chain-of-thought (CoT) approaches, allowing models to generate intermediate reasoning steps before reaching the final answer. Building on these advances, state-of-the-art LLMs are instruction-tuned to provide long and detailed CoT pathways when responding to reasoning-related questions. However, human beings are naturally cognitive misers and will prompt language models to give rather short responses, thus raising a significant conflict with CoT reasoning. In this paper, we delve into how LLMs' reasoning performance changes when users provide short-path prompts. The results and analysis reveal that language models can reason effectively and robustly without explicit CoT prompts, while under short-path prompting, LLMs' reasoning ability drops significantly and becomes unstable, even on grade-school problems. To address this issue, we propose two approaches: an instruction-guided approach and a fine-tuning approach, both designed to effectively manage the conflict. Experimental results show that both methods achieve high accuracy, providing insights into the trade-off between instruction adherence and reasoning accuracy in current models.

Large Language Models (LLMs) significantly benefit from Chain-of-Thought (CoT) prompting in performing various reasoning tasks. While CoT allows models to produce more comprehensive reasoning processes, its emphasis on intermediate reasoning steps can inadvertently introduce hallucinations and accumulated errors, thereby limiting models' ability to solve complex reasoning tasks. Inspired by how humans engage in careful and meticulous deductive logical reasoning processes to solve tasks, we seek to enable language models to perform explicit and rigorous deductive reasoning, and also ensure the trustworthiness of their reasoning process through self-verification. However, directly verifying the validity of an entire deductive reasoning process is challenging, even with advanced models like ChatGPT. In light of this, we propose to decompose a reasoning verification process into a series of step-by-step subprocesses, each only receiving their necessary context and premises. To facilitate this procedure, we propose Natural Program, a natural language-based deductive reasoning format. Our approach enables models to generate precise reasoning steps where subsequent steps are more rigorously grounded on prior steps. It also empowers language models to carry out reasoning self-verification in a step-by-step manner. By integrating this verification process into each deductive reasoning stage, we significantly enhance the rigor and trustfulness of generated reasoning steps. Along this process, we also improve the answer correctness on complex reasoning tasks. Code will be released at https://github.com/lz1oceani/verify_cot.

Large Language Models (LLMs) have demonstrated impressive reasoning abilities through test-time computation (TTC) techniques such as chain-of-thought prompting and tree-based reasoning. However, we argue that current reasoning LLMs (RLLMs) lack the ability to systematically explore the solution space. This paper formalizes what constitutes systematic problem solving and identifies common failure modes that reveal reasoning LLMs to be wanderers rather than systematic explorers. Through qualitative and quantitative analysis across multiple state-of-the-art LLMs, we uncover persistent issues: invalid reasoning steps, redundant explorations, hallucinated or unfaithful conclusions, and so on. Our findings suggest that current models' performance can appear to be competent on simple tasks yet degrade sharply as complexity increases. Based on the findings, we advocate for new metrics and tools that evaluate not just final outputs but the structure of the reasoning process itself.

With the rapid advancement of mathematical reasoning capabilities in Large Language Models (LLMs), AI systems are increasingly being adopted in educational settings to support students' comprehension of problem-solving processes. However, a critical component remains underexplored in current LLM-generated explanations: visual explanation. In real-world instructional contexts, human tutors routinely employ visual aids - such as diagrams, markings, and highlights - to enhance conceptual clarity. To bridge this gap, we introduce a novel task of visual solution explanation, which requires generating explanations that incorporate newly introduced visual elements essential for understanding (e.g., auxiliary lines, annotations, or geometric constructions). To evaluate model performance on this task, we propose MathExplain, a multimodal benchmark consisting of 997 math problems annotated with visual keypoints and corresponding explanatory text that references those elements. Our empirical results show that while some closed-source models demonstrate promising capabilities on visual solution-explaining, current open-source general-purpose models perform inconsistently, particularly in identifying relevant visual components and producing coherent keypoint-based explanations. We expect that visual solution-explaining and the MathExplain dataset will catalyze further research on multimodal LLMs in education and advance their deployment as effective, explanation-oriented AI tutors. Code and data will be released publicly.

Large Language Models (LLMs) have achieved impressive performance on complex reasoning tasks with Chain-of-Thought (CoT) prompting. However, conventional CoT relies on reasoning steps explicitly verbalized in natural language, introducing inefficiencies and limiting its applicability to abstract reasoning. To address this, there has been growing research interest in latent CoT reasoning, where inference occurs within latent spaces. By decoupling reasoning from language, latent reasoning promises richer cognitive representations and more flexible, faster inference. Researchers have explored various directions in this promising field, including training methodologies, structural innovations, and internal reasoning mechanisms. This paper presents a comprehensive overview and analysis of this reasoning paradigm. We begin by proposing a unified taxonomy from four perspectives: token-wise strategies, internal mechanisms, analysis, and applications. We then provide in-depth discussions and comparative analyses of representative methods, highlighting their design patterns, strengths, and open challenges. We aim to provide a structured foundation for advancing this emerging direction in LLM reasoning. The relevant papers will be regularly updated at https://github.com/EIT-NLP/Awesome-Latent-CoT.

Chain-of-Thought (CoT) prompting has been shown to improve Large Language Model (LLM) performance on various tasks. With this approach, LLMs appear to produce human-like reasoning steps before providing answers (a.k.a., CoT reasoning), which often leads to the perception that they engage in deliberate inferential processes. However, some initial findings suggest that CoT reasoning may be more superficial than it appears, motivating us to explore further. In this paper, we study CoT reasoning via a data distribution lens and investigate if CoT reasoning reflects a structured inductive bias learned from in-distribution data, allowing the model to conditionally generate reasoning paths that approximate those seen during training. Thus, its effectiveness is fundamentally bounded by the degree of distribution discrepancy between the training data and the test queries. With this lens, we dissect CoT reasoning via three dimensions: task, length, and format. To investigate each dimension, we design DataAlchemy, an isolated and controlled environment to train LLMs from scratch and systematically probe them under various distribution conditions. Our results reveal that CoT reasoning is a brittle mirage that vanishes when it is pushed beyond training distributions. This work offers a deeper understanding of why and when CoT reasoning fails, emphasizing the ongoing challenge of achieving genuine and generalizable reasoning.

Although most current large multimodal models (LMMs) can already understand photos of natural scenes and portraits, their understanding of abstract images, e.g., charts, maps, or layouts, and visual reasoning capabilities remains quite rudimentary. They often struggle with simple daily tasks, such as reading time from a clock, understanding a flowchart, or planning a route using a road map. In light of this, we design a multi-modal self-instruct, utilizing large language models and their code capabilities to synthesize massive abstract images and visual reasoning instructions across daily scenarios. Our strategy effortlessly creates a multimodal benchmark with 11,193 instructions for eight visual scenarios: charts, tables, simulated maps, dashboards, flowcharts, relation graphs, floor plans, and visual puzzles. This benchmark, constructed with simple lines and geometric elements, exposes the shortcomings of most advanced LMMs like Claude-3.5-Sonnet and GPT-4o in abstract image understanding, spatial relations reasoning, and visual element induction. Besides, to verify the quality of our synthetic data, we fine-tune an LMM using 62,476 synthetic chart, table and road map instructions. The results demonstrate improved chart understanding and map navigation performance, and also demonstrate potential benefits for other visual reasoning tasks. Our code is available at: https://github.com/zwq2018/Multi-modal-Self-instruct.

Multimodal reasoning is a challenging task that requires models to reason across multiple modalities to answer questions. Existing approaches have made progress by incorporating language and visual modalities into a two-stage reasoning framework, separating rationale generation from answer inference. However, these approaches often fall short due to the inadequate quality of the generated rationales. In this work, we delve into the importance of rationales in model reasoning. We observe that when rationales are completely accurate, the model's accuracy significantly improves, highlighting the need for high-quality rationale generation. Motivated by this, we propose MC-CoT, a self-consistency training strategy that generates multiple rationales and answers, subsequently selecting the most accurate through a voting process. This approach not only enhances the quality of generated rationales but also leads to more accurate and robust answers. Through extensive experiments, we demonstrate that our approach significantly improves model performance across various benchmarks. Remarkably, we show that even smaller base models, when equipped with our proposed approach, can achieve results comparable to those of larger models, illustrating the potential of our approach in harnessing the power of rationales for improved multimodal reasoning. The code is available at https://github.com/chengtan9907/mc-cot.

Reasoning ability is one of the most crucial capabilities of a foundation model, signifying its capacity to address complex reasoning tasks. Chain-of-Thought (CoT) technique is widely regarded as one of the effective methods for enhancing the reasoning ability of foundation models and has garnered significant attention. However, the reasoning process of CoT is linear, step-by-step, similar to personal logical reasoning, suitable for solving general and slightly complicated problems. On the contrary, the thinking pattern of an expert owns two prominent characteristics that cannot be handled appropriately in CoT, i.e., high-order multi-hop reasoning and multimodal comparative judgement. Therefore, the core motivation of this paper is transcending CoT to construct a reasoning paradigm that can think like an expert. The hyperedge of a hypergraph could connect various vertices, making it naturally suitable for modelling high-order relationships. Inspired by this, this paper innovatively proposes a multimodal Hypergraph-of-Thought (HoT) reasoning paradigm, which enables the foundation models to possess the expert-level ability of high-order multi-hop reasoning and multimodal comparative judgement. Specifically, a textual hypergraph-of-thought is constructed utilizing triple as the primary thought to model higher-order relationships, and a hyperedge-of-thought is generated through multi-hop walking paths to achieve multi-hop inference. Furthermore, we devise a visual hypergraph-of-thought to interact with the textual hypergraph-of-thought via Cross-modal Co-Attention Graph Learning for multimodal comparative verification. Experimentations on the ScienceQA benchmark demonstrate the proposed HoT-based T5 outperforms CoT-based GPT3.5 and chatGPT, which is on par with CoT-based GPT4 with a lower model size.

Visual reasoning is central to human cognition, enabling individuals to interpret and abstractly understand their environment. Although recent Multimodal Large Language Models (MLLMs) have demonstrated impressive performance across language and vision-language tasks, existing benchmarks primarily measure recognition-based skills and inadequately assess true visual reasoning capabilities. To bridge this critical gap, we introduce VERIFY, a benchmark explicitly designed to isolate and rigorously evaluate the visual reasoning capabilities of state-of-the-art MLLMs. VERIFY compels models to reason primarily from visual information, providing minimal textual context to reduce reliance on domain-specific knowledge and linguistic biases. Each problem is accompanied by a human-annotated reasoning path, making it the first to provide in-depth evaluation of model decision-making processes. Additionally, we propose novel metrics that assess visual reasoning fidelity beyond mere accuracy, highlighting critical imbalances in current model reasoning patterns. Our comprehensive benchmarking of leading MLLMs uncovers significant limitations, underscoring the need for a balanced and holistic approach to both perception and reasoning. For more teaser and testing, visit our project page (https://verify-eqh.pages.dev/).

Recent Large Language Models (LLMs) have reported high accuracy on reasoning benchmarks. However, it is still unclear whether the observed results arise from true reasoning or from statistical recall of the training set. Inspired by the ladder of causation (Pearl, 2009) and its three levels (associations, interventions and counterfactuals), this paper introduces RE-IMAGINE, a framework to characterize a hierarchy of reasoning ability in LLMs, alongside an automated pipeline to generate problem variations at different levels of the hierarchy. By altering problems in an intermediate symbolic representation, RE-IMAGINE generates arbitrarily many problems that are not solvable using memorization alone. Moreover, the framework is general and can work across reasoning domains, including math, code, and logic. We demonstrate our framework on four widely-used benchmarks to evaluate several families of LLMs, and observe reductions in performance when the models are queried with problem variations. These assessments indicate a degree of reliance on statistical recall for past performance, and open the door to further research targeting skills across the reasoning hierarchy.

Logical reasoning is a fundamental aspect of human intelligence and a key component of tasks like problem-solving and decision-making. Recent advancements have enabled Large Language Models (LLMs) to potentially exhibit reasoning capabilities, but complex logical reasoning remains a challenge. The state-of-the-art, solver-augmented language models, use LLMs to parse natural language logical questions into symbolic representations first and then adopt external logical solvers to take in the symbolic representations and output the answers. Despite their impressive performance, any parsing errors will inevitably result in the failure of the execution of the external logical solver and no answer to the logical questions. In this paper, we introduce LoGiPT, a novel language model that directly emulates the reasoning processes of logical solvers and bypasses the parsing errors by learning to strict adherence to solver syntax and grammar. LoGiPT is fine-tuned on a newly constructed instruction-tuning dataset derived from revealing and refining the invisible reasoning process of deductive solvers. Experimental results on two public deductive reasoning datasets demonstrate that LoGiPT outperforms state-of-the-art solver-augmented LMs and few-shot prompting methods on competitive LLMs like ChatGPT or GPT-4.

Recent developments, particularly OpenAI's O1 model, have demonstrated the remarkable potential of Large Language Models (LLMs) for complex reasoning tasks. Through analysis of O1's outputs and provided sample Chain-of-Thought (CoT) demonstrations, we observe that it approaches problem-solving in a distinctly human-like manner, systematically brainstorming ideas, testing hypotheses, verifying results, and planning comprehensive solutions. These sophisticated reasoning capabilities remain notably absent in other state-of-the-art language models. In this paper, we hypothesize that this performance gap stems from the limited availability of high-quality reasoning process data in current training sets. We demonstrate that by constructing a specialized dataset focused on explicit problem-solving workflows ("worked solutions"), we can elicit substantially improved planning capabilities from existing models. Additionally, we propose the Reasoning Enhancement Loop (REL), a method for generating synthetic worked solutions.

Large Language Models (LLMs) have succeeded remarkably in various natural language processing (NLP) tasks, yet their reasoning capabilities remain a fundamental challenge. While LLMs exhibit impressive fluency and factual recall, their ability to perform complex reasoning-spanning logical deduction, mathematical problem-solving, commonsense inference, and multi-step reasoning-often falls short of human expectations. This survey provides a comprehensive review of emerging techniques enhancing reasoning in LLMs. We categorize existing methods into key approaches, including prompting strategies (e.g., Chain-of-Thought reasoning, Self-Consistency, and Tree-of-Thought reasoning), architectural innovations (e.g., retrieval-augmented models, modular reasoning networks, and neuro-symbolic integration), and learning paradigms (e.g., fine-tuning with reasoning-specific datasets, reinforcement learning, and self-supervised reasoning objectives). Additionally, we explore evaluation frameworks used to assess reasoning in LLMs and highlight open challenges, such as hallucinations, robustness, and reasoning generalization across diverse tasks. By synthesizing recent advancements, this survey aims to provide insights into promising directions for future research and practical applications of reasoning-augmented 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.

Reasoning capabilities have significantly improved the performance of vision-language models (VLMs) in domains such as mathematical problem-solving, coding, and visual question-answering. However, their impact on real-world applications remains unclear. This paper presents the first empirical study on the effectiveness of reasoning-enabled VLMs in mobile GUI agents, a domain that requires interpreting complex screen layouts, understanding user instructions, and executing multi-turn interactions. We evaluate two pairs of commercial models--Gemini 2.0 Flash and Claude 3.7 Sonnet--comparing their base and reasoning-enhanced versions across two static benchmarks (ScreenSpot and AndroidControl) and one interactive environment (AndroidWorld). We surprisingly find the Claude 3.7 Sonnet reasoning model achieves state-of-the-art performance on AndroidWorld. However, reasoning VLMs generally offer marginal improvements over non-reasoning models on static benchmarks and even degrade performance in some agent setups. Notably, reasoning and non-reasoning VLMs fail on different sets of tasks, suggesting that reasoning does have an impact, but its benefits and drawbacks counterbalance each other. We attribute these inconsistencies to the limitations of benchmarks and VLMs. Based on the findings, we provide insights for further enhancing mobile GUI agents in terms of benchmarks, VLMs, and their adaptability in dynamically invoking reasoning VLMs. The experimental data are publicly available at https://github.com/LlamaTouch/VLM-Reasoning-Traces.

We introduce the task of text-to-diagram generation, which focuses on creating structured visual representations directly from textual descriptions. Existing approaches in text-to-image and text-to-code generation lack the logical organization and flexibility needed to produce accurate, editable diagrams, often resulting in outputs that are either unstructured or difficult to modify. To address this gap, we introduce DiagramGenBenchmark, a comprehensive evaluation framework encompassing eight distinct diagram categories, including flowcharts, model architecture diagrams, and mind maps. Additionally, we present DiagramAgent, an innovative framework with four core modules-Plan Agent, Code Agent, Check Agent, and Diagram-to-Code Agent-designed to facilitate both the generation and refinement of complex diagrams. Our extensive experiments, which combine objective metrics with human evaluations, demonstrate that DiagramAgent significantly outperforms existing baseline models in terms of accuracy, structural coherence, and modifiability. This work not only establishes a foundational benchmark for the text-to-diagram generation task but also introduces a powerful toolset to advance research and applications in this emerging area.

Chain of Thought (CoT) is significant in improving the reasoning abilities of large language models (LLMs). However, the correlation between the effectiveness of CoT and the length of reasoning steps in prompts remains largely unknown. To shed light on this, we have conducted several empirical experiments to explore the relations. Specifically, we design experiments that expand and compress the rationale reasoning steps within CoT demonstrations, while keeping all other factors constant. We have the following key findings. First, the results indicate that lengthening the reasoning steps in prompts, even without adding new information into the prompt, considerably enhances LLMs' reasoning abilities across multiple datasets. Alternatively, shortening the reasoning steps, even while preserving the key information, significantly diminishes the reasoning abilities of models. This finding highlights the importance of the number of steps in CoT prompts and provides practical guidance to make better use of LLMs' potential in complex problem-solving scenarios. Second, we also investigated the relationship between the performance of CoT and the rationales used in demonstrations. Surprisingly, the result shows that even incorrect rationales can yield favorable outcomes if they maintain the requisite length of inference. Third, we observed that the advantages of increasing reasoning steps are task-dependent: simpler tasks require fewer steps, whereas complex tasks gain significantly from longer inference sequences.

Rule-based reasoning, a fundamental type of legal reasoning, enables us to draw conclusions by accurately applying a rule to a set of facts. We explore causal language models as rule-based reasoners, specifically with respect to compositional rules - rules consisting of multiple elements which form a complex logical expression. Reasoning about compositional rules is challenging because it requires multiple reasoning steps, and attending to the logical relationships between elements. We introduce a new prompting method, Chain of Logic, which elicits rule-based reasoning through decomposition (solving elements as independent threads of logic), and recomposition (recombining these sub-answers to resolve the underlying logical expression). This method was inspired by the IRAC (Issue, Rule, Application, Conclusion) framework, a sequential reasoning approach used by lawyers. We evaluate chain of logic across eight rule-based reasoning tasks involving three distinct compositional rules from the LegalBench benchmark and demonstrate it consistently outperforms other prompting methods, including chain of thought and self-ask, using open-source and commercial language models.

Recently, Chain-of-Thought (CoT) prompting has delivered success on complex reasoning tasks, which aims at designing a simple prompt like ``Let's think step by step'' or multiple in-context exemplars with well-designed rationales to elicit Large Language Models (LLMs) to generate intermediate reasoning steps. However, the generated rationales often come with mistakes, making unfactual and unfaithful reasoning chains. To mitigate this brittleness, we propose a novel Chain-of-Knowledge (CoK) prompting, where we aim at eliciting LLMs to generate explicit pieces of knowledge evidence in the form of structure triple. This is inspired by our human behaviors, i.e., we can draw a mind map or knowledge map as the reasoning evidence in the brain before answering a complex question. Benefiting from CoK, we additionally introduce a F^2-Verification method to estimate the reliability of the reasoning chains in terms of factuality and faithfulness. For the unreliable response, the wrong evidence can be indicated to prompt the LLM to rethink. Extensive experiments demonstrate that our method can further improve the performance of commonsense, factual, symbolic, and arithmetic reasoning tasks.

As large language models (LLMs) perform more difficult tasks, it becomes harder to verify the correctness and safety of their behavior. One approach to help with this issue is to prompt LLMs to externalize their reasoning, e.g., by having them generate step-by-step reasoning as they answer a question (Chain-of-Thought; CoT). The reasoning may enable us to check the process that models use to perform tasks. However, this approach relies on the stated reasoning faithfully reflecting the model's actual reasoning, which is not always the case. To improve over the faithfulness of CoT reasoning, we have models generate reasoning by decomposing questions into subquestions. Decomposition-based methods achieve strong performance on question-answering tasks, sometimes approaching that of CoT while improving the faithfulness of the model's stated reasoning on several recently-proposed metrics. By forcing the model to answer simpler subquestions in separate contexts, we greatly increase the faithfulness of model-generated reasoning over CoT, while still achieving some of the performance gains of CoT. Our results show it is possible to improve the faithfulness of model-generated reasoning; continued improvements may lead to reasoning that enables us to verify the correctness and safety of LLM behavior.

Reasoning is a cognitive process of using evidence to reach a sound conclusion. The reasoning capability is essential for large language models (LLMs) to serve as the brain of the artificial general intelligence agent. Recent studies reveal that fine-tuning LLMs on data with the chain of thought (COT) reasoning process can significantly enhance their reasoning capabilities. However, we find that the fine-tuned LLMs suffer from an Assessment Misalignment problem, i.e., they frequently assign higher scores to subpar COTs, leading to potential limitations in their reasoning abilities. To address this problem, we introduce an Alignment Fine-Tuning (AFT) paradigm, which involves three steps: 1) fine-tuning LLMs with COT training data; 2) generating multiple COT responses for each question, and categorizing them into positive and negative ones based on whether they achieve the correct answer; 3) calibrating the scores of positive and negative responses given by LLMs with a novel constraint alignment loss. Specifically, the constraint alignment loss has two objectives: a) Alignment, which guarantees that positive scores surpass negative scores to encourage answers with high-quality COTs; b) Constraint, which keeps the negative scores confined to a reasonable range to prevent the model degradation. Beyond just the binary positive and negative feedback, the constraint alignment loss can be seamlessly adapted to the ranking situations when ranking feedback is accessible. Furthermore, we also delve deeply into recent ranking-based alignment methods, such as DPO, RRHF, and PRO, and discover that the constraint, which has been overlooked by these approaches, is also crucial for their performance. Extensive experiments on four reasoning benchmarks with both binary and ranking feedback demonstrate the effectiveness of AFT.

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.

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.

Visual reasoning refers to the task of solving questions about visual information. Current visual reasoning methods typically employ pre-trained vision-language model (VLM) strategies or deep neural network approaches. However, existing efforts are constrained by limited reasoning interpretability, while hindering by the phenomenon of underspecification in the question text. Additionally, the absence of fine-grained visual knowledge limits the precise understanding of subject behavior in visual reasoning tasks. To address these issues, we propose VIKSER (Visual Knowledge-Driven Self-Reinforcing Reasoning Framework). Specifically, VIKSER, trained using knowledge distilled from large language models, extracts fine-grained visual knowledge with the assistance of visual relationship detection techniques. Subsequently, VIKSER utilizes fine-grained visual knowledge to paraphrase the question with underspecification. Additionally, we design a novel prompting method called Chain-of-Evidence (CoE), which leverages the power of ``evidence for reasoning'' to endow VIKSER with interpretable reasoning capabilities. Meanwhile, the integration of self-reflection technology empowers VIKSER with the ability to learn and improve from its mistakes. Experiments conducted on widely used datasets demonstrate that VIKSER achieves new state-of-the-art (SOTA) results in relevant tasks.

Logical reasoning is fundamental for humans yet presents a substantial challenge in the domain of Artificial Intelligence. Initially, researchers used Knowledge Representation and Reasoning (KR) systems that did not scale and required non trivial manual effort. Recently, the emergence of large language models (LLMs) has demonstrated the ability to overcome various limitations of formal Knowledge Representation (KR) systems. Consequently, there is a growing interest in using LLMs for logical reasoning via natural language. This work strives to understand the proficiency of LLMs in logical reasoning by offering a brief review of the latest progress in this area; with a focus on the logical reasoning datasets, tasks, and the methods adopted to utilize LLMs for reasoning. To offer a thorough analysis, we have compiled a benchmark titled LogiGLUE. This includes 24 varied datasets encompassing deductive, abductive, and inductive reasoning. We have standardized these datasets into Seq2Seq tasks to facilitate straightforward training and evaluation for future research. Utilizing LogiGLUE as a foundation, we have trained an instruction fine tuned language model, resulting in LogiT5. We study single task training, multi task training, and a chain of thought knowledge distillation fine tuning technique to assess the performance of model across the different logical reasoning categories. By this comprehensive process, we aim to shed light on the capabilities and potential pathways for enhancing logical reasoning proficiency in LLMs, paving the way for more advanced and nuanced developments in this critical field.

Large language models (LLMs) have demonstrated impressive capabilities in various reasoning tasks, aided by techniques like chain-of-thought (CoT) prompting that elicits verbalized reasoning. However, LLMs often generate text with obvious mistakes and contradictions, raising doubts about their ability to robustly process and utilize generated rationales. In this work, we investigate CoT reasoning in LLMs through the lens of internal representations, focusing on how these representations are influenced by generated rationales. Our preliminary analysis reveals that while generated rationales improve answer accuracy, inconsistencies emerge between the model's internal representations in middle layers and those in final layers, potentially undermining the reliability of their reasoning processes. To address this, we propose internal consistency as a measure of the model's confidence by examining the agreement of latent predictions decoded from intermediate layers. Extensive empirical studies across different models and datasets demonstrate that internal consistency effectively distinguishes between correct and incorrect reasoning paths. Motivated by this, we propose a new approach to calibrate CoT reasoning by up-weighting reasoning paths with high internal consistency, resulting in a significant boost in reasoning performance. Further analysis uncovers distinct patterns in attention and feed-forward modules across layers, providing insights into the emergence of internal inconsistency. In summary, our results demonstrate the potential of using internal representations for self-evaluation of LLMs.

Mathematical reasoning is regarded as a necessary ability for Language Models (LMs). Recent works demonstrate large LMs' impressive performance in solving math problems. The success is attributed to their Chain-of-Thought (CoT) reasoning abilities, i.e., the ability to decompose complex questions into step-by-step reasoning chains, but such ability seems only to emerge from models with abundant parameters. This work investigates how to incorporate relatively small LMs with the capabilities of multi-step reasoning. We propose to inject such abilities by continually pre-training LMs on a synthetic dataset MsAT which is composed of Multi-step Arithmetic Tasks. Our experiments on four math word problem datasets show the effectiveness of the proposed method in enhancing LMs' math reasoning abilities.

Reasoning is an essential component of human intelligence as it plays a fundamental role in our ability to think critically, support responsible decisions, and solve challenging problems. Traditionally, AI has addressed reasoning in the context of logic-based representations of knowledge. However, the recent leap forward in natural language processing, with the emergence of language models based on transformers, is hinting at the possibility that these models exhibit reasoning abilities, particularly as they grow in size and are trained on more data. Despite ongoing discussions about what reasoning is in language models, it is still not easy to pin down to what extent these models are actually capable of reasoning. The goal of this workshop is to create a platform for researchers from different disciplines and/or AI perspectives, to explore approaches and techniques with the aim to reconcile reasoning between language models using transformers and using logic-based representations. The specific objectives include analyzing the reasoning abilities of language models measured alongside KR methods, injecting KR-style reasoning abilities into language models (including by neuro-symbolic means), and formalizing the kind of reasoning language models carry out. This exploration aims to uncover how language models can effectively integrate and leverage knowledge and reasoning with it, thus improving their application and utility in areas where precision and reliability are a key requirement.

Chain-of-thought (CoT) prompting enhances reasoning in large language models (LLMs) but often leads to verbose and redundant outputs, thus increasing inference cost. We hypothesize that many reasoning steps are unnecessary for producing correct answers. To investigate this, we start with a systematic study to examine what is the minimum reasoning required for a model to reach a stable decision. We find that on math reasoning tasks like math, models typically converge to their final answers after 60\% of the reasoning steps, suggesting substantial redundancy in the remaining content. Based on these insights, we propose three inference-time strategies to improve efficiency: (1) early stopping via answer consistency, (2) boosting the probability of generating end-of-reasoning signals, and (3) a supervised method that learns when to stop based on internal activations. Experiments across five benchmarks and five open-weights LLMs show that our methods significantly reduce token usage with little or no accuracy drop. In particular, on NaturalQuestions, Answer Consistency reduces tokens by over 40\% while further improving accuracy. Our work underscores the importance of cost-effective reasoning methods that operate at inference time, offering practical benefits for real-world applications.

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

Large language models have recently shown human level performance on a variety of reasoning tasks. However, the ability of these models to perform complex visual reasoning has not been studied in detail yet. A key challenge in many visual reasoning tasks is that the visual information needs to be tightly integrated in the reasoning process. We propose to address this challenge by drawing inspiration from human visual problem solving which depends on a variety of low-level visual capabilities. It can often be cast as the three step-process of ``Look, Remember, Reason'': visual information is incrementally extracted using low-level visual routines in a step-by-step fashion until a final answer is reached. We follow the same paradigm to enable existing large language models, with minimal changes to the architecture, to solve visual reasoning problems. To this end, we introduce rationales over the visual input that allow us to integrate low-level visual capabilities, such as object recognition and tracking, as surrogate tasks. We show competitive performance on diverse visual reasoning tasks from the CLEVR, CATER, and ACRE datasets over state-of-the-art models designed specifically for these tasks.

When leveraging language models for reasoning tasks, generating explicit chain-of-thought (CoT) steps often proves essential for achieving high accuracy in final outputs. In this paper, we investigate if models can be taught to internalize these CoT steps. To this end, we propose a simple yet effective method for internalizing CoT steps: starting with a model trained for explicit CoT reasoning, we gradually remove the intermediate steps and finetune the model. This process allows the model to internalize the intermediate reasoning steps, thus simplifying the reasoning process while maintaining high performance. Our approach enables a GPT-2 Small model to solve 9-by-9 multiplication with up to 99% accuracy, whereas standard training cannot solve beyond 4-by-4 multiplication. Furthermore, our method proves effective on larger language models, such as Mistral 7B, achieving over 50% accuracy on GSM8K without producing any intermediate steps.

Recent advances in Multimodal Large Language Models (MLLMs) have achieved remarkable progress in general domains and demonstrated promise in multimodal mathematical reasoning. However, applying MLLMs to geometry problem solving (GPS) remains challenging due to lack of accurate step-by-step solution data and severe hallucinations during reasoning. In this paper, we propose GeoGen, a pipeline that can automatically generates step-wise reasoning paths for geometry diagrams. By leveraging the precise symbolic reasoning, GeoGen produces large-scale, high-quality question-answer pairs. To further enhance the logical reasoning ability of MLLMs, we train GeoLogic, a Large Language Model (LLM) using synthetic data generated by GeoGen. Serving as a bridge between natural language and symbolic systems, GeoLogic enables symbolic tools to help verifying MLLM outputs, making the reasoning process more rigorous and alleviating hallucinations. Experimental results show that our approach consistently improves the performance of MLLMs, achieving remarkable results on benchmarks for geometric reasoning tasks. This improvement stems from our integration of the strengths of LLMs and symbolic systems, which enables a more reliable and interpretable approach for the GPS task. Codes are available at https://github.com/ycpNotFound/GeoGen.

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.

Diagrams serve as a fundamental form of visual language, representing complex concepts and their inter-relationships through structured symbols, shapes, and spatial arrangements. Unlike natural images, their inherently symbolic and abstract nature poses significant challenges for Multimodal Large Language Models (MLLMs). However, current benchmarks conflate perceptual and reasoning tasks, making it difficult to assess whether MLLMs genuinely understand mathematical diagrams beyond superficial pattern recognition. To address this gap, we introduce MATHGLANCE, a benchmark specifically designed to isolate and evaluate mathematical perception in MLLMs. MATHGLANCE comprises 1.2K images and 1.6K carefully curated questions spanning four perception tasks: shape classification, object counting, relationship identification, and object grounding, covering diverse domains including plane geometry, solid geometry, and graphical representations. Our evaluation of MLLMs reveals that their ability to understand diagrams is notably limited, particularly in fine-grained grounding tasks. In response, we construct GeoPeP, a perception-oriented dataset of 200K structured geometry image-text pairs explicitly annotated with geometric primitives and precise spatial relationships. Training MLLM on GeoPeP leads to significant gains in perceptual accuracy, which in turn substantially improves mathematical reasoning. Our benchmark and dataset establish critical standards for evaluating and advancing multimodal mathematical understanding, providing valuable resources and insights to foster future MLLM research.

We explore multi-step reasoning in vision-language models (VLMs). The problem is challenging, as reasoning data consisting of multiple steps of visual and language processing are barely available. To overcome the challenge, we first introduce a least-to-most visual reasoning paradigm, which interleaves steps of decomposing a question into sub-questions and invoking external tools for resolving sub-questions. Based on the paradigm, we further propose a novel data synthesis approach that can automatically create questions and multi-step reasoning paths for an image in a bottom-up manner. Our approach divides the complex synthesis task into a few simple sub-tasks, and (almost entirely) relies on open-sourced models to accomplish the sub-tasks. Therefore, the entire synthesis process is reproducible and cost-efficient, and the synthesized data is quality guaranteed. With the approach, we construct 50k visual reasoning examples. Then, we develop a visual reasoner through supervised fine-tuning, which is capable of generally enhancing the reasoning abilities of a wide range of existing VLMs in a plug-and-play fashion. Extensive experiments indicate that the visual reasoner can consistently and significantly improve four VLMs on four VQA benchmarks. Our code and dataset are available at https://github.com/steven-ccq/VisualReasoner.

Learning general-purpose reasoning capabilities has long been a challenging problem in AI. Recent research in large language models (LLMs), such as DeepSeek-R1, has shown that reinforcement learning techniques like GRPO can enable pre-trained LLMs to develop reasoning capabilities using simple question-answer pairs. In this paper, we aim to train visual language models (VLMs) to perform reasoning on image data through reinforcement learning and visual question-answer pairs, without any explicit chain-of-thought (CoT) supervision. Our findings indicate that simply applying reinforcement learning to a VLM -- by prompting the model to produce a reasoning chain before providing an answer -- can lead the model to develop shortcuts from easy questions, thereby reducing its ability to generalize across unseen data distributions. We argue that the key to mitigating shortcut learning is to encourage the model to interpret images prior to reasoning. Therefore, we train the model to adhere to a caption-reason-answer output format: initially generating a detailed caption for an image, followed by constructing an extensive reasoning chain. When trained on 273K CoT-free visual question-answer pairs and using only reinforcement learning, our model, named Visionary-R1, outperforms strong multimodal models, such as GPT-4o, Claude3.5-Sonnet, and Gemini-1.5-Pro, on multiple visual reasoning benchmarks.

Reasoning is a distinctive human capacity, enabling us to address complex problems by breaking them down into a series of manageable cognitive steps. Yet, complex logical reasoning is still cumbersome for language models. Based on the dual process theory in cognitive science, we are the first to unravel the cognitive reasoning abilities of language models. Our framework employs an iterative methodology to construct a Cognitive Tree (CogTree). The root node of this tree represents the initial query, while the leaf nodes consist of straightforward questions that can be answered directly. This construction involves two main components: the implicit extraction module (referred to as the intuitive system) and the explicit reasoning module (referred to as the reflective system). The intuitive system rapidly generates multiple responses by utilizing in-context examples, while the reflective system scores these responses using comparative learning. The scores guide the intuitive system in its subsequent generation step. Our experimental results on two popular and challenging reasoning tasks indicate that it is possible to achieve a performance level comparable to that of GPT-3.5 (with 175B parameters), using a significantly smaller language model that contains fewer parameters (<=7B) than 5% of GPT-3.5.

We report on a new, simple, modular, and flexible approach for automated generation of illustrations for (readable) synthetic geometry proofs. The underlying proofs are generated using the Larus automated prover for coherent logic, and corresponding illustrations are generated in the GCLC language. Animated illustrations are also supported.

Large Language Models (LLMs) have been shown to achieve breakthrough performance on complex logical reasoning tasks. Nevertheless, most existing research focuses on employing formal language to guide LLMs to derive reliable reasoning paths, while systematic evaluations of these capabilities are still limited. In this paper, we aim to conduct a comprehensive evaluation of LLMs across various logical reasoning problems utilizing formal languages. From the perspective of three dimensions, i.e., spectrum of LLMs, taxonomy of tasks, and format of trajectories, our key findings are: 1) Thinking models significantly outperform Instruct models, especially when formal language is employed; 2) All LLMs exhibit limitations in inductive reasoning capability, irrespective of whether they use a formal language; 3) Data with PoT format achieves the best generalization performance across other languages. Additionally, we also curate the formal-relative training data to further enhance the small language models, and the experimental results indicate that a simple rejected fine-tuning method can better enable LLMs to generalize across formal languages and achieve the best overall performance. Our codes and reports are available at https://github.com/jiangjin1999/FormalEval.

Large language models (LLMs) have gained enormous attention from both academia and industry, due to their exceptional ability in language generation and extremely powerful generalization. However, current LLMs still output unreliable content in practical reasoning tasks due to their inherent issues (e.g., hallucination). To better disentangle this problem, in this paper, we conduct an in-depth investigation to systematically explore the capability of LLMs in logical reasoning. More in detail, we first investigate the deficiency of LLMs in logical reasoning on different tasks, including event relation extraction and deductive reasoning. Our study demonstrates that LLMs are not good reasoners in solving tasks with rigorous reasoning and will produce counterfactual answers, which require us to iteratively refine. Therefore, we comprehensively explore different strategies to endow LLMs with logical reasoning ability, and thus enable them to generate more logically consistent answers across different scenarios. Based on our approach, we also contribute a synthesized dataset (LLM-LR) involving multi-hop reasoning for evaluation and pre-training. Extensive quantitative and qualitative analyses on different tasks also validate the effectiveness and necessity of teaching LLMs with logic and provide insights for solving practical tasks with LLMs in future work.

Reasoning models have demonstrated remarkable progress in solving complex and logic-intensive tasks by generating extended Chain-of-Thoughts (CoTs) prior to arriving at a final answer. Yet, the emergence of this "slow-thinking" paradigm, with numerous tokens generated in sequence, inevitably introduces substantial computational overhead. To this end, it highlights an urgent need for effective acceleration. This survey aims to provide a comprehensive overview of recent advances in efficient reasoning. It categorizes existing works into three key directions: (1) shorter - compressing lengthy CoTs into concise yet effective reasoning chains; (2) smaller - developing compact language models with strong reasoning capabilities through techniques such as knowledge distillation, other model compression techniques, and reinforcement learning; and (3) faster - designing efficient decoding strategies to accelerate inference. A curated collection of papers discussed in this survey is available in our GitHub repository.

The field of natural language processing (NLP) has witnessed significant progress in recent years, with a notable focus on improving large language models' (LLM) performance through innovative prompting techniques. Among these, prompt engineering coupled with structures has emerged as a promising paradigm, with designs such as Chain-of-Thought, Tree of Thoughts, or Graph of Thoughts, in which the overall LLM reasoning is guided by a structure such as a graph. As illustrated with numerous examples, this paradigm significantly enhances the LLM's capability to solve numerous tasks, ranging from logical or mathematical reasoning to planning or creative writing. To facilitate the understanding of this growing field and pave the way for future developments, we devise a general blueprint for effective and efficient LLM reasoning schemes. For this, we conduct an in-depth analysis of the prompt execution pipeline, clarifying and clearly defining different concepts. We then build the first taxonomy of structure-enhanced LLM reasoning schemes. We focus on identifying fundamental classes of harnessed structures, and we analyze the representations of these structures, algorithms executed with these structures, and many others. We refer to these structures as reasoning topologies, because their representation becomes to a degree spatial, as they are contained within the LLM context. Our study compares existing prompting schemes using the proposed taxonomy, discussing how certain design choices lead to different patterns in performance and cost. We also outline theoretical underpinnings, relationships between prompting and others parts of the LLM ecosystem such as knowledge bases, and the associated research challenges. Our work will help to advance future prompt engineering techniques.

Machine-assisted theorem proving refers to the process of conducting structured reasoning to automatically generate proofs for mathematical theorems. Recently, there has been a surge of interest in using machine learning models in conjunction with proof assistants to perform this task. In this paper, we introduce Pantograph, a tool that provides a versatile interface to the Lean 4 proof assistant and enables efficient proof search via powerful search algorithms such as Monte Carlo Tree Search. In addition, Pantograph enables high-level reasoning by enabling a more robust handling of Lean 4's inference steps. We provide an overview of Pantograph's architecture and features. We also report on an illustrative use case: using machine learning models and proof sketches to prove Lean 4 theorems. Pantograph's innovative features pave the way for more advanced machine learning models to perform complex proof searches and high-level reasoning, equipping future researchers to design more versatile and powerful theorem provers.

This study focuses on improving the performance of lightweight Large Language Models (LLMs) in mathematical reasoning tasks. We introduce a novel method for measuring mathematical logic similarity and design an automatic screening mechanism to construct a set of reference problems that integrate both semantic and logical similarity. By employing carefully crafted positive and negative example prompts, we guide the model towards adopting sound reasoning logic. To the best of our knowledge, this is the first attempt to utilize retrieval-enhanced generation for mathematical problem-solving. Experimental results demonstrate that our method achieves a 15.8% improvement over the Chain of Thought approach on the SVAMP dataset and a 21.5 % improvement on the GSM8K dataset. Further application of this method to a large-scale model with 175 billion parameters yields performance comparable to the best results on both aforementioned datasets. Finally, we conduct an analysis of errors during the reasoning process, providing valuable insights and directions for future research on reasoning tasks using large language models.

Chain-of-Thought (CoT) prompting has proven highly effective for enhancing complex reasoning in Large Language Models (LLMs) and Multimodal Large Language Models (MLLMs). Yet, it struggles in complex spatial reasoning tasks. Nonetheless, human cognition extends beyond language alone, enabling the remarkable capability to think in both words and images. Inspired by this mechanism, we propose a new reasoning paradigm, Multimodal Visualization-of-Thought (MVoT). It enables visual thinking in MLLMs by generating image visualizations of their reasoning traces. To ensure high-quality visualization, we introduce token discrepancy loss into autoregressive MLLMs. This innovation significantly improves both visual coherence and fidelity. We validate this approach through several dynamic spatial reasoning tasks. Experimental results reveal that MVoT demonstrates competitive performance across tasks. Moreover, it exhibits robust and reliable improvements in the most challenging scenarios where CoT fails. Ultimately, MVoT establishes new possibilities for complex reasoning tasks where visual thinking can effectively complement verbal reasoning.

Large Language Models (LLMs) have excelled in multi-hop question-answering (M-QA) due to their advanced reasoning abilities. However, the impact of the inherent reasoning structures on LLM M-QA performance remains unclear, largely due to the absence of QA datasets that provide fine-grained reasoning structures. To address this gap, we introduce the Graph Reasoning-Structured Question Answering Dataset (GRS-QA), which includes both semantic contexts and reasoning structures for QA pairs. Unlike existing M-QA datasets, where different reasoning structures are entangled together, GRS-QA explicitly captures intricate reasoning pathways by constructing reasoning graphs, where nodes represent textual contexts and edges denote logical flows. These reasoning graphs of different structures enable a fine-grained evaluation of LLM reasoning capabilities across various reasoning structures. Our empirical analysis reveals that LLMs perform differently when handling questions with varying reasoning structures. This finding facilitates the exploration of textual structures as compared with semantics.

The remarkable progress of Multi-modal Large Language Models (MLLMs) has garnered unparalleled attention, due to their superior performance in visual contexts. However, their capabilities in visual math problem-solving remain insufficiently evaluated and understood. We investigate current benchmarks to incorporate excessive visual content within textual questions, which potentially assist MLLMs in deducing answers without truly interpreting the input diagrams. To this end, we introduce MathVerse, an all-around visual math benchmark designed for an equitable and in-depth evaluation of MLLMs. We meticulously collect 2,612 high-quality, multi-subject math problems with diagrams from publicly available sources. Each problem is then transformed by human annotators into six distinct versions, each offering varying degrees of information content in multi-modality, contributing to 15K test samples in total. This approach allows MathVerse to comprehensively assess whether and how much MLLMs can truly understand the visual diagrams for mathematical reasoning. In addition, we propose a Chain-of-Thought (CoT) evaluation strategy for a fine-grained assessment of the output answers. Rather than naively judging True or False, we employ GPT-4(V) to adaptively extract crucial reasoning steps, and then score each step with detailed error analysis, which can reveal the intermediate CoT reasoning quality by MLLMs. We hope the MathVerse benchmark may provide unique insights to guide the future development of MLLMs. Project page: https://mathverse-cuhk.github.io

Proving geometric theorems constitutes a hallmark of visual reasoning combining both intuitive and logical skills. Therefore, automated theorem proving of Olympiad-level geometry problems is considered a notable milestone in human-level automated reasoning. The introduction of AlphaGeometry, a neuro-symbolic model trained with 100 million synthetic samples, marked a major breakthrough. It solved 25 of 30 International Mathematical Olympiad (IMO) problems whereas the reported baseline based on Wu's method solved only ten. In this note, we revisit the IMO-AG-30 Challenge introduced with AlphaGeometry, and find that Wu's method is surprisingly strong. Wu's method alone can solve 15 problems, and some of them are not solved by any of the other methods. This leads to two key findings: (i) Combining Wu's method with the classic synthetic methods of deductive databases and angle, ratio, and distance chasing solves 21 out of 30 methods by just using a CPU-only laptop with a time limit of 5 minutes per problem. Essentially, this classic method solves just 4 problems less than AlphaGeometry and establishes the first fully symbolic baseline strong enough to rival the performance of an IMO silver medalist. (ii) Wu's method even solves 2 of the 5 problems that AlphaGeometry failed to solve. Thus, by combining AlphaGeometry with Wu's method we set a new state-of-the-art for automated theorem proving on IMO-AG-30, solving 27 out of 30 problems, the first AI method which outperforms an IMO gold medalist.

Multimodal Large Language Models (MLLMs) have powered Graphical User Interface (GUI) Agents, showing promise in automating tasks on computing devices. Recent works have begun exploring reasoning in GUI tasks with encouraging results. However, many current approaches rely on manually designed reasoning templates, which may result in reasoning that is not sufficiently robust and adaptive for complex GUI environments. Meanwhile, some existing agents continue to operate as Reactive Actors, relying primarily on implicit reasoning that may lack sufficient depth for GUI tasks demanding planning and error recovery. We argue that advancing these agents requires a shift from reactive acting towards acting based on deliberate reasoning. To facilitate this transformation, we introduce InfiGUI-R1, an MLLM-based GUI agent developed through our Actor2Reasoner framework, a reasoning-centric, two-stage training approach designed to progressively evolve agents from Reactive Actors to Deliberative Reasoners. The first stage, Reasoning Injection, focuses on establishing a basic reasoner. We employ Spatial Reasoning Distillation to transfer cross-modal spatial reasoning capabilities from teacher models to MLLMs through trajectories with explicit reasoning steps, enabling models to integrate GUI visual-spatial information with logical reasoning before action generation. The second stage, Deliberation Enhancement, refines the basic reasoner into a deliberative one using Reinforcement Learning. This stage introduces two approaches: Sub-goal Guidance, which rewards models for generating accurate intermediate sub-goals, and Error Recovery Scenario Construction, which creates failure-and-recovery training scenarios from identified prone-to-error steps. Experimental results show InfiGUI-R1 achieves strong performance in GUI grounding and trajectory tasks. Resources at https://github.com/Reallm-Labs/InfiGUI-R1.

Mathematical reasoning remains a significant challenge for large language models (LLMs), despite progress in prompting techniques such as Chain-of-Thought (CoT). We present Chain of Mathematically Annotated Thought (CoMAT), which enhances reasoning through two stages: Symbolic Conversion (converting natural language queries into symbolic form) and Reasoning Execution (deriving answers from symbolic representations). CoMAT operates entirely with a single LLM and without external solvers. Across four LLMs, CoMAT outperforms traditional CoT on six out of seven benchmarks, achieving gains of 4.48% on MMLU-Redux (MATH) and 4.58% on GaoKao MCQ. In addition to improved performance, CoMAT ensures faithfulness and verifiability, offering a transparent reasoning process for complex mathematical tasks

Recent work has shown that language models (LMs) have strong multi-step (i.e., procedural) reasoning capabilities. However, it is unclear whether LMs perform these tasks by cheating with answers memorized from pretraining corpus, or, via a multi-step reasoning mechanism. In this paper, we try to answer this question by exploring a mechanistic interpretation of LMs for multi-step reasoning tasks. Concretely, we hypothesize that the LM implicitly embeds a reasoning tree resembling the correct reasoning process within it. We test this hypothesis by introducing a new probing approach (called MechanisticProbe) that recovers the reasoning tree from the model's attention patterns. We use our probe to analyze two LMs: GPT-2 on a synthetic task (k-th smallest element), and LLaMA on two simple language-based reasoning tasks (ProofWriter & AI2 Reasoning Challenge). We show that MechanisticProbe is able to detect the information of the reasoning tree from the model's attentions for most examples, suggesting that the LM indeed is going through a process of multi-step reasoning within its architecture in many cases.

Numerous applications of large language models (LLMs) rely on their ability to perform step-by-step reasoning. However, the reasoning behavior of LLMs remains poorly understood, posing challenges to research, development, and safety. To address this gap, we introduce landscape of thoughts-the first visualization tool for users to inspect the reasoning paths of chain-of-thought and its derivatives on any multi-choice dataset. Specifically, we represent the states in a reasoning path as feature vectors that quantify their distances to all answer choices. These features are then visualized in two-dimensional plots using t-SNE. Qualitative and quantitative analysis with the landscape of thoughts effectively distinguishes between strong and weak models, correct and incorrect answers, as well as different reasoning tasks. It also uncovers undesirable reasoning patterns, such as low consistency and high uncertainty. Additionally, users can adapt our tool to a model that predicts the property they observe. We showcase this advantage by adapting our tool to a lightweight verifier that evaluates the correctness of reasoning paths. The code is publicly available at: https://github.com/tmlr-group/landscape-of-thoughts.

Large Language Models (LLMs) are highly proficient in language-based tasks. Their language capabilities have positioned them at the forefront of the future AGI (Artificial General Intelligence) race. However, on closer inspection, Valmeekam et al. (2024); Zecevic et al. (2023); Wu et al. (2024) highlight a significant gap between their language proficiency and reasoning abilities. Reasoning in LLMs and Vision Language Models (VLMs) aims to bridge this gap by enabling these models to think and re-evaluate their actions and responses. Reasoning is an essential capability for complex problem-solving and a necessary step toward establishing trust in Artificial Intelligence (AI). This will make AI suitable for deployment in sensitive domains, such as healthcare, banking, law, defense, security etc. In recent times, with the advent of powerful reasoning models like OpenAI O1 and DeepSeek R1, reasoning endowment has become a critical research topic in LLMs. In this paper, we provide a detailed overview and comparison of existing reasoning techniques and present a systematic survey of reasoning-imbued language models. We also study current challenges and present our findings.

Large language models (LLMs) can perform complex reasoning in few- and zero-shot settings by generating intermediate chain of thought (CoT) reasoning steps. Further, each reasoning step can rely on external tools to support computation beyond the core LLM capabilities (e.g. search/running code). Prior work on CoT prompting and tool use typically requires hand-crafting task-specific demonstrations and carefully scripted interleaving of model generations with tool use. We introduce Automatic Reasoning and Tool-use (ART), a framework that uses frozen LLMs to automatically generate intermediate reasoning steps as a program. Given a new task to solve, ART selects demonstrations of multi-step reasoning and tool use from a task library. At test time, ART seamlessly pauses generation whenever external tools are called, and integrates their output before resuming generation. ART achieves a substantial improvement over few-shot prompting and automatic CoT on unseen tasks in the BigBench and MMLU benchmarks, and matches performance of hand-crafted CoT prompts on a majority of these tasks. ART is also extensible, and makes it easy for humans to improve performance by correcting errors in task-specific programs or incorporating new tools, which we demonstrate by drastically improving performance on select tasks with minimal human intervention.

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.

Recent large language models (LLMs) have witnessed significant advancement in various tasks, including mathematical reasoning and theorem proving. As these two tasks require strict and formal multi-step inference, they are appealing domains for exploring the reasoning ability of LLMs but still face important challenges. Previous studies such as Chain-of-Thought (CoT) have revealed the effectiveness of intermediate steps guidance. However, such step-wise annotation requires heavy labor, leading to insufficient training steps for current benchmarks. To fill this gap, this work introduces MUSTARD, a data generation framework that masters uniform synthesis of theorem and proof data of high quality and diversity. MUSTARD synthesizes data in three stages: (1) It samples a few mathematical concept seeds as the problem category. (2) Then, it prompts a generative language model with the sampled concepts to obtain both the problems and their step-wise formal solutions. (3) Lastly, the framework utilizes a proof assistant (e.g., Lean Prover) to filter the valid proofs. With the proposed MUSTARD, we present a theorem-and-proof benchmark MUSTARDSAUCE with 5,866 valid data points. Each data point contains an informal statement, an informal proof, and a translated formal proof that passes the prover validation. We perform extensive analysis and demonstrate that MUSTARD generates validated high-quality step-by-step data. We further apply the MUSTARDSAUCE for fine-tuning smaller language models. The fine-tuned Llama 2-7B achieves a 15.41% average relative performance gain in automated theorem proving, and 8.18% in math word problems. Codes and data are available at https://github.com/Eleanor-H/MUSTARD.

Recent advances in Chain-of-Thought (CoT) prompting have substantially improved the reasoning capabilities of Large Language Models (LLMs). However, these methods often suffer from overthinking, leading to unnecessarily lengthy or redundant reasoning traces. Existing approaches attempt to mitigate this issue through curating multiple reasoning chains for training LLMs, but their effectiveness is often constrained by the quality of the generated data and prone to overfitting. To address the challenge, we propose Reasoning Compression ThroUgh Stepwise Trials (ReCUT), a novel method aimed at balancing the accuracy and length of reasoning trajectory. Specifically, ReCUT employs a stepwise exploration mechanism and a long-short switched sampling strategy, enabling LLMs to incrementally generate diverse reasoning paths. These paths are evaluated and used to construct preference pairs to train two specialized models (Gemini LLMs)-one optimized for reasoning accuracy, the other for shorter reasoning. A final integrated model is obtained by interpolating the parameters of these two models. Experimental results across multiple math reasoning datasets and backbone models demonstrate that ReCUT significantly reduces reasoning lengths by approximately 30-50%, while maintaining or improving reasoning accuracy compared to various baselines. All codes and data will be released via https://github.com/NEUIR/ReCUT.

Logical reasoning, i.e., deductively inferring the truth value of a conclusion from a set of premises, is an important task for artificial intelligence with wide potential impacts on science, mathematics, and society. While many prompting-based strategies have been proposed to enable Large Language Models (LLMs) to do such reasoning more effectively, they still appear unsatisfactory, often failing in subtle and unpredictable ways. In this work, we investigate the validity of instead reformulating such tasks as modular neurosymbolic programming, which we call LINC: Logical Inference via Neurosymbolic Computation. In LINC, the LLM acts as a semantic parser, translating premises and conclusions from natural language to expressions in first-order logic. These expressions are then offloaded to an external theorem prover, which symbolically performs deductive inference. Leveraging this approach, we observe significant performance gains on FOLIO and a balanced subset of ProofWriter for three different models in nearly all experimental conditions we evaluate. On ProofWriter, augmenting the comparatively small open-source StarCoder+ (15.5B parameters) with LINC even outperforms GPT-3.5 and GPT-4 with Chain-of-Thought (CoT) prompting by an absolute 38% and 10%, respectively. When used with GPT-4, LINC scores 26% higher than CoT on ProofWriter while performing comparatively on FOLIO. Further analysis reveals that although both methods on average succeed roughly equally often on this dataset, they exhibit distinct and complementary failure modes. We thus provide promising evidence for how logical reasoning over natural language can be tackled through jointly leveraging LLMs alongside symbolic provers. All corresponding code is publicly available at https://github.com/benlipkin/linc

Recent advancements, such as DeepSeek-Prover-V2-671B and Kimina-Prover-Preview-72B, demonstrate a prevailing trend in leveraging reinforcement learning (RL)-based large-scale training for automated theorem proving. Surprisingly, we discover that even without any training, careful neuro-symbolic coordination of existing off-the-shelf reasoning models and tactic step provers can achieve comparable performance. This paper introduces DSP+, an improved version of the Draft, Sketch, and Prove framework, featuring a fine-grained and integrated neuro-symbolic enhancement for each phase: (1) In the draft phase, we prompt reasoning models to generate concise natural-language subgoals to benefit the sketch phase, removing thinking tokens and references to human-written proofs; (2) In the sketch phase, subgoals are autoformalized with hypotheses to benefit the proving phase, and sketch lines containing syntactic errors are masked according to predefined rules; (3) In the proving phase, we tightly integrate symbolic search methods like Aesop with step provers to establish proofs for the sketch subgoals. Experimental results show that, without any additional model training or fine-tuning, DSP+ solves 80.7\%, 32.8\%, and 24 out of 644 problems from miniF2F, ProofNet, and PutnamBench, respectively, while requiring fewer budgets compared to state-of-the-arts. DSP+ proves imo\_2019\_p1, an IMO problem in miniF2F that is not solved by any prior work. Additionally, DSP+ generates proof patterns comprehensible by human experts, facilitating the identification of formalization errors; For example, eight wrongly formalized statements in miniF2F are discovered. Our results highlight the potential of classical reasoning patterns besides the RL-based training. All components will be open-sourced.

Despite notable advancements in multimodal reasoning, leading Multimodal Large Language Models (MLLMs) still underperform on vision-centric multimodal reasoning tasks in general scenarios. This shortfall stems from their predominant reliance on logic- and knowledge-based slow thinking strategies, while effective for domains like math and science, fail to integrate visual information effectively during reasoning. Consequently, these models often fail to adequately ground visual cues, resulting in suboptimal performance in tasks that require multiple plausible visual interpretations and inferences. To address this, we present GThinker (General Thinker), a novel reasoning MLLM excelling in multimodal reasoning across general scenarios, mathematics, and science. GThinker introduces Cue-Rethinking, a flexible reasoning pattern that grounds inferences in visual cues and iteratively reinterprets these cues to resolve inconsistencies. Building on this pattern, we further propose a two-stage training pipeline, including pattern-guided cold start and incentive reinforcement learning, designed to enable multimodal reasoning capabilities across domains. Furthermore, to support the training, we construct GThinker-11K, comprising 7K high-quality, iteratively-annotated reasoning paths and 4K curated reinforcement learning samples, filling the data gap toward general multimodal reasoning. Extensive experiments demonstrate that GThinker achieves 81.5% on the challenging comprehensive multimodal reasoning benchmark M^3CoT, surpassing the latest O4-mini model. It also shows an average improvement of 2.1% on general scenario multimodal reasoning benchmarks, while maintaining on-par performance in mathematical reasoning compared to counterpart advanced reasoning models. The code, model, and data will be released soon at https://github.com/jefferyZhan/GThinker.

The pursuit of automated scientific discovery has fueled progress from symbolic logic to modern AI, forging new frontiers in reasoning and pattern recognition. Transformers function as potential systems, where every possible relationship remains latent potentiality until tasks impose constraints, akin to measurement. Yet, refining their sampling requires more than probabilistic selection: solutions must conform to specific structures or rules, ensuring consistency and the invocation of general principles. We present Graph-PReFLexOR (Graph-based Preference-based Recursive Language Modeling for Exploratory Optimization of Reasoning), a framework that combines graph reasoning with symbolic abstraction to dynamically expand domain knowledge. Inspired by reinforcement learning, Graph-PReFLexOR defines reasoning as a structured mapping, where tasks yield knowledge graphs, abstract patterns, and ultimately, final answers. Inspired by category theory, it encodes concepts as nodes and their relationships as edges, supporting hierarchical inference and adaptive learning through isomorphic representations. Demonstrations include hypothesis generation, materials design, and creative reasoning, such as discovering relationships between mythological concepts like 'thin places' with materials science. We propose a 'knowledge garden growth' strategy that integrates insights across domains, promoting interdisciplinary connections. Results with a 3-billion-parameter Graph-PReFLexOR model show superior reasoning depth and adaptability, underscoring the potential for transparent, multidisciplinary AI-driven discovery. It lays the groundwork for general autonomous reasoning solutions.

Chain-of-thought (CoT) prompting for language models demonstrates impressive performance across reasoning tasks, but typically needs labeled exemplars of the reasoning process. In this work, we introduce a new prompting approach, Analogical Prompting, designed to automatically guide the reasoning process of large language models. Inspired by analogical reasoning, a cognitive process in which humans draw from relevant past experiences to tackle new problems, our approach prompts language models to self-generate relevant exemplars or knowledge in the context, before proceeding to solve the given problem. This method presents several advantages: it obviates the need for labeling or retrieving exemplars, offering generality and convenience; it can also tailor the generated exemplars and knowledge to each problem, offering adaptability. Experimental results show that our approach outperforms 0-shot CoT and manual few-shot CoT in a variety of reasoning tasks, including math problem solving in GSM8K and MATH, code generation in Codeforces, and other reasoning tasks in BIG-Bench.

Visual reasoning (VR), which is crucial in many fields for enabling human-like visual understanding, remains highly challenging. Recently, compositional visual reasoning approaches, which leverage the reasoning abilities of large language models (LLMs) with integrated tools to solve problems, have shown promise as more effective strategies than end-to-end VR methods. However, these approaches face limitations, as frozen LLMs lack tool awareness in VR, leading to performance bottlenecks. While leveraging LLMs for reasoning is widely used in other domains, they are not directly applicable to VR due to limited training data, imperfect tools that introduce errors and reduce data collection efficiency in VR, and challenging in fine-tuning on noisy workflows. To address these challenges, we propose DWIM: i) Discrepancy-aware training Workflow generation, which assesses tool usage and extracts more viable workflows for training; and ii) Instruct-Masking fine-tuning, which guides the model to only clone effective actions, enabling the generation of more practical solutions. Our experiments demonstrate that DWIM achieves state-of-the-art performance across various VR tasks, exhibiting strong generalization on multiple widely-used datasets.

Charts are very popular for analyzing data. When exploring charts, people often ask a variety of complex reasoning questions that involve several logical and arithmetic operations. They also commonly refer to visual features of a chart in their questions. However, most existing datasets do not focus on such complex reasoning questions as their questions are template-based and answers come from a fixed-vocabulary. In this work, we present a large-scale benchmark covering 9.6K human-written questions as well as 23.1K questions generated from human-written chart summaries. To address the unique challenges in our benchmark involving visual and logical reasoning over charts, we present two transformer-based models that combine visual features and the data table of the chart in a unified way to answer questions. While our models achieve the state-of-the-art results on the previous datasets as well as on our benchmark, the evaluation also reveals several challenges in answering complex reasoning questions.

Analytical reasoning is an essential and challenging task that requires a system to analyze a scenario involving a set of particular circumstances and perform reasoning over it to make conclusions. In this paper, we study the challenge of analytical reasoning of text and introduce a new dataset consisting of questions from the Law School Admission Test from 1991 to 2016. We analyze what knowledge understanding and reasoning abilities are required to do well on this task. Furthermore, to address this reasoning challenge, we design two different baselines: (1) a Transformer-based method which leverages the state-of-the-art pre-trained language models and (2) Analytical Reasoning Machine (ARM), a logical-level reasoning framework extracting symbolic knowledge (e.g, participants, facts, logical functions) to deduce legitimate solutions. In our experiments, we find that the Transformer-based models struggle to solve this task as their performance is close to random guess and ARM achieves better performance by leveraging symbolic knowledge and interpretable reasoning steps. Results show that both methods still lag far behind human performance, which leave further space for future research.

Recent advances in visual reasoning (VR), particularly with the aid of Large Vision-Language Models (VLMs), show promise but require access to large-scale datasets and face challenges such as high computational costs and limited generalization capabilities. Compositional visual reasoning approaches have emerged as effective strategies; however, they heavily rely on the commonsense knowledge encoded in Large Language Models (LLMs) to perform planning, reasoning, or both, without considering the effect of their decisions on the visual reasoning process, which can lead to errors or failed procedures. To address these challenges, we introduce HYDRA, a multi-stage dynamic compositional visual reasoning framework designed for reliable and incrementally progressive general reasoning. HYDRA integrates three essential modules: a planner, a Reinforcement Learning (RL) agent serving as a cognitive controller, and a reasoner. The planner and reasoner modules utilize an LLM to generate instruction samples and executable code from the selected instruction, respectively, while the RL agent dynamically interacts with these modules, making high-level decisions on selection of the best instruction sample given information from the historical state stored through a feedback loop. This adaptable design enables HYDRA to adjust its actions based on previous feedback received during the reasoning process, leading to more reliable reasoning outputs and ultimately enhancing its overall effectiveness. Our framework demonstrates state-of-the-art performance in various VR tasks on four different widely-used datasets.

Mathematical reasoning serves as a cornerstone for assessing the fundamental cognitive capabilities of human intelligence. In recent times, there has been a notable surge in the development of Large Language Models (LLMs) geared towards the automated resolution of mathematical problems. However, the landscape of mathematical problem types is vast and varied, with LLM-oriented techniques undergoing evaluation across diverse datasets and settings. This diversity makes it challenging to discern the true advancements and obstacles within this burgeoning field. This survey endeavors to address four pivotal dimensions: i) a comprehensive exploration of the various mathematical problems and their corresponding datasets that have been investigated; ii) an examination of the spectrum of LLM-oriented techniques that have been proposed for mathematical problem-solving; iii) an overview of factors and concerns affecting LLMs in solving math; and iv) an elucidation of the persisting challenges within this domain. To the best of our knowledge, this survey stands as one of the first extensive examinations of the landscape of LLMs in the realm of mathematics, providing a holistic perspective on the current state, accomplishments, and future challenges in this rapidly evolving field.

Recent advances in language models have demonstrated their capability to solve mathematical reasoning problems, achieving near-perfect accuracy on grade-school level math benchmarks like GSM8K. In this paper, we formally study how language models solve these problems. We design a series of controlled experiments to address several fundamental questions: (1) Can language models truly develop reasoning skills, or do they simply memorize templates? (2) What is the model's hidden (mental) reasoning process? (3) Do models solve math questions using skills similar to or different from humans? (4) Do models trained on GSM8K-like datasets develop reasoning skills beyond those necessary for solving GSM8K problems? (5) What mental process causes models to make reasoning mistakes? (6) How large or deep must a model be to effectively solve GSM8K-level math questions? Our study uncovers many hidden mechanisms by which language models solve mathematical questions, providing insights that extend beyond current understandings of LLMs.

While the recent Chain-of-Thought (CoT) technique enhances the reasoning ability of large language models (LLMs) with the theory of mind, it might still struggle in handling logical reasoning that relies much on symbolic expressions and rigid deducing rules. To strengthen the logical reasoning capability of LLMs, we propose a novel Symbolic Chain-of-Thought, namely SymbCoT, a fully LLM-based framework that integrates symbolic expressions and logic rules with CoT prompting. Technically, building upon an LLM, SymbCoT 1) first translates the natural language context into the symbolic format, and then 2) derives a step-by-step plan to solve the problem with symbolic logical rules, 3) followed by a verifier to check the translation and reasoning chain. Via thorough evaluations on 5 standard datasets with both First-Order Logic and Constraint Optimization symbolic expressions, SymbCoT shows striking improvements over the CoT method consistently, meanwhile refreshing the current state-of-the-art performances. We further demonstrate that our system advances in more faithful, flexible, and explainable logical reasoning. To our knowledge, this is the first to combine symbolic expressions and rules into CoT for logical reasoning with LLMs. Code is open at https://github.com/Aiden0526/SymbCoT.

We introduce Skywork-R1V3, an advanced, open-source vision-language model (VLM) that pioneers a new approach to visual reasoning. Its key innovation lies in effectively transferring reasoning skills from text-only Large Language Models (LLMs) to visual tasks. The strong performance of Skywork-R1V3 primarily stems from our elaborate post-training RL framework, which effectively activates and enhances the model's reasoning ability, without the need for additional continue pre-training. Through this framework, we further uncover the fundamental role of the connector module in achieving robust cross-modal alignment for multimodal reasoning models. In addition, we introduce a unique indicator of reasoning capability, the entropy of critical reasoning tokens, which has proven highly effective for checkpoint selection during RL training. Skywork-R1V3 achieves state-of-the-art results on MMMU, significantly improving from 64.3% to 76.0%. This performance matches entry-level human capabilities. Remarkably, our RL-powered post-training approach enables even the 38B parameter model to rival top closed-source VLMs. The implementation successfully transfers mathematical reasoning to other subject-related reasoning tasks. We also include an analysis of curriculum learning and reinforcement finetuning strategies, along with a broader discussion on multimodal reasoning. Skywork-R1V3 represents a significant leap in multimodal reasoning, showcasing RL as a powerful engine for advancing open-source VLM capabilities.

Chain-of-thought reasoning has significantly improved the performance of Large Language Models (LLMs) across various domains. However, this reasoning process has been confined exclusively to textual space, limiting its effectiveness in visually intensive tasks. To address this limitation, we introduce the concept of reasoning in the pixel-space. Within this novel framework, Vision-Language Models (VLMs) are equipped with a suite of visual reasoning operations, such as zoom-in and select-frame. These operations enable VLMs to directly inspect, interrogate, and infer from visual evidences, thereby enhancing reasoning fidelity for visual tasks. Cultivating such pixel-space reasoning capabilities in VLMs presents notable challenges, including the model's initially imbalanced competence and its reluctance to adopt the newly introduced pixel-space operations. We address these challenges through a two-phase training approach. The first phase employs instruction tuning on synthesized reasoning traces to familiarize the model with the novel visual operations. Following this, a reinforcement learning (RL) phase leverages a curiosity-driven reward scheme to balance exploration between pixel-space reasoning and textual reasoning. With these visual operations, VLMs can interact with complex visual inputs, such as information-rich images or videos to proactively gather necessary information. We demonstrate that this approach significantly improves VLM performance across diverse visual reasoning benchmarks. Our 7B model, \model, achieves 84\% on V* bench, 74\% on TallyQA-Complex, and 84\% on InfographicsVQA, marking the highest accuracy achieved by any open-source model to date. These results highlight the importance of pixel-space reasoning and the effectiveness of our framework.

Logical reasoning is central to human cognition and intelligence. Past research of logical reasoning within AI uses formal language as knowledge representation~(and symbolic reasoners). However, reasoning with formal language has proved challenging~(e.g., brittleness and knowledge-acquisition bottleneck). This paper provides a comprehensive overview on a new paradigm of logical reasoning, which uses natural language as knowledge representation~(and pretrained language models as reasoners), including philosophical definition and categorization of logical reasoning, advantages of the new paradigm, benchmarks and methods, challenges of the new paradigm, desirable tasks & methods in the future, and relation to related NLP fields. This new paradigm is promising since it not only alleviates many challenges of formal representation but also has advantages over end-to-end neural methods.

Recent advancements in large language models have showcased their remarkable generalizability across various domains. However, their reasoning abilities still have significant room for improvement, especially when confronted with scenarios requiring multi-step reasoning. Although large language models possess extensive knowledge, their behavior, particularly in terms of reasoning, often fails to effectively utilize this knowledge to establish a coherent thinking paradigm. Generative language models sometimes show hallucinations as their reasoning procedures are unconstrained by logical principles. Aiming to improve the zero-shot chain-of-thought reasoning ability of large language models, we propose Logical Chain-of-Thought (LogiCoT), a neurosymbolic framework that leverages principles from symbolic logic to verify and revise the reasoning processes accordingly. Experimental evaluations conducted on language tasks in diverse domains, including arithmetic, commonsense, symbolic, causal inference, and social problems, demonstrate the efficacy of the enhanced reasoning paradigm by logic.

Large language models (LLMs) have shown remarkable reasoning capabilities, especially when prompted to generate intermediate reasoning steps (e.g., Chain-of-Thought, CoT). However, LLMs can still struggle with problems that are easy for humans, such as generating action plans for executing tasks in a given environment, or performing complex math, logical, and commonsense reasoning. The deficiency stems from the key fact that LLMs lack an internal world model to predict the world state (e.g., environment status, intermediate variable values) and simulate long-term outcomes of actions. This prevents LLMs from performing deliberate planning akin to human brains, which involves exploring alternative reasoning paths, anticipating future states and rewards, and iteratively refining existing reasoning steps. To overcome the limitations, we propose a new LLM reasoning framework, Reasoning via Planning (RAP). RAP repurposes the LLM as both a world model and a reasoning agent, and incorporates a principled planning algorithm (based on Monto Carlo Tree Search) for strategic exploration in the vast reasoning space. During reasoning, the LLM (as agent) incrementally builds a reasoning tree under the guidance of the LLM (as world model) and task-specific rewards, and obtains a high-reward reasoning path efficiently with a proper balance between exploration vs. exploitation. We apply RAP to a variety of challenging reasoning problems including plan generation, math reasoning, and logical inference. Empirical results on these tasks demonstrate the superiority of RAP over various strong baselines, including CoT and least-to-most prompting with self-consistency. RAP on LLAMA-33B surpasses CoT on GPT-4 with 33% relative improvement in a plan generation setting.

Vision-Language Models (VLMs) such as GPT-4V have recently demonstrated incredible strides on diverse vision language tasks. We dig into vision-based deductive reasoning, a more sophisticated but less explored realm, and find previously unexposed blindspots in the current SOTA VLMs. Specifically, we leverage Raven's Progressive Matrices (RPMs), to assess VLMs' abilities to perform multi-hop relational and deductive reasoning relying solely on visual clues. We perform comprehensive evaluations of several popular VLMs employing standard strategies such as in-context learning, self-consistency, and Chain-of-thoughts (CoT) on three diverse datasets, including the Mensa IQ test, IntelligenceTest, and RAVEN. The results reveal that despite the impressive capabilities of LLMs in text-based reasoning, we are still far from achieving comparable proficiency in visual deductive reasoning. We found that certain standard strategies that are effective when applied to LLMs do not seamlessly translate to the challenges presented by visual reasoning tasks. Moreover, a detailed analysis reveals that VLMs struggle to solve these tasks mainly because they are unable to perceive and comprehend multiple, confounding abstract patterns in RPM examples.

LLMs have demonstrated strong mathematical reasoning abilities by leveraging reinforcement learning with long chain-of-thought, yet they continue to struggle with theorem proving due to the lack of clear supervision signals when solely using natural language. Dedicated domain-specific languages like Lean provide clear supervision via formal verification of proofs, enabling effective training through reinforcement learning. In this work, we propose Seed-Prover, a lemma-style whole-proof reasoning model. Seed-Prover can iteratively refine its proof based on Lean feedback, proved lemmas, and self-summarization. To solve IMO-level contest problems, we design three test-time inference strategies that enable both deep and broad reasoning. Seed-Prover proves 78.1% of formalized past IMO problems, saturates MiniF2F, and achieves over 50\% on PutnamBench, outperforming the previous state-of-the-art by a large margin. To address the lack of geometry support in Lean, we introduce a geometry reasoning engine Seed-Geometry, which outperforms previous formal geometry engines. We use these two systems to participate in IMO 2025 and fully prove 5 out of 6 problems. This work represents a significant advancement in automated mathematical reasoning, demonstrating the effectiveness of formal verification with long chain-of-thought reasoning.

Large language models (LLMs) can perform complex reasoning by generating intermediate reasoning steps. Providing these steps for prompting demonstrations is called chain-of-thought (CoT) prompting. CoT prompting has two major paradigms. One leverages a simple prompt like "Let's think step by step" to facilitate step-by-step thinking before answering a question. The other uses a few manual demonstrations one by one, each composed of a question and a reasoning chain that leads to an answer. The superior performance of the second paradigm hinges on the hand-crafting of task-specific demonstrations one by one. We show that such manual efforts may be eliminated by leveraging LLMs with the "Let's think step by step" prompt to generate reasoning chains for demonstrations one by one, i.e., let's think not just step by step, but also one by one. However, these generated chains often come with mistakes. To mitigate the effect of such mistakes, we find that diversity matters for automatically constructing demonstrations. We propose an automatic CoT prompting method: Auto-CoT. It samples questions with diversity and generates reasoning chains to construct demonstrations. On ten public benchmark reasoning tasks with GPT-3, Auto-CoT consistently matches or exceeds the performance of the CoT paradigm that requires manual designs of demonstrations. Code is available at https://github.com/amazon-research/auto-cot

Traditional language model-based theorem proving assumes that by training on a sufficient amount of formal proof data, a model will learn to prove theorems. Our key observation is that a wealth of informal information that is not present in formal proofs can be useful for learning to prove theorems. For instance, humans think through steps of a proof, but this thought process is not visible in the resulting code. We present Lean-STaR, a framework for training language models to produce informal thoughts prior to each step of a proof, thereby boosting the model's theorem-proving capabilities. Lean-STaR uses retrospective ground-truth tactics to generate synthetic thoughts for training the language model. At inference time, the trained model directly generates the thoughts prior to the prediction of the tactics in each proof step. Building on the self-taught reasoner framework, we then apply expert iteration to further fine-tune the model on the correct proofs it samples and verifies using the Lean solver. Lean-STaR achieves state-of-the-art results on the miniF2F-test benchmark within the Lean theorem proving environment, significantly outperforming base models (43.4% rightarrow 46.3%, Pass@64). We also analyze the impact of the augmented thoughts on various aspects of the theorem proving process, providing insights into their effectiveness.

The reasoning abilities of large language models (LLMs) have improved with chain-of-thought (CoT) prompting, allowing models to solve complex tasks in a stepwise manner. However, training CoT capabilities requires detailed reasoning data, which is often scarce. The self-taught reasoner (STaR) framework addresses this by using reinforcement learning to automatically generate reasoning steps, reducing reliance on human-labeled data. Although STaR and its variants have demonstrated empirical success, a theoretical foundation explaining these improvements is lacking. This work provides a theoretical framework for understanding the effectiveness of reinforcement learning on CoT reasoning and STaR. Our contributions are: (1) an analysis of policy improvement, showing why LLM reasoning improves iteratively with STaR; (2) conditions for convergence to an optimal reasoning policy; (3) an examination of STaR's robustness, explaining how it can improve reasoning even when incorporating occasional incorrect steps; and (4) criteria for the quality of pre-trained models necessary to initiate effective reasoning improvement. This framework aims to bridge empirical findings with theoretical insights, advancing reinforcement learning approaches for reasoning in LLMs.

Although Large Language Models (LLMs) achieve remarkable performance across various tasks, they often struggle with complex reasoning tasks, such as answering mathematical questions. Recent efforts to address this issue have primarily focused on leveraging mathematical datasets through supervised fine-tuning or self-improvement techniques. However, these methods often depend on high-quality datasets that are difficult to prepare, or they require substantial computational resources for fine-tuning. Inspired by findings that LLMs know how to produce the right answer but struggle to select the correct reasoning path, we propose a purely inference-based searching method -- MindStar (M*). This method formulates reasoning tasks as searching problems and proposes two search ideas to identify the optimal reasoning paths. We evaluate the M* framework on both the GSM8K and MATH datasets, comparing its performance with existing open and closed-source LLMs. Our results demonstrate that M* significantly enhances the reasoning abilities of open-source models, such as Llama-2-13B and Mistral-7B, and achieves comparable performance to GPT-3.5 and Grok-1, but with substantially reduced model size and computational costs.

To achieve faithful reasoning that aligns with human expectations, large language models (LLMs) need to ground their reasoning to real-world knowledge (e.g., web facts, math and physical rules). Tools help LLMs access this external knowledge, but there remains challenges for fine-tuning LLM agents (e.g., Toolformer) to invoke tools in multi-step reasoning problems, where inter-connected tool calls require holistic and efficient tool usage planning. In this work, we propose a new method for LLMs to better leverage tools in multi-step reasoning. Our method, Chain-of-Abstraction (CoA), trains LLMs to first decode reasoning chains with abstract placeholders, and then call domain tools to reify each reasoning chain by filling in specific knowledge. This planning with abstract chains enables LLMs to learn more general reasoning strategies, which are robust to shifts of domain knowledge (e.g., math results) relevant to different reasoning questions. It also allows LLMs to perform decoding and calling of external tools in parallel, which avoids the inference delay caused by waiting for tool responses. In mathematical reasoning and Wiki QA domains, we show that our method consistently outperforms previous chain-of-thought and tool-augmented baselines on both in-distribution and out-of-distribution test sets, with an average ~6% absolute QA accuracy improvement. LLM agents trained with our method also show more efficient tool use, with inference speed being on average ~1.4x faster than baseline tool-augmented LLMs.

Recent advancements in Large Language Models (LLMs) and their multimodal extensions (MLLMs) have substantially enhanced machine reasoning across diverse tasks. However, these models predominantly rely on pure text as the medium for both expressing and structuring reasoning, even when visual information is present. In this work, we argue that language may not always be the most natural or effective modality for reasoning, particularly in tasks involving spatial and geometrical information. Motivated by this, we propose a new paradigm, Visual Planning, which enables planning through purely visual representations, independent of text. In this paradigm, planning is executed via sequences of images that encode step-by-step inference in the visual domain, akin to how humans sketch or visualize future actions. We introduce a novel reinforcement learning framework, Visual Planning via Reinforcement Learning (VPRL), empowered by GRPO for post-training large vision models, leading to substantial improvements in planning in a selection of representative visual navigation tasks, FrozenLake, Maze, and MiniBehavior. Our visual planning paradigm outperforms all other planning variants that conduct reasoning in the text-only space. Our results establish Visual Planning as a viable and promising alternative to language-based reasoning, opening new avenues for tasks that benefit from intuitive, image-based inference.

This paper presents our winning submission to the AI Mathematical Olympiad - Progress Prize 2 (AIMO-2) competition. Our recipe for building state-of-the-art mathematical reasoning models relies on three key pillars. First, we create a large-scale dataset comprising 540K unique high-quality math problems, including olympiad-level problems, and their 3.2M long-reasoning solutions. Second, we develop a novel method to integrate code execution with long reasoning models through iterative training, generation, and quality filtering, resulting in 1.7M high-quality Tool-Integrated Reasoning solutions. Third, we create a pipeline to train models to select the most promising solution from many candidates. We show that such generative solution selection (GenSelect) can significantly improve upon majority voting baseline. Combining these ideas, we train a series of models that achieve state-of-the-art results on mathematical reasoning benchmarks. To facilitate further research, we release our code, models, and the complete OpenMathReasoning dataset under a commercially permissive license.

Recent large language model (LLM) reasoning, despite its success, suffers from limited domain knowledge, susceptibility to hallucinations, and constrained reasoning depth, particularly in small-scale models deployed in resource-constrained environments. This paper presents the first investigation into integrating step-wise knowledge graph retrieval with step-wise reasoning to address these challenges, introducing a novel paradigm termed as graph-augmented reasoning. Our goal is to enable frozen, small-scale LLMs to retrieve and process relevant mathematical knowledge in a step-wise manner, enhancing their problem-solving abilities without additional training. To this end, we propose KG-RAR, a framework centered on process-oriented knowledge graph construction, a hierarchical retrieval strategy, and a universal post-retrieval processing and reward model (PRP-RM) that refines retrieved information and evaluates each reasoning step. Experiments on the Math500 and GSM8K benchmarks across six models demonstrate that KG-RAR yields encouraging results, achieving a 20.73\% relative improvement with Llama-3B on Math500.

Graphs are a powerful tool for representing and analyzing complex relationships in real-world applications such as social networks, recommender systems, and computational finance. Reasoning on graphs is essential for drawing inferences about the relationships between entities in a complex system, and to identify hidden patterns and trends. Despite the remarkable progress in automated reasoning with natural text, reasoning on graphs with large language models (LLMs) remains an understudied problem. In this work, we perform the first comprehensive study of encoding graph-structured data as text for consumption by LLMs. We show that LLM performance on graph reasoning tasks varies on three fundamental levels: (1) the graph encoding method, (2) the nature of the graph task itself, and (3) interestingly, the very structure of the graph considered. These novel results provide valuable insight on strategies for encoding graphs as text. Using these insights we illustrate how the correct choice of encoders can boost performance on graph reasoning tasks inside LLMs by 4.8% to 61.8%, depending on the task.

Chart understanding presents a unique challenge for large vision-language models (LVLMs), as it requires the integration of sophisticated textual and visual reasoning capabilities. However, current LVLMs exhibit a notable imbalance between these skills, falling short on visual reasoning that is difficult to perform in text. We conduct a case study using a synthetic dataset solvable only through visual reasoning and show that model performance degrades significantly with increasing visual complexity, while human performance remains robust. We then introduce ChartMuseum, a new Chart Question Answering (QA) benchmark containing 1,162 expert-annotated questions spanning multiple reasoning types, curated from real-world charts across 184 sources, specifically built to evaluate complex visual and textual reasoning. Unlike prior chart understanding benchmarks -- where frontier models perform similarly and near saturation -- our benchmark exposes a substantial gap between model and human performance, while effectively differentiating model capabilities: although humans achieve 93% accuracy, the best-performing model Gemini-2.5-Pro attains only 63.0%, and the leading open-source LVLM Qwen2.5-VL-72B-Instruct achieves only 38.5%. Moreover, on questions requiring primarily visual reasoning, all models experience a 35%-55% performance drop from text-reasoning-heavy question performance. Lastly, our qualitative error analysis reveals specific categories of visual reasoning that are challenging for current LVLMs.

Knowledge Graphs (KGs) are valuable tools for representing relationships between entities in a structured format. Traditionally, these knowledge bases are queried to extract specific information. However, question-answering (QA) over such KGs poses a challenge due to the intrinsic complexity of natural language compared to the structured format and the size of these graphs. Despite these challenges, the structured nature of KGs can provide a solid foundation for grounding the outputs of Large Language Models (LLMs), offering organizations increased reliability and control. Recent advancements in LLMs have introduced reasoning methods at inference time to improve their performance and maximize their capabilities. In this work, we propose integrating these reasoning strategies with KGs to anchor every step or "thought" of the reasoning chains in KG data. Specifically, we evaluate both agentic and automated search methods across several reasoning strategies, including Chain-of-Thought (CoT), Tree-of-Thought (ToT), and Graph-of-Thought (GoT), using GRBench, a benchmark dataset for graph reasoning with domain-specific graphs. Our experiments demonstrate that this approach consistently outperforms baseline models, highlighting the benefits of grounding LLM reasoning processes in structured KG data.

With the widespread use of large language models (LLMs) in NLP tasks, researchers have discovered the potential of Chain-of-thought (CoT) to assist LLMs in accomplishing complex reasoning tasks by generating intermediate steps. However, human thought processes are often non-linear, rather than simply sequential chains of thoughts. Therefore, we propose Graph-of-Thought (GoT) reasoning, which models human thought processes not only as a chain but also as a graph. By representing thought units as nodes and connections between them as edges, our approach captures the non-sequential nature of human thinking and allows for a more realistic modeling of thought processes. Similar to Multimodal-CoT, we modeled GoT reasoning as a two-stage framework, generating rationales first and then producing the final answer. Specifically, we employ an additional graph-of-thoughts encoder for GoT representation learning and fuse the GoT representation with the original input representation through a gated fusion mechanism. We implement a GoT reasoning model on the T5 pre-trained model and evaluate its performance on a text-only reasoning task (GSM8K) and a multimodal reasoning task (ScienceQA). Our model achieves significant improvement over the strong CoT baseline with 3.41% and 5.08% on the GSM8K test set with T5-base and T5-large architectures, respectively. Additionally, our model boosts accuracy from 84.91% to 91.54% using the T5-base model and from 91.68% to 92.77% using the T5-large model over the state-of-the-art Multimodal-CoT on the ScienceQA test set. Experiments have shown that GoT achieves comparable results to Multimodal-CoT(large) with over 700M parameters, despite having fewer than 250M backbone model parameters, demonstrating the effectiveness of GoT.

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

Logical reasoning is a critical component of Large Language Models (LLMs), and substantial research efforts in recent years have aimed to enhance their deductive reasoning capabilities. However, existing deductive reasoning benchmarks, which are crucial for evaluating and advancing LLMs, are inadequate due to their lack of task complexity, presence of prior knowledge as a confounder, and superficial error analysis. To address these deficiencies, we introduce JustLogic, a synthetically generated deductive reasoning benchmark designed for rigorous evaluation of LLMs. JustLogic is (i) highly complex, capable of generating a diverse range of linguistic patterns, vocabulary, and argument structures; (ii) prior knowledge independent, eliminating the advantage of models possessing prior knowledge and ensuring that only deductive reasoning is used to answer questions; and (iii) capable of in-depth error analysis on the heterogeneous effects of reasoning depth and argument form on model accuracy. Our experimental results on JustLogic reveal that most state-of-the-art (SOTA) LLMs perform significantly worse than the human average, demonstrating substantial room for model improvement. All code and data are available at https://github.com/michaelchen-lab/JustLogic

Large language models (LLMs) have exhibited impressive performance in language comprehension and various reasoning tasks. However, their abilities in spatial reasoning, a crucial aspect of human cognition, remain relatively unexplored. Human possess a remarkable ability to create mental images of unseen objects and actions through a process known as the Mind's Eye, enabling the imagination of the unseen world. Inspired by this cognitive capacity, we propose Visualization-of-Thought (VoT) prompting. VoT aims to elicit spatial reasoning of LLMs by visualizing their reasoning traces, thereby guiding subsequent reasoning steps. We employed VoT for multi-hop spatial reasoning tasks, including natural language navigation, visual navigation, and visual tiling in 2D grid worlds. Experimental results demonstrated that VoT significantly enhances the spatial reasoning abilities of LLMs. Notably, VoT outperformed existing multimodal large language models (MLLMs) in these tasks. While VoT works surprisingly well on LLMs, the ability to generate mental images to facilitate spatial reasoning resembles the mind's eye process, suggesting its potential viability in MLLMs.

Advanced models such as OpenAI o1 exhibit impressive problem-solving capabilities through step-by-step reasoning. However, they may still falter on more complex problems, making errors that disrupt their reasoning paths. We attribute this to the expansive solution space, where each step has the risk of diverging into mistakes. To enhance language model reasoning, we introduce a specialized training framework called Reasoning Paths Optimization (RPO), which enables learning to reason and explore from diverse paths. Our approach encourages favorable branches at each reasoning step while penalizing unfavorable ones, enhancing the model's overall problem-solving performance. Reasoning Paths Optimization does not rely on large-scale human-annotated rationales or outputs from closed-source models, making it scalable and data-efficient. We focus on multi-step reasoning tasks, such as math word problems and science-based exam questions. The experiments demonstrate that our framework significantly enhances the reasoning performance of large language models, with up to 3.1% and 4.3% improvement on GSM8K and MMLU (STEM) respectively. Our data and code can be found at https://reasoning-paths.github.io.

Language has long been conceived as an essential tool for human reasoning. The breakthrough of Large Language Models (LLMs) has sparked significant research interest in leveraging these models to tackle complex reasoning tasks. Researchers have moved beyond simple autoregressive token generation by introducing the concept of "thought" -- a sequence of tokens representing intermediate steps in the reasoning process. This innovative paradigm enables LLMs' to mimic complex human reasoning processes, such as tree search and reflective thinking. Recently, an emerging trend of learning to reason has applied reinforcement learning (RL) to train LLMs to master reasoning processes. This approach enables the automatic generation of high-quality reasoning trajectories through trial-and-error search algorithms, significantly expanding LLMs' reasoning capacity by providing substantially more training data. Furthermore, recent studies demonstrate that encouraging LLMs to "think" with more tokens during test-time inference can further significantly boost reasoning accuracy. Therefore, the train-time and test-time scaling combined to show a new research frontier -- a path toward Large Reasoning Model. The introduction of OpenAI's o1 series marks a significant milestone in this research direction. In this survey, we present a comprehensive review of recent progress in LLM reasoning. We begin by introducing the foundational background of LLMs and then explore the key technical components driving the development of large reasoning models, with a focus on automated data construction, learning-to-reason techniques, and test-time scaling. We also analyze popular open-source projects at building large reasoning models, and conclude with open challenges and future research directions.

Chain-of-Thought (CoT) has widely enhanced mathematical reasoning in Large Language Models (LLMs), but it still remains challenging for extending it to multimodal domains. Existing works either adopt a similar textual reasoning for image input, or seek to interleave visual signals into mathematical CoT. However, they face three key limitations for math problem-solving: reliance on coarse-grained box-shaped image regions, limited perception of vision encoders on math content, and dependence on external capabilities for visual modification. In this paper, we propose MINT-CoT, introducing Mathematical INterleaved Tokens for Chain-of-Thought visual reasoning. MINT-CoT adaptively interleaves relevant visual tokens into textual reasoning steps via an Interleave Token, which dynamically selects visual regions of any shapes within math figures. To empower this capability, we construct the MINT-CoT dataset, containing 54K mathematical problems aligning each reasoning step with visual regions at the token level, accompanied by a rigorous data generation pipeline. We further present a three-stage MINT-CoT training strategy, progressively combining text-only CoT SFT, interleaved CoT SFT, and interleaved CoT RL, which derives our MINT-CoT-7B model. Extensive experiments demonstrate the effectiveness of our method for effective visual interleaved reasoning in mathematical domains, where MINT-CoT-7B outperforms the baseline model by +34.08% on MathVista, +28.78% on GeoQA, and +23.2% on MMStar, respectively. Our code and data are available at https://github.com/xinyan-cxy/MINT-CoT

Recent works have shown that Large Language Models (LLMs) could empower traditional neuro-symbolic models via programming capabilities to translate language into module descriptions, thus achieving strong visual reasoning results while maintaining the model's transparency and efficiency. However, these models usually exhaustively generate the entire code snippet given each new instance of a task, which is extremely ineffective. We propose generative neuro-symbolic visual reasoning by growing and reusing modules. Specifically, our model consists of three unique stages, module initialization, module generation, and module execution. First, given a vision-language task, we adopt LLMs to examine whether we could reuse and grow over established modules to handle this new task. If not, we initialize a new module needed by the task and specify the inputs and outputs of this new module. After that, the new module is created by querying LLMs to generate corresponding code snippets that match the requirements. In order to get a better sense of the new module's ability, we treat few-shot training examples as test cases to see if our new module could pass these cases. If yes, the new module is added to the module library for future reuse. Finally, we evaluate the performance of our model on the testing set by executing the parsed programs with the newly made visual modules to get the results. We find the proposed model possesses several advantages. First, it performs competitively on standard tasks like visual question answering and referring expression comprehension; Second, the modules learned from one task can be seamlessly transferred to new tasks; Last but not least, it is able to adapt to new visual reasoning tasks by observing a few training examples and reusing modules.

Reasoning lies at the heart of intelligence, shaping the ability to make decisions, draw conclusions, and generalize across domains. In artificial intelligence, as systems increasingly operate in open, uncertain, and multimodal environments, reasoning becomes essential for enabling robust and adaptive behavior. Large Multimodal Reasoning Models (LMRMs) have emerged as a promising paradigm, integrating modalities such as text, images, audio, and video to support complex reasoning capabilities and aiming to achieve comprehensive perception, precise understanding, and deep reasoning. As research advances, multimodal reasoning has rapidly evolved from modular, perception-driven pipelines to unified, language-centric frameworks that offer more coherent cross-modal understanding. While instruction tuning and reinforcement learning have improved model reasoning, significant challenges remain in omni-modal generalization, reasoning depth, and agentic behavior. To address these issues, we present a comprehensive and structured survey of multimodal reasoning research, organized around a four-stage developmental roadmap that reflects the field's shifting design philosophies and emerging capabilities. First, we review early efforts based on task-specific modules, where reasoning was implicitly embedded across stages of representation, alignment, and fusion. Next, we examine recent approaches that unify reasoning into multimodal LLMs, with advances such as Multimodal Chain-of-Thought (MCoT) and multimodal reinforcement learning enabling richer and more structured reasoning chains. Finally, drawing on empirical insights from challenging benchmarks and experimental cases of OpenAI O3 and O4-mini, we discuss the conceptual direction of native large multimodal reasoning models (N-LMRMs), which aim to support scalable, agentic, and adaptive reasoning and planning in complex, real-world environments.

To augment language models with the ability to reason, researchers usually prompt or finetune them to produce chain of thought reasoning steps before producing the final answer. However, although people use natural language to reason effectively, it may be that LMs could reason more effectively with some intermediate computation that is not in natural language. In this work, we explore an alternative reasoning approach: instead of explicitly producing the chain of thought reasoning steps, we use the language model's internal hidden states to perform implicit reasoning. The implicit reasoning steps are distilled from a teacher model trained on explicit chain-of-thought reasoning, and instead of doing reasoning "horizontally" by producing intermediate words one-by-one, we distill it such that the reasoning happens "vertically" among the hidden states in different layers. We conduct experiments on a multi-digit multiplication task and a grade school math problem dataset and find that this approach enables solving tasks previously not solvable without explicit chain-of-thought, at a speed comparable to no chain-of-thought.

Multimodal reasoning, which integrates language and visual cues into problem solving and decision making, is a fundamental aspect of human intelligence and a crucial step toward artificial general intelligence. However, the evaluation of multimodal reasoning capabilities in Multimodal Large Language Models (MLLMs) remains inadequate. Most existing reasoning benchmarks are constrained by limited data size, narrow domain coverage, and unstructured knowledge distribution. To close these gaps, we introduce MDK12-Bench, a multi-disciplinary benchmark assessing the reasoning capabilities of MLLMs via real-world K-12 examinations. Spanning six disciplines (math, physics, chemistry, biology, geography, and information science), our benchmark comprises 140K reasoning instances across diverse difficulty levels from primary school to 12th grade. It features 6,827 instance-level knowledge point annotations based on a well-organized knowledge structure, detailed answer explanations, difficulty labels and cross-year partitions, providing a robust platform for comprehensive evaluation. Additionally, we present a novel dynamic evaluation framework to mitigate data contamination issues by bootstrapping question forms, question types, and image styles during evaluation. Extensive experiment on MDK12-Bench reveals the significant limitation of current MLLMs in multimodal reasoning. The findings on our benchmark provide insights into the development of the next-generation models. Our data and codes are available at https://github.com/LanceZPF/MDK12.

Reasoning models are large language models that emit a long chain-of-thought before answering, providing both higher accuracy and explicit reasoning for their response. A major question has been whether language model reasoning generalizes beyond mathematics, programming, and logic, where most previous work has focused. We demonstrate that reasoning models can be post-trained for chemistry without additional domain pretraining, and require substantially less data compared to contemporary domain-specific models. We report ether0, a 24B parameter LLM (based on Mistral-Small-24B) that can reason in natural language and respond with chemical structures. This reasoning model was trained with reinforcement learning on 640,730 experimentally-grounded chemistry problems across 375 tasks ranging from synthesizability, to blood-brain barrier permeability, to human receptor activity, to scent. Our model exceeds general-purpose chemistry models, frontier models, and human experts on molecular design tasks. It is also more data efficient relative to specialized models. We anticipate that this method can be applied to train data-efficient language models specialized for tasks across a wide variety of scientific domains.

Multimodal large language models (MLLMs) have recently achieved significant progress in visual tasks, including semantic scene understanding and text-image alignment, with reasoning variants enhancing performance on complex tasks involving mathematics and logic. However, their capacity for reasoning tasks involving fine-grained visual understanding remains insufficiently evaluated. To address this gap, we introduce ReasonMap, a benchmark designed to assess the fine-grained visual understanding and spatial reasoning abilities of MLLMs. ReasonMap encompasses high-resolution transit maps from 30 cities across 13 countries and includes 1,008 question-answer pairs spanning two question types and three templates. Furthermore, we design a two-level evaluation pipeline that properly assesses answer correctness and quality. Comprehensive evaluations of 15 popular MLLMs, including both base and reasoning variants, reveal a counterintuitive pattern: among open-source models, base models outperform reasoning ones, while the opposite trend is observed in closed-source models. Additionally, performance generally degrades when visual inputs are masked, indicating that while MLLMs can leverage prior knowledge to answer some questions, fine-grained visual reasoning tasks still require genuine visual perception for strong performance. Our benchmark study offers new insights into visual reasoning and contributes to investigating the gap between open-source and closed-source models.

Although large language models (LLMs) have demonstrated strong reasoning abilities in structured tasks (e.g., coding and mathematics), it remains unexplored whether these abilities extend to strategic multi-agent environments. We investigate strategic reasoning capabilities -- the process of choosing an optimal course of action by predicting and adapting to others' actions -- of LLMs by analyzing their performance in three classical games from behavioral economics. We evaluate three standard LLMs (ChatGPT-4, Claude-2.1, Gemini 1.5) and three specialized reasoning LLMs (GPT-o1, Claude-3.5-Sonnet, Gemini Flash Thinking 2.0) using hierarchical models of bounded rationality. Our results show that reasoning LLMs exhibit superior strategic reasoning compared to standard LLMs (which do not demonstrate substantial capabilities), and often match or exceed human performance. Since strategic reasoning is fundamental to future AI systems (including Agentic AI and Artificial General Intelligence), our findings demonstrate the importance of dedicated reasoning capabilities in achieving effective strategic reasoning.

Deductive reasoning is a crucial logical capability that assists us in solving complex problems based on existing knowledge. Although augmented by Chain-of-Thought prompts, Large Language Models (LLMs) might not follow the correct reasoning paths. Enhancing the deductive reasoning abilities of LLMs, and leveraging their extensive built-in knowledge for various reasoning tasks, remains an open question. Attempting to mimic the human deductive reasoning paradigm, we propose a multi-stage Syllogistic-Reasoning Framework of Thought (SR-FoT) that enables LLMs to perform syllogistic deductive reasoning to handle complex knowledge-based reasoning tasks. Our SR-FoT begins by interpreting the question and then uses the interpretation and the original question to propose a suitable major premise. It proceeds by generating and answering minor premise questions in two stages to match the minor premises. Finally, it guides LLMs to use the previously generated major and minor premises to perform syllogistic deductive reasoning to derive the answer to the original question. Extensive and thorough experiments on knowledge-based reasoning tasks have demonstrated the effectiveness and advantages of our SR-FoT.

Large Language Models (LLMs) have shown superior capability to solve reasoning problems with programs. While being a promising direction, most of such frameworks are trained and evaluated in settings with a prior knowledge of task requirements. However, as LLMs become more capable, it is necessary to assess their reasoning abilities in more realistic scenarios where many real-world problems are open-ended with ambiguous scope, and often require multiple formalisms to solve. To investigate this, we introduce the task of reasoning in the wild, where an LLM is tasked to solve a reasoning problem of unknown type by identifying the subproblems and their corresponding formalisms, and writing a program to solve each subproblem, guided by a tactic. We create a large tactic-guided trajectory dataset containing detailed solutions to a diverse set of reasoning problems, ranging from well-defined single-form reasoning (e.g., math, logic), to ambiguous and hybrid ones (e.g., commonsense, combined math and logic). This allows us to test various aspects of LLMs reasoning at the fine-grained level such as the selection and execution of tactics, and the tendency to take undesired shortcuts. In experiments, we highlight that existing LLMs fail significantly on problems with ambiguous and mixed scope, revealing critical limitations and overfitting issues (e.g. accuracy on GSM8K drops by at least 50\%). We further show the potential of finetuning a local LLM on the tactic-guided trajectories in achieving better performance. Project repo is available at github.com/gblackout/Reason-in-the-Wild

Large language models (LLMs) have demonstrated impressive capabilities in natural language understanding and generation, but they exhibit problems with logical consistency in the output they generate. How can we harness LLMs' broad-coverage parametric knowledge in formal reasoning despite their inconsistency? We present a method for directly integrating an LLM into the interpretation function of the formal semantics for a paraconsistent logic. We provide experimental evidence for the feasibility of the method by evaluating the function using datasets created from several short-form factuality benchmarks. Unlike prior work, our method offers a theoretical framework for neuro-symbolic reasoning that leverages an LLM's knowledge while preserving the underlying logic's soundness and completeness properties.

We present SeePhys, a large-scale multimodal benchmark for LLM reasoning grounded in physics questions ranging from middle school to PhD qualifying exams. The benchmark covers 7 fundamental domains spanning the physics discipline, incorporating 21 categories of highly heterogeneous diagrams. In contrast to prior works where visual elements mainly serve auxiliary purposes, our benchmark features a substantial proportion of vision-essential problems (75\%) that mandate visual information extraction for correct solutions. Through extensive evaluation, we observe that even the most advanced visual reasoning models (e.g., Gemini-2.5-pro and o4-mini) achieve sub-60\% accuracy on our benchmark. These results reveal fundamental challenges in current large language models' visual understanding capabilities, particularly in: (i) establishing rigorous coupling between diagram interpretation and physics reasoning, and (ii) overcoming their persistent reliance on textual cues as cognitive shortcuts.

Recent works have shown that chain-of-thought (CoT) prompting can elicit language models to solve complex reasoning tasks, step-by-step. However, prompt-based CoT methods are dependent on very large models such as GPT-3 175B which are prohibitive to deploy at scale. In this paper, we use these large models as reasoning teachers to enable complex reasoning in smaller models and reduce model size requirements by several orders of magnitude. We propose Fine-tune-CoT, a method that generates reasoning samples from very large teacher models to fine-tune smaller models. We evaluate our method on a wide range of public models and complex tasks. We find that Fine-tune-CoT enables substantial reasoning capability in small models, far outperforming prompt-based baselines and even the teacher model in many tasks. Additionally, we extend our method by leveraging the teacher model's ability to generate multiple distinct rationales for each original sample. Enriching the fine-tuning data with such diverse reasoning results in a substantial performance boost across datasets, even for very small models. We conduct ablations and sample studies to understand the emergence of reasoning capabilities of student models. Our code implementation and data are available at https://github.com/itsnamgyu/reasoning-teacher.

Despite the success of chain of thought in enhancing language model reasoning, the underlying process remains less well understood. Although logically sound reasoning appears inherently crucial for chain of thought, prior studies surprisingly reveal minimal impact when using invalid demonstrations instead. Furthermore, the conventional chain of thought does not inform language models on what mistakes to avoid, which potentially leads to more errors. Hence, inspired by how humans can learn from both positive and negative examples, we propose contrastive chain of thought to enhance language model reasoning. Compared to the conventional chain of thought, our approach provides both valid and invalid reasoning demonstrations, to guide the model to reason step-by-step while reducing reasoning mistakes. To improve generalization, we introduce an automatic method to construct contrastive demonstrations. Our experiments on reasoning benchmarks demonstrate that contrastive chain of thought can serve as a general enhancement of chain-of-thought prompting.

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.

Logical reasoning is central to complex human activities, such as thinking, debating, and planning; it is also a central component of many AI systems as well. In this paper, we investigate the extent to which encoder-only transformer language models (LMs) can reason according to logical rules. We ask whether those LMs can deduce theorems in propositional calculus and first-order logic; if their relative success in these problems reflects general logical capabilities; and which layers contribute the most to the task. First, we show for several encoder-only LMs that they can be trained, to a reasonable degree, to determine logical validity on various datasets. Next, by cross-probing fine-tuned models on these datasets, we show that LMs have difficulty in transferring their putative logical reasoning ability, which suggests that they may have learned dataset-specific features, instead of a general capability. Finally, we conduct a layerwise probing experiment, which shows that the hypothesis classification task is mostly solved through higher layers.

Visual reasoning -- the ability to interpret the visual world -- is crucial for embodied agents that operate within three-dimensional scenes. Progress in AI has led to vision and language models capable of answering questions from images. However, their performance declines when tasked with 3D spatial reasoning. To tackle the complexity of such reasoning problems, we introduce an agentic program synthesis approach where LLM agents collaboratively generate a Pythonic API with new functions to solve common subproblems. Our method overcomes limitations of prior approaches that rely on a static, human-defined API, allowing it to handle a wider range of queries. To assess AI capabilities for 3D understanding, we introduce a new benchmark of queries involving multiple steps of grounding and inference. We show that our method outperforms prior zero-shot models for visual reasoning in 3D and empirically validate the effectiveness of our agentic framework for 3D spatial reasoning tasks. Project website: https://glab-caltech.github.io/vadar/

Large Language Models (LLMs) exhibit impressive performance across various domains but still struggle with arithmetic reasoning tasks. Recent work shows the effectiveness of prompt design methods in enhancing reasoning capabilities. However, these approaches overlook crucial requirements for prior knowledge of specific concepts, theorems, and tricks to tackle most arithmetic reasoning problems successfully. To address this issue, we propose a novel and effective Teaching-Inspired Integrated Framework, which emulates the instructional process of a teacher guiding students. This method equips LLMs with essential concepts, relevant theorems, and similar problems with analogous solution approaches, facilitating the enhancement of reasoning abilities. Additionally, we introduce two new Chinese datasets, MathMC and MathToF, both with detailed explanations and answers. Experiments are conducted on nine benchmarks which demonstrates that our approach improves the reasoning accuracy of LLMs. With GPT-4 and our framework, we achieve new state-of-the-art performance on four math benchmarks (AddSub, SVAMP, Math23K and AQuA) with accuracies of 98.2% (+3.3%), 93.9% (+0.2%), 94.3% (+7.2%) and 81.1% (+1.2%). Our data and code are available at https://github.com/SallyTan13/Teaching-Inspired-Prompting.

Long chain-of-thought (CoT) is an essential ingredient in effective usage of modern large language models, but our understanding of the reasoning strategies underlying these capabilities remains limited. While some prior works have attempted to categorize CoTs using predefined strategy types, such approaches are constrained by human intuition and fail to capture the full diversity of model behaviors. In this work, we introduce the CoT Encyclopedia, a bottom-up framework for analyzing and steering model reasoning. Our method automatically extracts diverse reasoning criteria from model-generated CoTs, embeds them into a semantic space, clusters them into representative categories, and derives contrastive rubrics to interpret reasoning behavior. Human evaluations show that this framework produces more interpretable and comprehensive analyses than existing methods. Moreover, we demonstrate that this understanding enables performance gains: we can predict which strategy a model is likely to use and guide it toward more effective alternatives. Finally, we provide practical insights, such as that training data format (e.g., free-form vs. multiple-choice) has a far greater impact on reasoning behavior than data domain, underscoring the importance of format-aware model design.

Large Language Models (LLMs) excel in natural language tasks but still face challenges in Question Answering (QA) tasks requiring complex, multi-step reasoning. We outline the types of reasoning required in some of these tasks, and reframe them in terms of meta-level reasoning (akin to high-level strategic reasoning or planning) and object-level reasoning (embodied in lower-level tasks such as mathematical reasoning). Franklin, a novel dataset with requirements of meta- and object-level reasoning, is introduced and used along with three other datasets to evaluate four LLMs at question answering tasks requiring multiple steps of reasoning. Results from human annotation studies suggest LLMs demonstrate meta-level reasoning with high frequency, but struggle with object-level reasoning tasks in some of the datasets used. Additionally, evidence suggests that LLMs find the object-level reasoning required for the questions in the Franklin dataset challenging, yet they do exhibit strong performance with respect to the meta-level reasoning requirements.

Enhancing the capability of large language models (LLMs) in reasoning has gained significant attention in recent years. Previous studies have demonstrated the effectiveness of various prompting strategies in aiding LLMs in reasoning (called "reasoning actions"), such as step-by-step thinking, reflecting before answering, solving with programs, and their combinations. However, these approaches often applied static, predefined reasoning actions uniformly to all questions, without considering the specific characteristics of each question or the capability of the task-solving LLM. In this paper, we propose DOTS, an approach enabling LLMs to reason dynamically via optimal reasoning trajectory search, tailored to the specific characteristics of each question and the inherent capability of the task-solving LLM. Our approach involves three key steps: i) defining atomic reasoning action modules that can be composed into various reasoning action trajectories; ii) searching for the optimal action trajectory for each training question through iterative exploration and evaluation for the specific task-solving LLM; and iii) using the collected optimal trajectories to train an LLM to plan for the reasoning trajectories of unseen questions. In particular, we propose two learning paradigms, i.e., fine-tuning an external LLM as a planner to guide the task-solving LLM, or directly fine-tuning the task-solving LLM with an internalized capability for reasoning actions planning. Our experiments across eight reasoning tasks show that our method consistently outperforms static reasoning techniques and the vanilla instruction tuning approach. Further analysis reveals that our method enables LLMs to adjust their computation based on problem complexity, allocating deeper thinking and reasoning to harder problems.

Visual reasoning is a core component of human intelligence and a critical capability for advanced multimodal models. Yet current reasoning evaluations of multimodal large language models (MLLMs) often rely on text descriptions and allow language-based reasoning shortcuts, failing to measure genuine vision-centric reasoning. To address this, we introduce VisuLogic: a benchmark of 1,000 human-verified problems across six categories (e.g., quantitative shifts, spatial relations, attribute comparisons). These various types of questions can be evaluated to assess the visual reasoning capabilities of MLLMs from multiple perspectives. We evaluate leading MLLMs on this benchmark and analyze their results to identify common failure modes. Most models score below 30% accuracy-only slightly above the 25% random baseline and far below the 51.4% achieved by humans-revealing significant gaps in visual reasoning. Furthermore, we provide a supplementary training dataset and a reinforcement-learning baseline to support further progress.

The output quality of large language models (LLMs) can be improved via "reasoning": generating segments of chain-of-thought (CoT) content to further condition the model prior to producing user-facing output. While these chains contain valuable information, they are verbose and lack explicit organization, making them tedious to review. Moreover, they lack opportunities for user feedback, such as to remove unwanted considerations, add desired ones, or clarify unclear assumptions. We introduce Interactive Reasoning, an interaction design that visualizes chain-of-thought outputs as a hierarchy of topics and enables user review and modification. We implement interactive reasoning in Hippo, a prototype for AI-assisted decision making in the face of uncertain trade-offs. In a user study with 16 participants, we find that interactive reasoning in Hippo allows users to quickly identify and interrupt erroneous generations, efficiently steer the model towards customized responses, and better understand both model reasoning and model outputs. Our work contributes to a new paradigm that incorporates user oversight into LLM reasoning processes.

Reasoning-capable language models achieve state-of-the-art performance in diverse complex tasks by generating long, explicit Chain-of-Thought (CoT) traces. While recent works show that base models can acquire such reasoning traces via reinforcement learning or distillation from stronger models like DeepSeek-R1, previous works demonstrate that even short CoT prompting without fine-tuning is able to improve reasoning. We ask whether long CoT can be induced in a base model using only prompting or minimal tuning. Using just 20 long CoT examples from the reasoning model QwQ-32B-Preview, we lightly fine-tune the base model Qwen2.5-32B. The resulting model outperforms the much larger Qwen2.5-Math-72B-Instruct, showing that a handful of high-quality examples can unlock strong reasoning capabilities. We further explore using CoT data from non-reasoning models and human annotators, enhanced with prompt engineering, multi-pass editing, and structural guidance. However, neither matches the performance of reasoning model traces, suggesting that certain latent qualities of expert CoT are difficult to replicate. We analyze key properties of reasoning data, such as problem difficulty, diversity, and answer length, that influence reasoning distillation. While challenges remain, we are optimistic that carefully curated human-written CoT, even in small quantities, can activate reasoning behaviors in base models. We release our human-authored dataset across refinement stages and invite further investigation into what makes small-scale reasoning supervision so effective.

Reasoning, a crucial ability for complex problem-solving, plays a pivotal role in various real-world settings such as negotiation, medical diagnosis, and criminal investigation. It serves as a fundamental methodology in the field of Artificial General Intelligence (AGI). With the ongoing development of foundation models, e.g., Large Language Models (LLMs), there is a growing interest in exploring their abilities in reasoning tasks. In this paper, we introduce seminal foundation models proposed or adaptable for reasoning, highlighting the latest advancements in various reasoning tasks, methods, and benchmarks. We then delve into the potential future directions behind the emergence of reasoning abilities within foundation models. We also discuss the relevance of multimodal learning, autonomous agents, and super alignment in the context of reasoning. By discussing these future research directions, we hope to inspire researchers in their exploration of this field, stimulate further advancements in reasoning with foundation models, and contribute to the development of AGI.

Remarkable progress has been made on automated reasoning with natural text, by using Language Models (LMs) and methods such as Chain-of-Thought and Selection-Inference. These techniques search for proofs in the forward direction from axioms to the conclusion, which suffers from a combinatorial explosion of the search space, and thus high failure rates for problems requiring longer chains of reasoning. The classical automated reasoning literature has shown that reasoning in the backward direction (i.e. from the intended conclusion to supporting axioms) is significantly more efficient at proof-finding. Importing this intuition into the LM setting, we develop a Backward Chaining algorithm, called LAMBADA, that decomposes reasoning into four sub-modules. These sub-modules are simply implemented by few-shot prompted LM inference. We show that LAMBADA achieves sizable accuracy boosts over state-of-the-art forward reasoning methods on challenging logical reasoning datasets, particularly when deep and accurate proof chains are required.