Daily Papers

Lung cancer clinical decision support demands precise reasoning across complex, multi-stage oncological workflows. Existing multimodal large language models (MLLMs) fail to handle guideline-constrained staging and treatment reasoning. We formalize three oncological precision treatment (OPT) tasks for lung cancer, spanning TNM staging, treatment recommendation, and end-to-end clinical decision support. We introduce LungCURE, the first standardized multimodal benchmark built from 1,000 real-world, clinician-labeled cases across more than 10 hospitals. We further propose LCAgent, a multi-agent framework that ensures guideline-compliant lung cancer clinical decision-making by suppressing cascading reasoning errors across the clinical pathway. Experiments reveal large differences across various large language models (LLMs) in their capabilities for complex medical reasoning, when given precise treatment requirements. We further verify that LCAgent, as a simple yet effective plugin, enhances the reasoning performance of LLMs in real-world medical scenarios.

Tool-augmented language agents frequently fail in real-world deployment due to tool malfunctions--timeouts, API exceptions, or inconsistent outputs--triggering cascading reasoning errors and task abandonment. Existing agent training pipelines optimize only for success trajectories, failing to expose models to the tool failures that dominate real-world usage. We propose PALADIN, a generalizable framework for equipping language agents with robust failure recovery capabilities. PALADIN trains on 50,000+ recovery-annotated trajectories constructed via systematic failure injection and expert demonstrations on an enhanced ToolBench dataset. Training uses LoRA-based fine-tuning to retain base capabilities while injecting recovery competence. At inference, PALADIN detects execution-time errors and retrieves the most similar case from a curated bank of 55+ failure exemplars aligned with ToolScan's taxonomy, then executes the corresponding recovery action. This approach generalizes to novel failures beyond the training distribution, retaining 95.2\% recovery performance on unseen tool APIs. Evaluation across PaladinEval and ToolReflectEval demonstrates consistent improvements in Recovery Rate (RR), Task Success Rate (TSR), Catastrophic Success Rate (CSR), and Efficiency Score (ES). PALADIN improves RR from 32.76% to 89.68% (+57% relative) over ToolBench and outperforms the strongest baseline CRITIC (76.34%) by +13.3%. Against vanilla agents, PALADIN achieves 89.86\% RR (+66% relative improvement from 23.75%). These results establish PALADIN as an effective method for building fault-tolerant agents capable of robust recovery in real-world tool environments.

Recent advances in Multimodal Large Language Models (MLLMs) have led to substantial progress in video understanding, accompanied by a growing number of long video benchmarks. However, existing benchmarks rely predominantly on web-sourced videos that lack inter-clip spatiotemporal continuity, making it difficult to assess whether models can maintain consistent memory across days or weeks of real-world experience. We introduce EgoMonth, the first month-level egocentric video understanding benchmark. EgoMonth comprises over 300 hours of first-person daily-life recordings from 20 participants spanning 20 to 120 days, paired with 1,443 human-crafted multiple-choice question-answer pairs. We design a cognitively grounded 14-task evaluation framework organized into three hierarchical cognitive levels: Schema Consolidation, Episodic Indexing, and Cascading Reasoning. Evaluation of state-of-the-art open-source and closed-source MLLMs reveals that even the best-performing model, Gemini 2.5 Pro, achieves only 71.8% macro-average accuracy, remaining 22.4 percentage points below the corrected human baseline of 94.2%. Several models perform near or below the 25% chance level on tasks such as Route Reasoning, Cross-view Spatial Reasoning, and Direction Judgement, while even the strongest closed-source model remains substantially below human performance. These results indicate that current MLLMs function as lossy summarizers rather than faithful memorizers, highlighting the need for architectures with genuine long-term spatiotemporal memory.

While large audio language models (LALMs) have achieved remarkable progress in audio processing at the second- or minute-level scale, understanding hour-level audio remains a fundamental bottleneck. Existing benchmarks predominantly rely on short clips or artificially concatenated segments, failing to faithfully assess LALM capacity for long-range information comprehension in real-world scenarios such as podcasts and lengthy speeches. To address this gap, we introduce VoiceGiraffe, a novel benchmark designed to rigorously evaluate LALMs across diverse real-world scenarios, modalities, and languages under long-context settings. It comprises 1500 curated triplets structured into a dual-level taxonomy of single-hop perception and multi-hop reasoning. We evaluate a broad suite of open-source and proprietary LALMs against human performance. Results underscore three fundamental findings. First, VoiceGiraffe remains highly challenging and far from saturation. Second, we show that no single inference paradigm universally dominates. The E2E inference benefits models with native long-context audio understanding, cascaded caption aggregation stabilizes small models overwhelmed by hour-scale audio, and reasoning-enhanced cascading with external LLM helps weaker models but can bottleneck stronger proprietary systems. Third, we reveal long-range memory persistence as a key bottleneck. LALMs are better at answering questions that require connecting salient causal cues than those requiring sustained tracking of sparse events across long audio, whereas humans show the opposite pattern. These findings position VoiceGiraffe as a challenging and diagnostic testbed for long-form audio understanding, highlighting the need for LALMs with persistent memory and robust long-range aggregation.

In Greek mythology, Pistis symbolized good faith, trust, and reliability, echoing the core principles of RAG in LLM systems. Pistis-RAG, a scalable multi-stage framework, effectively addresses the challenges of large-scale retrieval-augmented generation (RAG). Each stage plays a distinct role: matching refines the search space, pre-ranking prioritizes semantically relevant documents, and ranking aligns with the large language model's (LLM) preferences. The reasoning and aggregating stage supports the implementation of complex chain-of-thought (CoT) methods within this cascading structure. We argue that the lack of strong alignment between LLMs and the external knowledge ranking methods used in RAG tasks is relevant to the reliance on the model-centric paradigm in RAG frameworks. A content-centric approach would prioritize seamless integration between the LLMs and external information sources, optimizing the content transformation process for each specific task. Critically, our ranking stage deviates from traditional RAG approaches by recognizing that semantic relevance alone may not directly translate to improved generation. This is due to the sensitivity of the few-shot prompt order, as highlighted in prior work lu2021fantastically. Current RAG frameworks fail to account for this crucial factor. We introduce a novel ranking stage specifically designed for RAG systems. It adheres to information retrieval principles while considering the unique business scenario captured by LLM preferences and user feedback. Our approach integrates in-context learning (ICL) methods and reasoning steps to incorporate user feedback, ensuring efficient alignment. Experiments on the MMLU benchmark demonstrate a 9.3\% performance improvement. The model and code will be open-sourced on GitHub. Experiments on real-world, large-scale data validate our framework's scalability.

Although large multimodal models (LMMs) have demonstrated remarkable capabilities in visual scene interpretation and reasoning, their capacity for complex and precise 3-dimensional spatial reasoning remains uncertain. Existing benchmarks focus predominantly on 2D spatial understanding and lack a framework to comprehensively evaluate 6D spatial reasoning across varying complexities. To address this limitation, we present PulseCheck457, a scalable and unbiased synthetic dataset designed with 4 key capability for spatial reasoning: multi-object recognition, 2D location, 3D location, and 3D orientation. We develop a cascading evaluation structure, constructing 7 question types across 5 difficulty levels that range from basic single object recognition to our new proposed complex 6D spatial reasoning tasks. We evaluated various large multimodal models (LMMs) on PulseCheck457, observing a general decline in performance as task complexity increases, particularly in 3D reasoning and 6D spatial tasks. To quantify these challenges, we introduce the Relative Performance Dropping Rate (RPDR), highlighting key weaknesses in 3D reasoning capabilities. Leveraging the unbiased attribute design of our dataset, we also uncover prediction biases across different attributes, with similar patterns observed in real-world image settings.

Large Language Models (LLMs) for complex reasoning is often hindered by high computational costs and latency, while resource-efficient Small Language Models (SLMs) typically lack the necessary reasoning capacity. Existing collaborative approaches, such as cascading or routing, operate at a coarse granularity by offloading entire queries to LLMs, resulting in significant computational waste when the SLM is capable of handling the majority of reasoning steps. To address this, we propose RelayLLM, a novel framework for efficient reasoning via token-level collaborative decoding. Unlike routers, RelayLLM empowers the SLM to act as an active controller that dynamically invokes the LLM only for critical tokens via a special command, effectively "relaying" the generation process. We introduce a two-stage training framework, including warm-up and Group Relative Policy Optimization (GRPO) to teach the model to balance independence with strategic help-seeking. Empirical results across six benchmarks demonstrate that RelayLLM achieves an average accuracy of 49.52%, effectively bridging the performance gap between the two models. Notably, this is achieved by invoking the LLM for only 1.07% of the total generated tokens, offering a 98.2% cost reduction compared to performance-matched random routers.

Recent multimodal large language models have shown great promise in clinical image reasoning, but existing post-training pipelines remain predominantly outcome-centric, relying on final answer correctness or sequence-level preferences. This suffers from sparse credit assignment, making it difficult to optimize the reasoning process essential for clinical applications. Our analysis reveals that cascading errors from early-stage reasoning failures are a leading cause of incorrect predictions in medical visual question answering (VQA) benchmarks. Motivated by this, we propose Medical Reasoning-aware Policy Optimization (MRPO), an RL algorithm that incorporates step-wise process rewards. When the final answer is incorrect, MRPO assigns exponentially larger penalties to tokens in earlier invalid reasoning steps, breaking failure cascades without compromising successful paths. Across three multimodal LLM backbones, MRPO consistently outperforms standard GRPO and a recent RL baseline, and on Qwen3-VL-8B-Instruct even surpasses substantially larger medical MLLMs such as HuatuoGPT-Vision-34B by 2.79 points. Moreover, MRPO reduces early-stage reasoning failures from 64.0% to 13.0%, showing that targeted mitigation of cascading failures improves both reasoning quality and final answer accuracy. Our code is available at https://github.com/dmis-lab/MRPO

Vision Language Models (VLMs) achieve strong performance on many vision-language tasks but often struggle with spatial reasoningx2014a prerequisite for many applications. Empirically, we find that a dataset produced by a current training data generation pipeline has a 57.6% human validation rate. These rates stem from current limitations: single-image 3D reconstruction introduces cascading modeling errors and requires wide answer tolerances, while caption-based methods require hyper-detailed annotations and suffer from generative hallucinations. We present GRAID, built on the key insight that qualitative spatial relationships can be reliably determined from 2D geometric primitives alone. By operating exclusively on 2D bounding boxes from standard object detectors, GRAID avoids both 3D reconstruction errors and generative hallucinations, resulting in datasets that are of higher quality than existing tools that produce similar datasets as validated by human evaluations. We apply our framework to the BDD100k, NuImages, and Waymo datasets, generating over 8.5 million high-quality VQA pairs creating questions spanning spatial relations, counting, ranking, and size comparisons. We evaluate one of the datasets and find it achieves 91.16% human-validated accuracyx2014compared to 57.6% on a dataset generated by recent work. Critically, we demonstrate that when trained on GRAID data, models learn spatial reasoning concepts that generalize: models fine-tuned on 6 question types improve on over 10 held-out types, with accuracy gains of 47.5% on BDD and 37.9% on NuImages for Llama 3.2B 11B, and when trained on all questions types, achieve improvements on several existing benchmarks such as BLINK. The GRAID framework, datasets, and additional information can be found this https URL{here}.

Chemical reasoning usually involves complex, multi-step processes that demand precise calculations, where even minor errors can lead to cascading failures. Furthermore, large language models (LLMs) encounter difficulties handling domain-specific formulas, executing reasoning steps accurately, and integrating code effectively when tackling chemical reasoning tasks. To address these challenges, we present ChemAgent, a novel framework designed to improve the performance of LLMs through a dynamic, self-updating library. This library is developed by decomposing chemical tasks into sub-tasks and compiling these sub-tasks into a structured collection that can be referenced for future queries. Then, when presented with a new problem, ChemAgent retrieves and refines pertinent information from the library, which we call memory, facilitating effective task decomposition and the generation of solutions. Our method designs three types of memory and a library-enhanced reasoning component, enabling LLMs to improve over time through experience. Experimental results on four chemical reasoning datasets from SciBench demonstrate that ChemAgent achieves performance gains of up to 46% (GPT-4), significantly outperforming existing methods. Our findings suggest substantial potential for future applications, including tasks such as drug discovery and materials science. Our code can be found at https://github.com/gersteinlab/chemagent

Retrieval-Augmented Generation (RAG) has emerged as a powerful paradigm for Large Language Models (LLMs) to address knowledge-intensive queries requiring domain-specific or up-to-date information. To handle complex multi-hop questions that are challenging for single-step retrieval, iterative RAG approaches incorporating reinforcement learning have been proposed. However, existing iterative RAG systems typically plan to decompose questions without leveraging information about the available retrieval corpus, leading to inefficient retrieval and reasoning chains that cascade into suboptimal performance. In this paper, we introduce Early Knowledge Alignment (EKA), a simple but effective module that aligns LLMs with retrieval set before planning in iterative RAG systems with contextually relevant retrieved knowledge. Extensive experiments on six standard RAG datasets demonstrate that by establishing a stronger reasoning foundation, EKA significantly improves retrieval precision, reduces cascading errors, and enhances both performance and efficiency. Our analysis from an entropy perspective demonstrate that incorporating early knowledge reduces unnecessary exploration during the reasoning process, enabling the model to focus more effectively on relevant information subsets. Moreover, EKA proves effective as a versatile, training-free inference strategy that scales seamlessly to large models. Generalization tests across diverse datasets and retrieval corpora confirm the robustness of our approach. Overall, EKA advances the state-of-the-art in iterative RAG systems while illuminating the critical interplay between structured reasoning and efficient exploration in reinforcement learning-augmented frameworks. The code is released at https://github.com/yxzwang/EarlyKnowledgeAlignment{Github}.

Robots operating in open-world environments must seamlessly integrate localization, spatial reasoning, navigation, and long-horizon planning. While specialist models excel at individual tasks, deploying a multi-model stack is computationally expensive and prone to cascading errors. We present Vesta, a unified embodied generalist that consolidates these capabilities into a single foundation model. Our approach combines a diverse and massive curated corpus designed to induce spatial grounding and a simple multimodal memory harness that enables reasoning over extended time horizons. Across diverse benchmarks, Vesta on average beats individual SOTA baselines by >20% and beats an ensemble of per-category-best baselines by >10% -- thus demonstrating that a generalist model can match or exceed specialists. On real-world robotic tasks requiring memory and reasoning, Vesta improves task success by >35\%. Our work thus demonstrates that a single generalist is a feasible, scalable, and arguably preferable alternative to combining specialists.

Generative image editing models struggle with structured statistical charts when data modifications require geometric synchronization. We formalize this task as Visuo-Logical Cascading Editing (VLCE). However, existing methods remain confined to localized text substitutions and struggle with dependency-aware cascading updates. To systematically evaluate this capability, we introduce ChartSync, an expert-validated benchmark constructed via a programmatic rendering pipeline that guarantees deterministic visuo-logical coupling for the ground truth. ChartSync comprises 870 triplets across 9 chart categories and 4 task types, including 235 geometry-coupled VLCE instances that specifically test cascading text-to-geometry synchronization. We further evaluate these instances via a two-tier framework combining objective visual metrics with a vision-language model judge paradigm to assess low-level fidelity alongside multimodal comprehension and reasoning. Evaluating 14 image editing models and one code-mediated pipeline reveals a nuanced capability gap: most open-source models suffer severe drops in geometric synchronization, while only two frontier proprietary models show emerging VLCE capability, with their residual errors mainly involving semantic isolation and background corruption. Our detailed error analysis deconstructs these failure paradigms to identify core meta-abilities for guiding future multimodal architectures. The ChartSync dataset and code are publicly released at https://github.com/kaka-yjk/ChartSyncCodebase.

Despite the remarkable capabilities of large language models (LLMs) in various reasoning tasks, they still struggle with table reasoning tasks, particularly in maintaining consistency throughout multi-step reasoning processes. While existing approaches have explored various decomposition strategies, they often lack effective mechanisms to identify and correct errors in intermediate reasoning steps, leading to cascading error propagation. To address these issues, we propose Table-Critic, a novel multi-agent framework that facilitates collaborative criticism and iterative refinement of the reasoning process until convergence to correct solutions. Our framework consists of four specialized agents: a Judge for error identification, a Critic for comprehensive critiques, a Refiner for process improvement, and a Curator for pattern distillation. To effectively deal with diverse and unpredictable error types, we introduce a self-evolving template tree that systematically accumulates critique knowledge through experience-driven learning and guides future reflections. Extensive experiments have demonstrated that Table-Critic achieves substantial improvements over existing methods, achieving superior accuracy and error correction rates while maintaining computational efficiency and lower solution degradation rate.

While Multi-Agent Systems (MAS) excel in complex reasoning, they suffer from the cascading impact of erroneous information generated by individual participants. Current solutions often resort to rigid structural engineering or expensive fine-tuning, limiting their deployability and adaptability. We propose AgentDropoutV2, a test-time rectify-or-reject pruning framework designed to dynamically optimize MAS information flow without retraining. Our approach acts as an active firewall, intercepting agent outputs and employing a retrieval-augmented rectifier to iteratively correct errors based on a failure-driven indicator pool. This mechanism allows for the precise identification of potential errors using distilled failure patterns as prior knowledge. Irreparable outputs are subsequently pruned to prevent error propagation, while a fallback strategy preserves system integrity. Empirical results on extensive math benchmarks show that AgentDropoutV2 significantly boosts the MAS's task performance, achieving an average accuracy gain of 6.3 percentage points on math benchmarks. Furthermore, the system exhibits robust generalization and adaptivity, dynamically modulating rectification efforts based on task difficulty while leveraging context-aware indicators to resolve a wide spectrum of error patterns. Our code and dataset are released at https://github.com/TonySY2/AgentDropoutV2.

3D fragment reassembly aims to recover the rigid poses of unordered fragment point clouds or meshes in a common object coordinate system to reconstruct the complete shape. The problem becomes particularly challenging as the number of fragments grows, since the target shape is unknown and fragments provide weak semantic cues. Existing end-to-end approaches are prone to cascading failures due to unreliable contact reasoning, most notably inaccurate fragment adjacencies. To address this, we propose Structure-Aware Reassembly (SARe), a generative framework with SARe-Gen for Euclidean-space assembly generation and SARe-Refine for inference-time refinement, with explicit contact modeling. SARe-Gen jointly predicts fracture-surface token probabilities and an inter-fragment contact graph to localize contact regions and infer candidate adjacencies. It adopts a query-point-based conditioning scheme and extracts aligned local geometric tokens at query locations from a frozen geometry encoder, yielding queryable structural representations without additional structural pretraining. We further introduce an inference-time refinement stage, SARe-Refine. By verifying candidate contact edges with geometric-consistency checks, it selects reliable substructures and resamples the remaining uncertain regions while keeping verified parts fixed, leading to more stable and consistent assemblies in the many-fragment regime. We evaluate SARe across three settings, including synthetic fractures, simulated fractures from scanned real objects, and real physically fractured scans. The results demonstrate state-of-the-art performance, with more graceful degradation and higher success rates as the fragment count increases in challenging large-scale reassembly.

Retrieval-augmented language models (RALMs) hold promise to produce language understanding systems that are are factual, efficient, and up-to-date. An important desideratum of RALMs, is that retrieved information helps model performance when it is relevant, and does not harm performance when it is not. This is particularly important in multi-hop reasoning scenarios, where misuse of irrelevant evidence can lead to cascading errors. However, recent work has shown that retrieval augmentation can sometimes have a negative effect on performance. In this work, we present a thorough analysis on five open-domain question answering benchmarks, characterizing cases when retrieval reduces accuracy. We then propose two methods to mitigate this issue. First, a simple baseline that filters out retrieved passages that do not entail question-answer pairs according to a natural language inference (NLI) model. This is effective in preventing performance reduction, but at a cost of also discarding relevant passages. Thus, we propose a method for automatically generating data to fine-tune the language model to properly leverage retrieved passages, using a mix of relevant and irrelevant contexts at training time. We empirically show that even 1,000 examples suffice to train the model to be robust to irrelevant contexts while maintaining high performance on examples with relevant ones.

Deep search has become a crucial capability for frontier multimodal agents, enabling models to solve complex questions through active search, evidence verification, and multi-step reasoning. Despite rapid progress, top-tier multimodal search agents remain difficult to reproduce, largely due to the absence of open high-quality training data, transparent trajectory synthesis pipelines, or detailed training recipes. To this end, we introduce OpenSearch-VL, a fully open-source recipe for training frontier multimodal deep search agents with agentic reinforcement learning. First, we curated a dedicated pipeline to construct high-quality training data through Wikipedia path sampling, fuzzy entity rewriting, and source-anchor visual grounding, which jointly reduce shortcuts and one-step retrieval collapse. Based on this pipeline, we curate two training datasets, SearchVL-SFT-36k for SFT and SearchVL-RL-8k for RL. Besides, we design a diverse tool environment that unifies text search, image search, OCR, cropping, sharpening, super-resolution, and perspective correction, enabling agents to combine active perception with external knowledge acquisition. Finally, we propose a multi-turn fatal-aware GRPO training algorithm that handles cascading tool failures by masking post-failure tokens while preserving useful pre-failure reasoning through one-sided advantage clamping. Built on this recipe, OpenSearch-VL delivers substantial performance gains, with over 10-point average improvements across seven benchmarks, and achieves results comparable to proprietary commercial models on several tasks. We will release all data, code, and models to support open research on multimodal deep search agents.

Agentic LLM frameworks that rely on prompted orchestration, where the model itself determines workflow transitions, often suffer from hallucinated routing, infinite loops, and non-reproducible execution. We introduce GraphBit, an engine-orchestrated framework that defines workflows explicitly and deterministically as a directed acyclic graph (DAG). Unlike prompted orchestration, agents in GraphBit operate as typed functions, while a Rust-based engine governs routing, state transitions, and tool invocation, ensuring reproducibility and auditability. The engine supports parallel branch execution, conditional control flow over structured state predicates, and configurable error recovery. A three-tier memory architecture consisting of ephemeral scratch space, structured state, and external connectors isolates context across stages, preventing cascading context bloat that degrades reasoning in long-running pipelines. Across GAIA benchmark tasks spanning zero-tool, document-augmented, and web-enabled workflows, GraphBit outperforms six existing frameworks, achieving the highest accuracy (67.6 percent), zero framework-induced hallucinations, the lowest latency (11.9 ms overhead), and the highest throughput. Ablation studies demonstrate that each memory tier contributes measurably to performance, with deterministic execution providing the greatest gains on tool-intensive tasks representative of real-world deployments.

We present NUPunkt and CharBoundary, two sentence boundary detection libraries optimized for high-precision, high-throughput processing of legal text in large-scale applications such as due diligence, e-discovery, and legal research. These libraries address the critical challenges posed by legal documents containing specialized citations, abbreviations, and complex sentence structures that confound general-purpose sentence boundary detectors. Our experimental evaluation on five diverse legal datasets comprising over 25,000 documents and 197,000 annotated sentence boundaries demonstrates that NUPunkt achieves 91.1% precision while processing 10 million characters per second with modest memory requirements (432 MB). CharBoundary models offer balanced and adjustable precision-recall tradeoffs, with the large model achieving the highest F1 score (0.782) among all tested methods. Notably, NUPunkt provides a 29-32% precision improvement over general-purpose tools while maintaining exceptional throughput, processing multi-million document collections in minutes rather than hours. Both libraries run efficiently on standard CPU hardware without requiring specialized accelerators. NUPunkt is implemented in pure Python with zero external dependencies, while CharBoundary relies only on scikit-learn and optional ONNX runtime integration for optimized performance. Both libraries are available under the MIT license, can be installed via PyPI, and can be interactively tested at https://sentences.aleainstitute.ai/. These libraries address critical precision issues in retrieval-augmented generation systems by preserving coherent legal concepts across sentences, where each percentage improvement in precision yields exponentially greater reductions in context fragmentation, creating cascading benefits throughout retrieval pipelines and significantly enhancing downstream reasoning quality.

Despite the progress of foundation models, knowledge-based reasoning remains a persistent challenge due to their limited capacity for knowledge recall and inference. Existing methods primarily focus on encouraging these models to plan and solve problems or extensively sample reasoning chains independently. However, these methods often overlook conceptual errors and inferential fallacies, inevitably leading to a series of notorious issues such as misleading conclusions, cognitive biases, and reduced decision quality. While explicit modeling of causality is argued to hold promise in addressing these issues, contemporary research efforts have thus far fallen short in achieving causality-based foundation models. Drawing inspiration from the orchestration of diverse specialized agents collaborating to tackle intricate tasks, we propose a framework named Causal-Consistency Chain-of-Thought (CaCo-CoT) that harnesses multi-agent collaboration to bolster the faithfulness and causality of foundation models, involving a set of reasoners and evaluators. These agents collaboratively work within a reasoning-and-consensus paradigm to improve faithfulness. The reasoners are tasked with generating reasoning chains for knowledge-intensive problems by mimicking human causal reasoning. Meanwhile, the evaluator scrutinizes the causal consistency of a reasoner's reasoning chain from a non-causal and a counterfactual perspective. Our framework demonstrates significant superiority over state-of-the-art methods through extensive and comprehensive evaluations across text-based and multi-modal knowledge reasoning tasks (e.g., science question answering and commonsense reasoning).

Large language models have achieved near-expert performance in structured reasoning domains like mathematics and programming, yet their ability to perform compositional multi-hop reasoning in specialized scientific fields remains limited. We propose a bottom-up learning paradigm in which models are grounded in axiomatic domain facts and compose them to solve complex, unseen tasks. To this end, we present a post-training pipeline, based on a combination of supervised fine-tuning and reinforcement learning (RL), in which knowledge graphs act as implicit reward models. By deriving novel reward signals from knowledge graph paths, we provide verifiable, scalable, and grounded supervision that encourages models to compose intermediate axioms rather than optimize only final answers during RL. We validate this approach in the medical domain, training a 14B model on short-hop reasoning paths (1-3 hops) and evaluating its zero-shot generalization to complex multi-hop queries (4-5 hops). Our experiments show that path-derived rewards act as a "compositional bridge", enabling our model to significantly outperform much larger models and frontier systems like GPT-5.2 and Gemini 3 Pro, on the most difficult reasoning tasks. Furthermore, we demonstrate the robustness of our approach to adversarial perturbations against option-shuffling stress tests. This work suggests that grounding the reasoning process in structured knowledge is a scalable and efficient path toward intelligent reasoning.

Logical reading comprehension is a challenging task that entails grasping the underlying semantics of text and applying reasoning to deduce the correct answer. Prior researches have primarily focused on enhancing logical reasoning capabilities through Chain-of-Thought (CoT) or data augmentation. However, previous work constructing chain-of-thought rationales concentrates solely on analyzing correct options, neglecting the incorrect alternatives. Addtionally, earlier efforts on data augmentation by altering contexts rely on rule-based methods, which result in generated contexts that lack diversity and coherence. To address these issues, we propose a Premise-Oriented Data Augmentation (PODA) framework. This framework can generate CoT rationales including analyses for both correct and incorrect options, while constructing diverse and high-quality counterfactual contexts from incorrect candidate options. We integrate summarizing premises and identifying premises for each option into rationales. Subsequently, we employ multi-step prompts with identified premises to construct counterfactual context. To facilitate the model's capabilities to better differentiate the reasoning process associated with each option, we introduce a novel thought-path contrastive learning method that compares reasoning paths between the original and counterfactual samples. Experimental results on three representative LLMs demonstrate that our method can improve the baselines substantially across two challenging logical reasoning benchmarks (ReClor and LogiQA 2.0). The data and code are released at https://github.com/lalalamdbf/TPReasoner.

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.

Deep iterative chain-of-thought (CoT) reasoning enables LLMs to tackle complex tasks by progressively activating relevant pre-trained knowledge. However, it faces challenges in ensuring continual improvement and determining a stopping criterion. In this paper, we investigate whether the relevant knowledge that contributes directly to solving the given question can be activated from the initial reasoning path, thus circumventing the need for iterative refinement. Our experiments reveal that increasing the diversity of initial reasoning paths can achieve comparable or superior performance, a concept we term breadth reasoning. However, existing breadth reasoning approaches, such as self-consistency, offer limited diversity. To address this limitation, we propose a simple yet effective method that enhances reasoning breadth by integrating contextual exploration with reduced sampling randomness. Extensive experiments demonstrate that our approach significantly outperforms deep iterative reasoning. Our code is provided in https://github.com/zongqianwu/breadth.

Time series reasoning treats time as a first-class axis and incorporates intermediate evidence directly into the answer. This survey defines the problem and organizes the literature by reasoning topology with three families: direct reasoning in one step, linear chain reasoning with explicit intermediates, and branch-structured reasoning that explores, revises, and aggregates. The topology is crossed with the main objectives of the field, including traditional time series analysis, explanation and understanding, causal inference and decision making, and time series generation, while a compact tag set spans these axes and captures decomposition and verification, ensembling, tool use, knowledge access, multimodality, agent loops, and LLM alignment regimes. Methods and systems are reviewed across domains, showing what each topology enables and where it breaks down in faithfulness or robustness, along with curated datasets, benchmarks, and resources that support study and deployment (https://github.com/blacksnail789521/Time-Series-Reasoning-Survey). Evaluation practices that keep evidence visible and temporally aligned are highlighted, and guidance is distilled on matching topology to uncertainty, grounding with observable artifacts, planning for shift and streaming, and treating cost and latency as design budgets. We emphasize that reasoning structures must balance capacity for grounding and self-correction against computational cost and reproducibility, while future progress will likely depend on benchmarks that tie reasoning quality to utility and on closed-loop testbeds that trade off cost and risk under shift-aware, streaming, and long-horizon settings. Taken together, these directions mark a shift from narrow accuracy toward reliability at scale, enabling systems that not only analyze but also understand, explain, and act on dynamic worlds with traceable evidence and credible outcomes.

Chain-of-thought emerges as a promising technique for eliciting reasoning capabilities from Large Language Models (LLMs). However, it does not always improve task performance or accurately represent reasoning processes, leaving unresolved questions about its usage. In this paper, we diagnose the underlying mechanism by comparing the reasoning process of LLMs with humans, using causal analysis to understand the relationships between the problem instruction, reasoning, and the answer in LLMs. Our empirical study reveals that LLMs often deviate from the ideal causal chain, resulting in spurious correlations and potential consistency errors (inconsistent reasoning and answers). We also examine various factors influencing the causal structure, finding that in-context learning with examples strengthens it, while post-training techniques like supervised fine-tuning and reinforcement learning on human feedback weaken it. To our surprise, the causal structure cannot be strengthened by enlarging the model size only, urging research on new techniques. We hope that this preliminary study will shed light on understanding and improving the reasoning process in LLM.

The availability of a wide range of large language models (LLMs) embedded in various agentic systems has significantly increased the potential of model selection strategies to improve the cost-performance tradeoff. Existing strategies involve either routing, where a single model is chosen per query, or cascading, which sequentially runs increasingly larger models until a satisfactory answer is found. However, current approaches face three key limitations: they (1) lack formal proofs of optimality, (2) fail to identify the conditions under which these strategies are most effective to improve the cost-performance tradeoff, and (3) are unable to combine both paradigms for further improvements. To address these issues, we first derive a novel optimal strategy for cascading and prove the optimality of an existing routing strategy. Further, we propose cascade routing, a unified framework that integrates routing and cascading into a theoretically optimal strategy. Through our analysis, we identify good quality estimators as the critical factor for the success of model selection paradigms. Finally, in our experiments, we show that cascade routing consistently outperforms the individual approaches by a large margin and we analyze quality estimators to determine when routing and/or cascading are useful paradigms for model selection.

Recent advancements in reasoning with large language models (RLLMs), such as OpenAI-O1 and DeepSeek-R1, have demonstrated their impressive capabilities in complex domains like mathematics and coding. A central factor in their success lies in the application of long chain-of-thought (Long CoT) characteristics, which enhance reasoning abilities and enable the solution of intricate problems. However, despite these developments, a comprehensive survey on Long CoT is still lacking, limiting our understanding of its distinctions from traditional short chain-of-thought (Short CoT) and complicating ongoing debates on issues like "overthinking" and "test-time scaling." This survey seeks to fill this gap by offering a unified perspective on Long CoT. (1) We first distinguish Long CoT from Short CoT and introduce a novel taxonomy to categorize current reasoning paradigms. (2) Next, we explore the key characteristics of Long CoT: deep reasoning, extensive exploration, and feasible reflection, which enable models to handle more complex tasks and produce more efficient, coherent outcomes compared to the shallower Short CoT. (3) We then investigate key phenomena such as the emergence of Long CoT with these characteristics, including overthinking, and test-time scaling, offering insights into how these processes manifest in practice. (4) Finally, we identify significant research gaps and highlight promising future directions, including the integration of multi-modal reasoning, efficiency improvements, and enhanced knowledge frameworks. By providing a structured overview, this survey aims to inspire future research and further the development of logical reasoning in artificial intelligence.

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 models enhance performance by tackling problems in a step-by-step manner, decomposing them into sub-problems and exploring long chains of thought before producing an answer. However, applying extended reasoning to every step introduces substantial redundancy, as sub-problems vary widely in difficulty and complexity: a small number of pivotal steps are genuinely challenging and decisive for the final answer, while many others only involve straightforward revisions or simple computations. Therefore, a natural idea is to endow reasoning models with the ability to adaptively respond to this variation, rather than treating all steps with the same level of elaboration. To this end, we propose MixReasoning, a framework that dynamically adjusts the depth of reasoning within a single response. The resulting chain of thought then becomes a mixture of detailed reasoning on difficult steps and concise inference on simpler ones. Experiments on GSM8K, MATH-500, and AIME show that MixReasoning shortens reasoning length and substantially improves efficiency without compromising accuracy.

Large Reasoning Models (LRMs) have significantly enhanced their capabilities in complex problem-solving by introducing a thinking draft that enables multi-path Chain-of-Thought explorations before producing final answers. Ensuring the faithfulness of these intermediate reasoning processes is crucial for reliable monitoring, interpretation, and effective control. In this paper, we propose a systematic counterfactual intervention framework to rigorously evaluate thinking draft faithfulness. Our approach focuses on two complementary dimensions: (1) Intra-Draft Faithfulness, which assesses whether individual reasoning steps causally influence subsequent steps and the final draft conclusion through counterfactual step insertions; and (2) Draft-to-Answer Faithfulness, which evaluates whether final answers are logically consistent with and dependent on the thinking draft, by perturbing the draft's concluding logic. We conduct extensive experiments across six state-of-the-art LRMs. Our findings show that current LRMs demonstrate selective faithfulness to intermediate reasoning steps and frequently fail to faithfully align with the draft conclusions. These results underscore the need for more faithful and interpretable reasoning in advanced LRMs.

Large Reasoning Models (LRMs) increasingly rely on reasoning traces with complex internal structures. However, existing work lacks a unified answer to three fundamental questions: (1) what defines high-quality reasoning, (2) how to reliably evaluate long, implicitly structured reasoning traces, and (3) how to use such evaluation signals for reasoning optimization. To address these challenges, we provide a unified perspective. (1) We introduce the ME^2 principle to characterize reasoning quality along macro- and micro-level concerning efficiency and effectiveness. (2) Built on this principle, we model reasoning traces as directed acyclic graphs (DAGs) and develop a DAG-based pairwise evaluation method, capturing complex reasoning structures. (3) Based on this method, we construct the TRM-Preference dataset and train a Thinking Reward Model (TRM) to evaluate reasoning quality at scale. Experiments show that thinking rewards serve as an effective optimization signal. At test time, selecting better reasoning leads to better outcomes (up to 19.3\% gain), and during RL training, thinking rewards enhance reasoning and performance (up to 3.9\% gain) across diverse tasks. Code and data are available at https://github.com/Simplified-Reasoning/TRM.

Most work interpreting reasoning models studies only a single chain-of-thought (CoT), yet these models define distributions over many possible CoTs. We argue that studying a single sample is inadequate for understanding causal influence and the underlying computation. Though fully specifying this distribution is intractable, it can be understood by sampling. We present case studies using resampling to investigate model decisions. First, when a model states a reason for its action, does that reason actually cause the action? In "agentic misalignment" scenarios, we resample specific sentences to measure their downstream effects. Self-preservation sentences have small causal impact, suggesting they do not meaningfully drive blackmail. Second, are artificial edits to CoT sufficient for steering reasoning? These are common in literature, yet take the model off-policy. Resampling and selecting a completion with the desired property is a principled on-policy alternative. We find off-policy interventions yield small and unstable effects compared to resampling in decision-making tasks. Third, how do we understand the effect of removing a reasoning step when the model may repeat it post-edit? We introduce a resilience metric that repeatedly resamples to prevent similar content from reappearing downstream. Critical planning statements resist removal but have large effects when eliminated. Fourth, since CoT is sometimes "unfaithful", can our methods teach us anything in these settings? Adapting causal mediation analysis, we find that hints that have a causal effect on the output without being explicitly mentioned exert a subtle and cumulative influence on the CoT that persists even if the hint is removed. Overall, studying distributions via resampling enables reliable causal analysis, clearer narratives of model reasoning, and principled CoT interventions.

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.

Chain-of-thought reasoning, a cognitive process fundamental to human intelligence, has garnered significant attention in the realm of artificial intelligence and natural language processing. However, there still remains a lack of a comprehensive survey for this arena. To this end, we take the first step and present a thorough survey of this research field carefully and widely. We use X-of-Thought to refer to Chain-of-Thought in a broad sense. In detail, we systematically organize the current research according to the taxonomies of methods, including XoT construction, XoT structure variants, and enhanced XoT. Additionally, we describe XoT with frontier applications, covering planning, tool use, and distillation. Furthermore, we address challenges and discuss some future directions, including faithfulness, multi-modal, and theory. We hope this survey serves as a valuable resource for researchers seeking to innovate within the domain of chain-of-thought reasoning.

Recently, slow-thinking reasoning systems, such as o1, have demonstrated remarkable capabilities in solving complex reasoning tasks. These systems typically engage in an extended thinking process before responding to a query, allowing them to generate more thorough, accurate, and well-reasoned solutions. These systems are primarily developed and maintained by industry, with their core techniques not publicly disclosed. In response, an increasing number of studies from the research community aim to explore the technical foundations underlying these powerful reasoning systems. Building on these prior efforts, this paper presents a reproduction report on implementing o1-like reasoning systems. We introduce an "imitate, explore, and self-improve" framework as our primary technical approach to train the reasoning model. In the initial phase, we use distilled long-form thought data to fine-tune the reasoning model, enabling it to invoke a slow-thinking mode. The model is then encouraged to explore challenging problems by generating multiple rollouts, which can result in increasingly more high-quality trajectories that lead to correct answers. Furthermore, the model undergoes self-improvement by iteratively refining its training dataset. To verify the effectiveness of this approach, we conduct extensive experiments on three challenging benchmarks. The experimental results demonstrate that our approach achieves competitive performance compared to industry-level reasoning systems on these benchmarks.

Current long chain-of-thought (long-CoT) models excel at mathematical reasoning but rely on slow and error-prone natural language traces. Tool-augmented agents address arithmetic via code execution, but often falter on complex logical tasks. We introduce a fine-tuning framework, DualDistill, that distills complementary reasoning strategies from multiple teachers into a unified student model. Using this approach, we train Agentic-R1, which dynamically selects the optimal strategy for each query, invoking tools for arithmetic and algorithmic problems, and using text-based reasoning for abstract ones. Our method improves accuracy across a range of tasks, including both computation-intensive and standard benchmarks, demonstrating the effectiveness of multi-strategy distillation in achieving robust and efficient reasoning. Our project is available at https://github.com/StigLidu/DualDistill

While Large Language Models (LLMs) have emerged with remarkable capabilities in complex tasks through Chain-of-Thought reasoning, practical resource constraints have sparked interest in transferring these abilities to smaller models. However, achieving both domain performance and cross-domain generalization remains challenging. Existing approaches typically restrict students to following a single golden rationale and treat different reasoning paths independently. Due to distinct inductive biases and intrinsic preferences, alongside the student's evolving capacity and reasoning preferences during training, a teacher's "optimal" rationale could act as out-of-distribution noise. This misalignment leads to a degeneration of the student's latent reasoning distribution, causing suboptimal performance. To bridge this gap, we propose MIND, a capability-adaptive framework that transitions distillation from passive mimicry to active cognitive construction. We synthesize diverse teacher perspectives through a novel "Teaching Assistant" network. By employing a Feedback-Driven Inertia Calibration mechanism, this network utilizes inertia-filtered training loss to align supervision with the student's current adaptability, effectively enhancing performance while mitigating catastrophic forgetting. Extensive experiments demonstrate that MIND achieves state-of-the-art performance on both in-distribution and out-of-distribution benchmarks, and our sophisticated latent space analysis further confirms the mechanism of reasoning ability internalization.

This paper presents ReasonFormer, a unified reasoning framework for mirroring the modular and compositional reasoning process of humans in complex decision-making. Inspired by dual-process theory in cognitive science, the representation module (automatic thinking) and reasoning modules (controlled thinking) are decoupled to capture different levels of cognition. Upon the top of the representation module, the pre-trained reasoning modules are modular and professional in specific and fundamental reasoning skills (e.g., logic, simple QA, etc). To mimic the controlled compositional thinking process, different reasoning modules are dynamically activated and composed in both parallel and cascaded manners to control what reasoning skills are activated and how deep the reasoning process will be reached to solve the current problems. The unified reasoning framework solves multiple tasks with a single model, and is trained and inferred in an end-to-end manner. Evaluated on 11 datasets requiring different reasoning skills and complexity, ReasonFormer demonstrates substantial performance boosts, revealing the compositional reasoning ability. Few-shot experiments exhibit better generalization ability by learning to compose pre-trained skills for new tasks with limited data, and decoupling the representation module and the reasoning modules. Further analysis shows the modularity of reasoning modules as different tasks activate distinct reasoning skills at different reasoning depths.

As Large Language Model (LLM) agents are increasingly tasked with high-stakes autonomous decision-making, the transparency of their reasoning processes has become a critical safety concern. While Chain-of-Thought (CoT) prompting allows agents to generate human-readable reasoning traces, it remains unclear whether these traces are faithful generative drivers of the model's output or merely post-hoc rationalizations. We introduce Project Ariadne, a novel XAI framework that utilizes Structural Causal Models (SCMs) and counterfactual logic to audit the causal integrity of agentic reasoning. Unlike existing interpretability methods that rely on surface-level textual similarity, Project Ariadne performs hard interventions (do-calculus) on intermediate reasoning nodes -- systematically inverting logic, negating premises, and reversing factual claims -- to measure the Causal Sensitivity (φ) of the terminal answer. Our empirical evaluation of state-of-the-art models reveals a persistent Faithfulness Gap. We define and detect a widespread failure mode termed Causal Decoupling, where agents exhibit a violation density (ρ) of up to 0.77 in factual and scientific domains. In these instances, agents arrive at identical conclusions despite contradictory internal logic, proving that their reasoning traces function as "Reasoning Theater" while decision-making is governed by latent parametric priors. Our findings suggest that current agentic architectures are inherently prone to unfaithful explanation, and we propose the Ariadne Score as a new benchmark for aligning stated logic with model action.

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

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.

Reasoning is a fundamental cognitive process underlying inference, problem-solving, and decision-making. While large language models (LLMs) demonstrate strong reasoning capabilities in closed-world settings, they struggle in open-ended and dynamic environments. Agentic reasoning marks a paradigm shift by reframing LLMs as autonomous agents that plan, act, and learn through continual interaction. In this survey, we organize agentic reasoning along three complementary dimensions. First, we characterize environmental dynamics through three layers: foundational agentic reasoning, which establishes core single-agent capabilities including planning, tool use, and search in stable environments; self-evolving agentic reasoning, which studies how agents refine these capabilities through feedback, memory, and adaptation; and collective multi-agent reasoning, which extends intelligence to collaborative settings involving coordination, knowledge sharing, and shared goals. Across these layers, we distinguish in-context reasoning, which scales test-time interaction through structured orchestration, from post-training reasoning, which optimizes behaviors via reinforcement learning and supervised fine-tuning. We further review representative agentic reasoning frameworks across real-world applications and benchmarks, including science, robotics, healthcare, autonomous research, and mathematics. This survey synthesizes agentic reasoning methods into a unified roadmap bridging thought and action, and outlines open challenges and future directions, including personalization, long-horizon interaction, world modeling, scalable multi-agent training, and governance for real-world deployment.

Developing models that can learn to reason is a notoriously challenging problem. We focus on reasoning in relational domains, where the use of Graph Neural Networks (GNNs) seems like a natural choice. However, previous work has shown that regular GNNs lack the ability to systematically generalize from training examples on test graphs requiring longer inference chains, which fundamentally limits their reasoning abilities. A common solution relies on neuro-symbolic methods that systematically reason by learning rules, but their scalability is often limited and they tend to make unrealistically strong assumptions, e.g.\ that the answer can always be inferred from a single relational path. We propose the Epistemic GNN (EpiGNN), a novel parameter-efficient and scalable GNN architecture with an epistemic inductive bias for systematic reasoning. Node embeddings in EpiGNNs are treated as epistemic states, and message passing is implemented accordingly. We show that EpiGNNs achieve state-of-the-art results on link prediction tasks that require systematic reasoning. Furthermore, for inductive knowledge graph completion, EpiGNNs rival the performance of state-of-the-art specialized approaches. Finally, we introduce two new benchmarks that go beyond standard relational reasoning by requiring the aggregation of information from multiple paths. Here, existing neuro-symbolic approaches fail, yet EpiGNNs learn to reason accurately. Code and datasets are available at https://github.com/erg0dic/gnn-sg.

Reasoning large language models have recently achieved state-of-the-art performance in many fields. However, their long-form chain-of-thought reasoning creates interpretability challenges as each generated token depends on all previous ones, making the computation harder to decompose. We argue that analyzing reasoning traces at the sentence level is a promising approach to understanding reasoning processes. We present three complementary attribution methods: (1) a black-box method measuring each sentence's counterfactual importance by comparing final answers across 100 rollouts conditioned on the model generating that sentence or one with a different meaning; (2) a white-box method of aggregating attention patterns between pairs of sentences, which identified ``broadcasting'' sentences that receive disproportionate attention from all future sentences via ``receiver'' attention heads; (3) a causal attribution method measuring logical connections between sentences by suppressing attention toward one sentence and measuring the effect on each future sentence's tokens. Each method provides evidence for the existence of thought anchors, reasoning steps that have outsized importance and that disproportionately influence the subsequent reasoning process. These thought anchors are typically planning or backtracking sentences. We provide an open-source tool (www.thought-anchors.com) for visualizing the outputs of our methods, and present a case study showing converging patterns across methods that map how a model performs multi-step reasoning. The consistency across methods demonstrates the potential of sentence-level analysis for a deeper understanding of reasoning models.

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

The emergence of Large Reasoning Models has introduced exceptionally long Chain-of-Thought traces, creating a transparency burden where critical logic is often buried under massive procedural text. To address this, we present ReasoningLens, an open-source framework designed for the hierarchical visualization and diagnostic auditing of complex reasoning chains. ReasoningLens addresses information necropsy by: (1) structuring traces into interactive hierarchies that separate high-level strategy from low-level execution; (2) leveraging an agentic auditor for automated error detection and tool-augmented verification; and (3) synthesizing systemic reasoning profiles to reveal model-specific blind spots. By transforming unstructured walls of text into actionable insights, ReasoningLens provides a modular foundation for interpreting, debugging, and optimizing the next generation of reasoning-centric AI.

Cascading bandits have gained popularity in recent years due to their applicability to recommendation systems and online advertising. In the cascading bandit model, at each timestep, an agent recommends an ordered subset of items (called an item list) from a pool of items, each associated with an unknown attraction probability. Then, the user examines the list, and clicks the first attractive item (if any), and after that, the agent receives a reward. The goal of the agent is to maximize the expected cumulative reward. However, the prior literature on cascading bandits ignores the influences of user states (e.g., historical behaviors) on recommendations and the change of states as the session proceeds. Motivated by this fact, we propose a generalized cascading RL framework, which considers the impact of user states and state transition into decisions. In cascading RL, we need to select items not only with large attraction probabilities but also leading to good successor states. This imposes a huge computational challenge due to the combinatorial action space. To tackle this challenge, we delve into the properties of value functions, and design an oracle BestPerm to efficiently find the optimal item list. Equipped with BestPerm, we develop two algorithms CascadingVI and CascadingBPI, which are both computationally-efficient and sample-efficient, and provide near-optimal regret and sample complexity guarantees. Furthermore, we present experiments to show the improved computational and sample efficiencies of our algorithms compared to straightforward adaptations of existing RL algorithms in practice.

Although contemporary large language models (LMs) demonstrate impressive question-answering capabilities, their answers are typically the product of a single call to the model. This entails an unwelcome degree of opacity and compromises performance, especially on problems that are inherently multi-step. To address these limitations, we show how LMs can be made to perform faithful multi-step reasoning via a process whose causal structure mirrors the underlying logical structure of the problem. Our approach works by chaining together reasoning steps, where each step results from calls to two fine-tuned LMs, one for selection and one for inference, to produce a valid reasoning trace. Our method carries out a beam search through the space of reasoning traces to improve reasoning quality. We demonstrate the effectiveness of our model on multi-step logical deduction and scientific question-answering, showing that it outperforms baselines on final answer accuracy, and generates humanly interpretable reasoning traces whose validity can be checked by the user.

While Large Reasoning Models (LRMs) generate extensive chain-of-thought reasoning, we lack a principled framework for understanding how these thoughts are structured. In this paper, we introduce a novel approach by applying Schoenfeld's Episode Theory, a classic cognitive framework for human mathematical problem-solving, to analyze the reasoning traces of LRMs. We annotated thousands of sentences and paragraphs from model-generated solutions to math problems using seven cognitive labels (e.g., Plan, Implement, Verify). The result is the first publicly available benchmark for the fine-grained analysis of machine reasoning, including a large annotated corpus and detailed annotation guidebooks. Our preliminary analysis reveals distinct patterns in LRM reasoning, such as the transition dynamics between cognitive states. This framework provides a theoretically grounded methodology for interpreting LRM cognition and enables future work on more controllable and transparent reasoning systems.

Despite the success of test-time scaling, Large Reasoning Models (LRMs) frequently encounter repetitive loops that lead to computational waste and inference failure. In this paper, we identify a distinct failure mode termed Circular Reasoning. Unlike traditional model degeneration, this phenomenon manifests as a self-reinforcing trap where generated content acts as a logical premise for its own recurrence, compelling the reiteration of preceding text. To systematically analyze this phenomenon, we introduce LoopBench, a dataset designed to capture two distinct loop typologies: numerical loops and statement loops. Mechanistically, we characterize circular reasoning as a state collapse exhibiting distinct boundaries, where semantic repetition precedes textual repetition. We reveal that reasoning impasses trigger the loop onset, which subsequently persists as an inescapable cycle driven by a self-reinforcing V-shaped attention mechanism. Guided by these findings, we employ the Cumulative Sum (CUSUM) algorithm to capture these precursors for early loop prediction. Experiments across diverse LRMs validate its accuracy and elucidate the stability of long-chain reasoning.

When people reason about cause and effect, they often consider many competing "what if" scenarios before deciding which explanation fits best. Analogously, advanced language models capable of causal inference can consider multiple interventions and counterfactuals to judge the validity of causal claims. Crucially, this type of reasoning is less like a single calculation and more like an internal dialogue between alternative hypotheses. In this paper, we make this dialogue explicit through a dual-agent debate framework where one model provides a structured causal inference, and the other critically examines this reasoning for logical flaws. When disagreements arise, agents attempt to persuade each other, challenging each other's logic and revising their conclusions until they converge on a mutually agreed answer. To take advantage of this deliberative process, we specifically use reasoning language models, whose strengths in both causal inference and adversarial debate remain under-explored relative to standard large language models. We evaluate our approach on the CLadder dataset, a benchmark linking natural language questions to formally defined causal graphs across all three rungs of Pearl's ladder of causation. With Qwen3 and DeepSeek-R1 as debater agents, we demonstrate that multi-agent debate improves DeepSeek-R1's overall accuracy in causal inference from 78.03% to 87.45%, with the counterfactual category specifically improving from 67.94% to 80.04% accuracy. Similarly, Qwen3's overall accuracy improves from 84.16% to 89.41%, and counterfactual questions from 71.53% to 80.35%, showing that strong models can still benefit greatly from debate with weaker agents. Our results highlight the potential of reasoning models as building blocks for multi-agent systems in causal inference, and demonstrate the importance of diverse perspectives in causal problem-solving.

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.

Specialized reasoning language models (RLMs) have demonstrated that scaling test-time computation through detailed reasoning traces significantly enhances performance. Although these traces effectively facilitate knowledge distillation into smaller, instruction-tuned models, the precise nature of transferred reasoning remains unclear. In this study, we investigate to what extent distilled models internalize replicated stylistic patterns during reasoning. To this end, we systematically analyze reasoning traces, identifying structural and lexical patterns that characterize successful reasoning. We then introduce two new datasets -- a dataset of emergent reasoning traces and a synthetic dataset explicitly constructed to replicate these stylistic patterns -- to precisely examine their influence on distilled models' reasoning capabilities. We find that models trained on the synthetic traces achieve comparable performance, indicating that distilled reasoning abilities rely significantly on surface-level patterns. Surprisingly, we observe an increase in performance even when the synthetic traces are altered to lead to the wrong answer. Our findings highlight how stylistic patterns can be leveraged to efficiently enhance LM reasoning across diverse model families.

While Large Language Models (LLMs) have demonstrated their proficiency in complex reasoning tasks, their performance in dynamic, interactive, and competitive scenarios - such as business strategy and stock market analysis - remains underexplored. To bridge this gap, we formally explore the dynamic reasoning capabilities of LLMs for decision-making in rapidly evolving environments. We introduce two game theory-based pilot challenges that mirror the complexities of real-world dynamic decision-making. These challenges are well-defined, enabling clear, controllable, and precise evaluation of LLMs' dynamic reasoning abilities. Through extensive experiments, we find that existing reasoning methods tend to falter in dynamic settings that require k-level thinking - a key concept not tackled by previous works. To address this, we propose a novel reasoning approach for LLMs, named "K-Level Reasoning". This approach adopts the perspective of rivals to recursively employ k-level thinking based on available historical information, which significantly improves the prediction accuracy of rivals' subsequent moves and informs more strategic decision-making. This research not only sets a robust quantitative benchmark for the assessment of dynamic reasoning but also markedly enhances the proficiency of LLMs in dynamic contexts.

We propose a novel framework, Meta Chain-of-Thought (Meta-CoT), which extends traditional Chain-of-Thought (CoT) by explicitly modeling the underlying reasoning required to arrive at a particular CoT. We present empirical evidence from state-of-the-art models exhibiting behaviors consistent with in-context search, and explore methods for producing Meta-CoT via process supervision, synthetic data generation, and search algorithms. Finally, we outline a concrete pipeline for training a model to produce Meta-CoTs, incorporating instruction tuning with linearized search traces and reinforcement learning post-training. Finally, we discuss open research questions, including scaling laws, verifier roles, and the potential for discovering novel reasoning algorithms. This work provides a theoretical and practical roadmap to enable Meta-CoT in LLMs, paving the way for more powerful and human-like reasoning in artificial intelligence.

Large reasoning models (LRMs) have achieved remarkable progress on complex tasks by generating extended chains of thought (CoT). However, their uncontrolled output lengths pose significant challenges for real-world deployment, where inference-time budgets on tokens, latency, or compute are strictly constrained. We propose Elastic Reasoning, a novel framework for scalable chain of thoughts that explicitly separates reasoning into two phases--thinking and solution--with independently allocated budgets. At test time, Elastic Reasoning prioritize that completeness of solution segments, significantly improving reliability under tight resource constraints. To train models that are robust to truncated thinking, we introduce a lightweight budget-constrained rollout strategy, integrated into GRPO, which teaches the model to reason adaptively when the thinking process is cut short and generalizes effectively to unseen budget constraints without additional training. Empirical results on mathematical (AIME, MATH500) and programming (LiveCodeBench, Codeforces) benchmarks demonstrate that Elastic Reasoning performs robustly under strict budget constraints, while incurring significantly lower training cost than baseline methods. Remarkably, our approach also produces more concise and efficient reasoning even in unconstrained settings. Elastic Reasoning offers a principled and practical solution to the pressing challenge of controllable reasoning at scale.

Reasoning LLMs often spend substantial tokens on long intermediate reasoning traces (e.g., chain-of-thought) when solving new problems. We propose to summarize and store reusable reasoning skills distilled from extensive deliberation and trial-and-error exploration, and to retrieve these skills at inference time to guide future reasoning. Unlike the prevailing reasoning from scratch paradigm, our approach first recalls relevant skills for each query, helping the model avoid redundant detours and focus on effective solution paths. We evaluate our method on coding and mathematical reasoning tasks, and find that it significantly reduces reasoning tokens while improving overall performance. The resulting lower per-request cost indicates strong practical and economic potential for real-world deployment.

Large language models have achieved remarkable capabilities across domains, yet mechanisms underlying sophisticated reasoning remain elusive. Recent reasoning models outperform comparable instruction-tuned models on complex cognitive tasks, attributed to extended computation through longer chains of thought. Here we show that enhanced reasoning emerges not from extended computation alone, but from simulating multi-agent-like interactions -- a society of thought -- which enables diversification and debate among internal cognitive perspectives characterized by distinct personality traits and domain expertise. Through quantitative analysis and mechanistic interpretability methods applied to reasoning traces, we find that reasoning models like DeepSeek-R1 and QwQ-32B exhibit much greater perspective diversity than instruction-tuned models, activating broader conflict between heterogeneous personality- and expertise-related features during reasoning. This multi-agent structure manifests in conversational behaviors, including question-answering, perspective shifts, and the reconciliation of conflicting views, and in socio-emotional roles that characterize sharp back-and-forth conversations, together accounting for the accuracy advantage in reasoning tasks. Controlled reinforcement learning experiments reveal that base models increase conversational behaviors when rewarded solely for reasoning accuracy, and fine-tuning models with conversational scaffolding accelerates reasoning improvement over base models. These findings indicate that the social organization of thought enables effective exploration of solution spaces. We suggest that reasoning models establish a computational parallel to collective intelligence in human groups, where diversity enables superior problem-solving when systematically structured, which suggests new opportunities for agent organization to harness the wisdom of crowds.

The significant computational demands of large language models have increased interest in distilling reasoning abilities into smaller models via Chain-of-Thought (CoT) distillation. Current CoT distillation methods mainly focus on transferring teacher-generated rationales for complex reasoning to student models. However, they do not adequately explore teachers' dynamic attention toward critical information during reasoning. We find that language models exhibit progressive attention shifts towards key information during reasoning, which implies essential clues for drawing conclusions. Building on this observation and analysis, we introduce a novel CoT distillation framework that transfers the teacher's stepwise attention on key information to the student model. This establishes structured guidance for the student's progressive concentration on key information during reasoning. More importantly, we develop a Mixture of Layers module enabling dynamic alignment that adapts to different layers between the teacher and student. Our method achieves consistent performance improvements across multiple mathematical and commonsense reasoning datasets. To our knowledge, it is the first method to leverage stepwise attention within CoT distillation to improve small model reasoning.

Chain-of-thought (CoT) reasoning is the dominant paradigm for inference-time scaling in language models, yet the causal influence of individual steps on the final answer poorly understood. We estimate each step's causal importance via early exit and use this measure to study how answers form across the reasoning traces of several model families. Across diverse tasks, we find that reasoning typically crosses a commitment boundary -- a sharp transition from transient intermediate guesses to a stable, high-confidence answer. This transition often happens in a single step, well before the model's reasoning block ends, and is followed by epiphenomenal CoT steps that leave the final answer probability unaltered. Using attention probes, we show that answer-formation stages can be linearly decoded from intermediate reasoning steps with high accuracy and generalize robustly to unseen reasoning tasks. We exploit this signal to early-exit reasoning blocks at the commitment boundary, reducing the length of CoTs up to 55\% on average with negligible impact on model performance.

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.

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.

Recent work has demonstrated that Chain-of-Thought (CoT) often yields limited gains for soft-reasoning problems such as analytical and commonsense reasoning. CoT can also be unfaithful to a model's actual reasoning. We investigate the dynamics and faithfulness of CoT in soft-reasoning tasks across instruction-tuned, reasoning and reasoning-distilled models. Our findings reveal differences in how these models rely on CoT, and show that CoT influence and faithfulness are not always aligned.

Logical reasoning encompasses deduction, induction, and abduction. However, while Large Language Models (LLMs) have effectively mastered the former two, abductive reasoning remains significantly underexplored. Existing frameworks, predominantly designed for static deductive tasks, fail to generalize to abductive reasoning due to unstructured state representation and lack of explicit state control. Consequently, they are inevitably prone to Evidence Fabrication, Context Drift, Failed Backtracking, and Early Stopping. To bridge this gap, we introduce Graph of States (GoS), a general-purpose neuro-symbolic framework tailored for abductive tasks. GoS grounds multi-agent collaboration in a structured belief states, utilizing a causal graph to explicitly encode logical dependencies and a state machine to govern the valid transitions of the reasoning process. By dynamically aligning the reasoning focus with these symbolic constraints, our approach transforms aimless, unconstrained exploration into a convergent, directed search. Extensive evaluations on two real-world datasets demonstrate that GoS significantly outperforms all baselines, providing a robust solution for complex abductive tasks. Code repo and all prompts: https://anonymous.4open.science/r/Graph-of-States-5B4E.

Reasoning requires going beyond pattern matching or memorization of solutions to identify and implement "algorithmic procedures" that can be used to deduce answers to hard problems. Doing so requires realizing the most relevant primitives, intermediate results, or shared procedures, and building upon them. While RL post-training on long chains of thought ultimately aims to uncover this kind of algorithmic behavior, most reasoning traces learned by large models fail to consistently capture or reuse procedures, instead drifting into verbose and degenerate exploration. To address more effective reasoning, we introduce reasoning abstractions: concise natural language descriptions of procedural and factual knowledge that guide the model toward learning successful reasoning. We train models to be capable of proposing multiple abstractions given a problem, followed by RL that incentivizes building a solution while using the information provided by these abstractions. This results in a two-player RL training paradigm, abbreviated as RLAD, that jointly trains an abstraction generator and a solution generator. This setup effectively enables structured exploration, decouples learning signals of abstraction proposal and solution generation, and improves generalization to harder problems. We also show that allocating more test-time compute to generating abstractions is more beneficial for performance than generating more solutions at large test budgets, illustrating the role of abstractions in guiding meaningful exploration.

Video reasoning, the task of enabling machines to infer from dynamic visual content through multi-step logic, is crucial for advanced AI. While the Chain-of-Thought (CoT) mechanism has enhanced reasoning in text-based tasks, its application to video understanding remains underexplored. This paper presents a systematic analysis revealing that CoT often degrades performance in video reasoning, generating verbose but misleading internal monologues, and leading to hallucinated visual details and overridden correct intuitions - a phenomenon we term "visual thinking drift". We explain this drift through a Bayesian lens, positing that CoT traces often diverge from actual visual evidence, instead amplifying internal biases or language priors, causing models to storytell rather than engage in grounded reasoning. To counteract this, we introduce Visual Evidence Reward (VER), a novel reinforcement learning framework that explicitly rewards the generation of reasoning traces that are verifiably grounded in visual evidence. Comprehensive evaluation across 10 diverse video understanding benchmarks demonstrates that our Video-VER consistently achieves top performance. Our work sheds light on the distinct challenges of video-centric reasoning and encourages the development of AI that robustly grounds its inferences in visual evidence - for large multimodal models that not only "think before answering", but also "see while thinking".

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.

Large Language Models (LLMs) demonstrate impressive reasoning capabilities in familiar contexts, but struggle when the context conflicts with their parametric knowledge. To investigate this phenomenon, we introduce CounterLogic, a dataset containing 1,800 examples across 9 logical schemas, explicitly designed to evaluate logical reasoning through counterfactual (hypothetical knowledge-conflicting) scenarios. Our systematic evaluation of 11 LLMs across 6 different datasets reveals a consistent performance degradation, with accuracies dropping by 27% on average when reasoning through counterfactual information. We propose Self-Segregate, a prompting method enabling metacognitive awareness (explicitly identifying knowledge conflicts) before reasoning. Our method dramatically narrows the average performance gaps from 27% to just 11%, while significantly increasing the overall accuracy (+7.5%). We discuss the implications of these findings and draw parallels to human cognitive processes, particularly on how humans disambiguate conflicting information during reasoning tasks. Our findings offer practical insights for understanding and enhancing LLMs reasoning capabilities in real-world applications, especially where models must logically reason independently of their factual knowledge.

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.

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.

In most current research, large language models (LLMs) are able to perform reasoning tasks by generating chains of thought through the guidance of specific prompts. However, there still exists a significant discrepancy between their capability in solving complex reasoning problems and that of humans. At present, most approaches focus on chains of thought (COT) and tool use, without considering the adoption and application of human cognitive frameworks. It is well-known that when confronting complex reasoning challenges, humans typically employ various cognitive abilities, and necessitate interaction with all aspects of tools, knowledge, and the external environment information to accomplish intricate tasks. This paper introduces a novel intelligent framework, referred to as OlaGPT. OlaGPT carefully studied a cognitive architecture framework, and propose to simulate certain aspects of human cognition. The framework involves approximating different cognitive modules, including attention, memory, reasoning, learning, and corresponding scheduling and decision-making mechanisms. Inspired by the active learning mechanism of human beings, it proposes a learning unit to record previous mistakes and expert opinions, and dynamically refer to them to strengthen their ability to solve similar problems. The paper also outlines common effective reasoning frameworks for human problem-solving and designs Chain-of-Thought (COT) templates accordingly. A comprehensive decision-making mechanism is also proposed to maximize model accuracy. The efficacy of OlaGPT has been stringently evaluated on multiple reasoning datasets, and the experimental outcomes reveal that OlaGPT surpasses state-of-the-art benchmarks, demonstrating its superior performance. Our implementation of OlaGPT is available on GitHub: https://github.com/oladata-team/OlaGPT.

Despite significant advancements in multimodal reasoning tasks, existing Large Vision-Language Models (LVLMs) are prone to producing visually ungrounded responses when interpreting associated images. In contrast, when humans embark on learning new knowledge, they often rely on a set of fundamental pre-study principles: reviewing outlines to grasp core concepts, summarizing key points to guide their focus and enhance understanding. However, such preparatory actions are notably absent in the current instruction tuning processes. This paper presents Re-Critic, an easily scalable rationale-augmented framework designed to incorporate fundamental rules and chain-of-thought (CoT) as a bridge to enhance reasoning abilities. Specifically, Re-Critic develops a visual rationale synthesizer that scalably augments raw instructions with rationale explanation. To probe more contextually grounded responses, Re-Critic employs an in-context self-critic mechanism to select response pairs for preference tuning. Experiments demonstrate that models fine-tuned with our rationale-augmented dataset yield gains that extend beyond hallucination-specific tasks to broader multimodal reasoning tasks.

Artificial intelligence (AI) has undergone a renaissance recently, making major progress in key domains such as vision, language, control, and decision-making. This has been due, in part, to cheap data and cheap compute resources, which have fit the natural strengths of deep learning. However, many defining characteristics of human intelligence, which developed under much different pressures, remain out of reach for current approaches. In particular, generalizing beyond one's experiences--a hallmark of human intelligence from infancy--remains a formidable challenge for modern AI. The following is part position paper, part review, and part unification. We argue that combinatorial generalization must be a top priority for AI to achieve human-like abilities, and that structured representations and computations are key to realizing this objective. Just as biology uses nature and nurture cooperatively, we reject the false choice between "hand-engineering" and "end-to-end" learning, and instead advocate for an approach which benefits from their complementary strengths. We explore how using relational inductive biases within deep learning architectures can facilitate learning about entities, relations, and rules for composing them. We present a new building block for the AI toolkit with a strong relational inductive bias--the graph network--which generalizes and extends various approaches for neural networks that operate on graphs, and provides a straightforward interface for manipulating structured knowledge and producing structured behaviors. We discuss how graph networks can support relational reasoning and combinatorial generalization, laying the foundation for more sophisticated, interpretable, and flexible patterns of reasoning. As a companion to this paper, we have released an open-source software library for building graph networks, with demonstrations of how to use them in practice.

Humans have a powerful and mysterious capacity to reason. By working through a series of purely mental steps, we can make inferences we would not be capable of making directly -- despite the fact that we get no additional data from the world. Similarly, when large language models generate a series of intermediate steps (a chain of thought) before answering a question, they often produce better answers than they otherwise would. We investigate why and how chain-of-thought reasoning is useful in language models, testing the hypothesis that reasoning is effective when training data consists of local clusters of variables that influence each other strongly. These training conditions enable the chaining of accurate local inferences in order to estimate relationships between variables that were not seen together in training. We prove that there will exist a "reasoning gap", where reasoning through intermediate variables improves inference, for the simple case of an autoregressive density estimator trained on local samples from a chain-structured probabilistic model. We then test our hypothesis empirically in more complex models, training an autoregressive language model on samples from Bayes nets but only including a subset of variables in each sample. We test language models' ability to match conditional probabilities with and without intermediate reasoning steps, finding that intermediate steps are only helpful when the training data is locally structured with respect to dependencies between variables and that the combination of locally-structured observations and reasoning is much more data-efficient than training on all variables. Our results illustrate how the effectiveness of reasoning step by step is rooted in the local statistical structure of the training data.

Modern systems for multi-hop question answering (QA) typically break questions into a sequence of reasoning steps, termed chain-of-thought (CoT), before arriving at a final answer. Often, multiple chains are sampled and aggregated through a voting mechanism over the final answers, but the intermediate steps themselves are discarded. While such approaches improve performance, they do not consider the relations between intermediate steps across chains and do not provide a unified explanation for the predicted answer. We introduce Multi-Chain Reasoning (MCR), an approach which prompts large language models to meta-reason over multiple chains of thought, rather than aggregating their answers. MCR examines different reasoning chains, mixes information between them and selects the most relevant facts in generating an explanation and predicting the answer. MCR outperforms strong baselines on 7 multi-hop QA datasets. Moreover, our analysis reveals that MCR explanations exhibit high quality, enabling humans to verify its answers.

Recent advancements in large language models (LLMs) have demonstrated their impressive abilities in various reasoning and decision-making tasks. However, the quality and coherence of the reasoning process can still benefit from enhanced introspection and self-reflection. In this paper, we introduce Multiplex CoT (Chain of Thought), a method that enables LLMs to simulate a form of self-review while reasoning, by initiating double Chain of Thought (CoT) thinking. Multiplex CoT leverages the power of iterative reasoning, where the model generates an initial chain of thought and subsequently critiques and refines this reasoning with a second round of thought generation. This recursive approach allows for more coherent, logical, and robust answers, improving the overall decision-making process. We demonstrate how this method can be effectively implemented using simple prompt engineering in existing LLM architectures, achieving an effect similar to that of the Learning-Refinement Model (LRM) without the need for additional training. Additionally, we present a practical guide for implementing the method in Google Colab, enabling easy integration into real-world applications.

Chain-of-thought reasoning, while powerful, can produce unnecessarily verbose output for simpler problems. We present a framework for difficulty-aware reasoning that teaches models to dynamically adjust reasoning depth based on problem complexity. Remarkably, we show that models can be endowed with such dynamic inference pathways without any architectural modifications; we simply post-train on data that is carefully curated to include chain-of-thought traces that are proportional in length to problem difficulty. Our analysis reveals that post-training via supervised fine-tuning (SFT) primarily captures patterns like reasoning length and format, while direct preference optimization (DPO) preserves reasoning accuracy, with their combination reducing length and maintaining or improving performance. Both quantitative metrics and qualitative assessments confirm that models can learn to "think proportionally", reasoning minimally on simple problems while maintaining depth for complex ones.

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.

Recent studies have shown that Large Language Models (LLMs) can achieve strong reasoning performance by incorporating functional symbolic representations that abstractly describe graph traversal algorithms and step-by-step reasoning in few-shot learning settings. However, it remains unclear how LLMs genuinely understand the abstract meaning of each reasoning step and the overall algorithm from only a limited number of demonstrations. This work aims to localize the attention heads responsible for individual reasoning steps and characterize the types of information transferred among them. We first align constituent reasoning steps with their corresponding token logits under a symbolic-aided Chain-of-Thought (CoT) prompting framework. Our analysis shows that token positions that steer the reasoning process are associated with low confidence scores caused by constraints on satisfying reasoning behavior patterns in demonstrations. We then adopt causal mediation analysis techniques to identify the attention heads responsible for these patterns. In addition, our findings indicate that LLMs retrieve factual and rule-based information for individual sub-reasoning tasks through specialized attention heads (approximately 3% total heads), whereas higher layers predominantly facilitate information integration and the emergence of global reasoning strategies (e.g., graph traversal algorithms) that coordinate multiple intermediate reasoning steps to solve the overall task.

As AI systems progress, we rely more on them to make decisions with us and for us. To ensure that such decisions are aligned with human values, it is imperative for us to understand not only what decisions they make but also how they come to those decisions. Reasoning language models, which provide both final responses and (partially transparent) intermediate thinking traces, present a timely opportunity to study AI procedural reasoning. Unlike math and code problems which often have objectively correct answers, moral dilemmas are an excellent testbed for process-focused evaluation because they allow for multiple defensible conclusions. To do so, we present MoReBench: 1,000 moral scenarios, each paired with a set of rubric criteria that experts consider essential to include (or avoid) when reasoning about the scenarios. MoReBench contains over 23 thousand criteria including identifying moral considerations, weighing trade-offs, and giving actionable recommendations to cover cases on AI advising humans moral decisions as well as making moral decisions autonomously. Separately, we curate MoReBench-Theory: 150 examples to test whether AI can reason under five major frameworks in normative ethics. Our results show that scaling laws and existing benchmarks on math, code, and scientific reasoning tasks fail to predict models' abilities to perform moral reasoning. Models also show partiality towards specific moral frameworks (e.g., Benthamite Act Utilitarianism and Kantian Deontology), which might be side effects of popular training paradigms. Together, these benchmarks advance process-focused reasoning evaluation towards safer and more transparent AI.

Large Language Models (LLMs) increasingly rely on prolonged reasoning chains to solve complex tasks. However, this trial-and-error approach often leads to high computational overhead and error propagation, where early mistakes can derail subsequent steps. To address these issues, we introduce Meta-Reasoner, a framework that dynamically optimizes inference-time reasoning by enabling LLMs to "think about how to think." Drawing inspiration from human meta-cognition and dual-process theory, Meta-Reasoner operates as a strategic advisor, decoupling high-level guidance from step-by-step generation. It employs "contextual multi-armed bandits" to iteratively evaluate reasoning progress, and select optimal strategies (e.g., backtrack, clarify ambiguity, restart from scratch, or propose alternative approaches), and reallocates computational resources toward the most promising paths. Our evaluations on mathematical reasoning and puzzles highlight the potential of dynamic reasoning chains to overcome inherent challenges in the LLM reasoning process and also show promise in broader applications, offering a scalable and adaptable solution for reasoning-intensive tasks.

Large Reasoning Models (LRMs) have shown impressive capabilities in multi-step reasoning tasks. However, alongside these successes, a more deceptive form of model error has emerged--Reasoning Hallucination--where logically coherent but factually incorrect reasoning traces lead to persuasive yet faulty conclusions. Unlike traditional hallucinations, these errors are embedded within structured reasoning, making them more difficult to detect and potentially more harmful. In this work, we investigate reasoning hallucinations from a mechanistic perspective. We propose the Reasoning Score, which quantifies the depth of reasoning by measuring the divergence between logits obtained from projecting late layers of LRMs to the vocabulary space, effectively distinguishing shallow pattern-matching from genuine deep reasoning. Using this score, we conduct an in-depth analysis on the ReTruthQA dataset and identify two key reasoning hallucination patterns: early-stage fluctuation in reasoning depth and incorrect backtracking to flawed prior steps. These insights motivate our Reasoning Hallucination Detection (RHD) framework, which achieves state-of-the-art performance across multiple domains. To mitigate reasoning hallucinations, we further introduce GRPO-R, an enhanced reinforcement learning algorithm that incorporates step-level deep reasoning rewards via potential-based shaping. Our theoretical analysis establishes stronger generalization guarantees, and experiments demonstrate improved reasoning quality and reduced hallucination rates.

Large-scale pre-trained language models (PLMs) bring new opportunities to challenging problems, especially those that need high-level intelligence, such as the math word problem (MWPs). However, directly applying existing PLMs to MWPs can fail as the generation process lacks sufficient supervision and thus lacks fast adaptivity as humans. We notice that human reasoning has a dual reasoning framework that consists of an immediate reaction system (system 1) and a delicate reasoning system (system 2), where the entire reasoning is determined by their interaction. This inspires us to develop a cooperative reasoning-induced PLM for solving MWPs, called Cooperative Reasoning (CoRe), resulting in a human-like reasoning architecture with system 1 as the generator and system 2 as the verifier. In our approach, the generator is responsible for generating reasoning paths, and the verifiers are used to supervise the evaluation in order to obtain reliable feedback for the generator. We evaluate our CoRe framework on several mathematical reasoning datasets and achieve decent improvement over state-of-the-art methods, up to 9.6% increase over best baselines. Our codes are available at https://github.com/TianHongZXY/CoRe

We consider the question: when a large language reasoning model makes a choice, did it think first and then decide to, or decide first and then think? In this paper, we present evidence that detectable, early-encoded decisions shape chain-of-thought in reasoning models. Specifically, we show that a simple linear probe successfully decodes tool-calling decisions from pre-generation activations with very high confidence, and in some cases, even before a single reasoning token is produced. Activation steering supports this causally: perturbing the decision direction leads to inflated deliberation, and flips behavior in many examples (between 7 - 79% depending on model and benchmark). We also show through behavioral analysis that, when steering changes the decision, the chain-of-thought process often rationalizes the flip rather than resisting it. Together, these results suggest that reasoning models can encode action choices before they begin to deliberate in text.

While interpretability research has shed light on some internal algorithms utilized by transformer-based LLMs, reasoning in natural language, with its deep contextuality and ambiguity, defies easy categorization. As a result, formulating clear and motivating questions for circuit analysis that rely on well-defined in-domain and out-of-domain examples required for causal interventions is challenging. Although significant work has investigated circuits for specific tasks, such as indirect object identification (IOI), deciphering natural language reasoning through circuits remains difficult due to its inherent complexity. In this work, we take initial steps to characterize causal reasoning in LLMs by analyzing clear-cut cause-and-effect sentences like "I opened an umbrella because it started raining," where causal interventions may be possible through carefully crafted scenarios using GPT-2 small. Our findings indicate that causal syntax is localized within the first 2-3 layers, while certain heads in later layers exhibit heightened sensitivity to nonsensical variations of causal sentences. This suggests that models may infer reasoning by (1) detecting syntactic cues and (2) isolating distinct heads in the final layers that focus on semantic relationships.

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.

Large Language Models (LLMs) are known to acquire reasoning capabilities through shared inference patterns in pre-training data, which are further elicited via Chain-of-Thought (CoT) practices. However, whether fundamental reasoning patterns, such as induction, deduction, and abduction, can be decoupled from specific problem instances remains a critical challenge for model controllability, and for shedding light on reasoning controllability. In this paper, we present the first systematic investigation of this problem through the lens of reasoning conflicts: an explicit tension between parametric and contextual information induced by mandating logical schemata that deviate from those expected for a target task. Our evaluation reveals that LLMs consistently prioritize sensibility over compliance, favoring task-appropriate reasoning patterns despite conflicting instructions. Notably, task accuracy is not strictly determined by sensibility, with models often maintaining high performance even when using conflicting patterns, suggesting a reliance on internalized parametric memory that increases with model size. We further demonstrate that reasoning conflicts are internally detectable, as confidence scores significantly drop during conflicting episodes. Probing experiments confirm that reasoning types are linearly encoded from middle-to-late layers, indicating the potential for activation-level controllability. Leveraging these insights, we steer models towards compliance, increasing instruction following by up to 29%. Overall, our findings establish that while LLM reasoning is anchored to concrete instances, active mechanistic interventions can effectively decouple logical schemata from data, offering a path toward improved controllability, faithfulness, and generalizability.

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.

Reasoning-enhanced large language models (RLLMs), whether explicitly trained for reasoning or prompted via chain-of-thought (CoT), have achieved state-of-the-art performance on many complex reasoning tasks. However, we uncover a surprising and previously overlooked phenomenon: explicit CoT reasoning can significantly degrade instruction-following accuracy. Evaluating 15 models on two benchmarks: IFEval (with simple, rule-verifiable constraints) and ComplexBench (with complex, compositional constraints), we consistently observe performance drops when CoT prompting is applied. Through large-scale case studies and an attention-based analysis, we identify common patterns where reasoning either helps (e.g., with formatting or lexical precision) or hurts (e.g., by neglecting simple constraints or introducing unnecessary content). We propose a metric, constraint attention, to quantify model focus during generation and show that CoT reasoning often diverts attention away from instruction-relevant tokens. To mitigate these effects, we introduce and evaluate four strategies: in-context learning, self-reflection, self-selective reasoning, and classifier-selective reasoning. Our results demonstrate that selective reasoning strategies, particularly classifier-selective reasoning, can substantially recover lost performance. To our knowledge, this is the first work to systematically expose reasoning-induced failures in instruction-following and offer practical mitigation strategies.

LLMs' decision-making process is opaque, prompting the need for explanation techniques like Chain-of-Thought. To investigate the relationship between answer and reasoning, we design a novel evaluation framework, MATCHA. In domains like education and healthcare, reasoning is key for model trustworthiness. MATCHA reveals that LLMs under input perturbations can give inconsistent or nonsensical reasoning. Additionally, we use LLM judges to assess reasoning robustness across models. Our results show that LLMs exhibit greater vulnerability to input perturbations for multi-step and commonsense tasks than compared to logical tasks. Also, we show non-trivial transfer rates of our successful examples to black-box models. Our evaluation framework helps to better understand LLM reasoning mechanisms and guides future models toward more robust and reasoning-driven architectures, enforcing answer-reasoning consistency.

Reasoning requires adaptation to novel problem settings under limited data and distribution shift. This work introduces CausalARC: an experimental testbed for AI reasoning in low-data and out-of-distribution regimes, modeled after the Abstraction and Reasoning Corpus (ARC). Each CausalARC reasoning task is sampled from a fully specified causal world model, formally expressed as a structural causal model. Principled data augmentations provide observational, interventional, and counterfactual feedback about the world model in the form of few-shot, in-context learning demonstrations. As a proof-of-concept, we illustrate the use of CausalARC for four language model evaluation settings: (1) abstract reasoning with test-time training, (2) counterfactual reasoning with in-context learning, (3) program synthesis, and (4) causal discovery with logical reasoning.

Logical reasoning is a critical benchmark for evaluating the capabilities of large language models (LLMs), as it reflects their ability to derive valid conclusions from given premises. While the combination of test-time scaling with dedicated outcome or process reward models has opened up new avenues to enhance LLMs performance in complex reasoning tasks, this space is under-explored in deductive logical reasoning. We present a set of Outcome Reward Models (ORMs) for deductive reasoning. To train the ORMs we mainly generate data using Chain-of-Thought (CoT) with single and multiple samples. Additionally, we propose a novel tactic to further expand the type of errors covered in the training dataset of the ORM. In particular, we propose an echo generation technique that leverages LLMs' tendency to reflect incorrect assumptions made in prompts to extract additional training data, covering previously unexplored error types. While a standard CoT chain may contain errors likely to be made by the reasoner, the echo strategy deliberately steers the model toward incorrect reasoning. We show that ORMs trained on CoT and echo-augmented data demonstrate improved performance on the FOLIO, JustLogic, and ProverQA datasets across four different LLMs.

This work introduces Symbolic-Aided Chain-of-Thought (CoT), an improved approach to standard CoT, for logical reasoning in large language models (LLMs). The key idea is to integrate lightweight symbolic representations into few-shot prompts, structuring the inference steps with a consistent strategy to make reasoning patterns more explicit within a non-iterative reasoning process. By incorporating these symbolic structures, our method preserves the generalizability of standard prompting techniques while enhancing the transparency, interpretability, and analyzability of LLM logical reasoning. Extensive experiments on four well-known logical reasoning benchmarks -- ProofWriter, FOLIO, ProntoQA, and LogicalDeduction, which cover diverse reasoning scenarios -- demonstrate the effectiveness of the proposed approach, particularly in complex reasoning tasks that require navigating multiple constraints or rules. Notably, Symbolic-Aided CoT consistently improves LLMs' reasoning capabilities across various model sizes and significantly outperforms conventional CoT on three out of four datasets, ProofWriter, ProntoQA, and LogicalDeduction.

The chain-of-though (CoT) prompting methods were successful in various natural language processing (NLP) tasks thanks to their ability to unveil the underlying complex reasoning processes. Such reasoning processes typically exhibit implicitly structured steps. Recent efforts also started investigating methods to encourage more explicitly structured reasoning procedures to be captured. In this work, we propose Tab-CoT, a novel tabular-format CoT prompting method, which allows the complex reasoning process to be explicitly modelled in a highly structured manner. Despite its simplicity, we show that our approach is capable of performing reasoning across multiple dimensions (i.e., both rows and columns). We demonstrate our approach's strong zero-shot and few-shot capabilities through extensive experiments on a range of reasoning tasks.

The Abstraction and Reasoning Corpus (ARC) provides a compact laboratory for studying abstract reasoning, an ability central to human intelligence. Modern AI systems, including LLMs and ViTs, largely operate as sequence-of-behavior prediction machines: they match observable behaviors by modeling token statistics without a persistent, readable mental state. This creates a gap with human-like behavior: humans can explain an action by decoding internal state, while AI systems can produce fluent post-hoc rationalizations that are not grounded in such a state. We hypothesize that reasoning is a modality: reasoning should exist as a distinct channel separate from the low-level workspace on which rules are applied. To test this hypothesis, on solving ARC tasks as a visual reasoning problem, we designed a novel role-separated transformer block that splits global controller tokens from grid workspace tokens, enabling iterative rule execution. Trained and evaluated within the VARC vision-centric protocol, our method achieved 62.6% accuracy on ARC-1, surpassing average human performance (60.2%) and outperforming prior methods significantly. Qualitatively, our models exhibit more coherent rule-application structure than the dense ViT baseline, consistent with a shift away from plausible probability blobs toward controller-driven reasoning.

Human problem-solving is never the repetition of a single mindset, by which we mean a distinct mode of cognitive processing. When tackling a specific task, we do not rely on a single mindset; instead, we integrate multiple mindsets within the single solution process. However, existing LLM reasoning methods fall into a common trap: they apply the same fixed mindset across all steps, overlooking that different stages of solving the same problem require fundamentally different mindsets. This single-minded assumption prevents models from reaching the next level of intelligence. To address this limitation, we propose Chain of Mindset (CoM), a training-free agentic framework that enables step-level adaptive mindset orchestration. CoM decomposes reasoning into four functionally heterogeneous mindsets: Spatial, Convergent, Divergent, and Algorithmic. A Meta-Agent dynamically selects the optimal mindset based on the evolving reasoning state, while a bidirectional Context Gate filters cross-module information flow to maintain effectiveness and efficiency. Experiments across six challenging benchmarks spanning mathematics, code generation, scientific QA, and spatial reasoning demonstrate that CoM achieves state-of-the-art performance, outperforming the strongest baseline by 4.96\% and 4.72\% in overall accuracy on Qwen3-VL-32B-Instruct and Gemini-2.0-Flash, while balancing reasoning efficiency. Our code is publicly available at https://github.com/QuantaAlpha/chain-of-mindset{https://github.com/QuantaAlpha/chain-of-mindset}.

Chain-of-Thought (CoT) reasoning offers a promising window into model monitoring. However, monitoring relies on faithfulness, i.e., the model output strictly derives from its reasoning trace. We identify an alignment tension where a model must be faithful enough to be monitored, yet robust enough to reject unsafe reasoning. We demonstrate that this counterbalance exists in current Large Reasoning Models (LRMs), and show ways in which it can be addressed. We introduce HazMart, a human-written dataset set in an autonomous AI shopkeeper scenario. Unlike prior work that relies on providing hints in prompts to test faithfulness (e.g., "A Stanford professor said it should be Answer A"), we propose a novel replacement-based technique, which we call Targeted Reasoning Replacement (TRR), that directly intervenes in the reasoning chain to substitute in unsafe or illogical thoughts (e.g., "Wait, the answer must be Option B [was Option A] because it is the most fitting"). DeepSeek-R1-Llama-70B exhibits high faithfulness (97.5%) but fails to reject Unsafe Reasoning (12.3%), while QwQ-32B is more robust (73.9% safety) at the cost of lower faithfulness (74.7%). Mechanistic analyses of QwQ-32B reveal that these properties are represented by anti-correlated internal directions peaking at the action-commit token. Finally, we demonstrate that representation steering can independently amplify the safety direction, increasing safe behavior by 9 percentage points while maintaining base capabilities.

Reinforcement Learning (RL) has become a pivotal approach for enhancing the reasoning capabilities of Large Language Models (LLMs). However, a significant theoretical gap persists, as traditional token-level RL frameworks fail to align with the reasoning-level nature of complex, multi-step thought processes like Chain-of-Thought (CoT). To address this challenge, we introduce CoT-Space, a novel theoretical framework that recasts LLM reasoning from a discrete token-prediction task to an optimization process within a continuous, reasoning-level semantic space. By analyzing this process from both a noise perspective and a risk perspective, we demonstrate that the convergence to an optimal CoT length is a natural consequence of the fundamental trade-off between underfitting and overfitting. Furthermore, extensive experiments provide strong empirical validation for our theoretical findings. Our framework not only provides a coherent explanation for empirical phenomena such as overthinking but also offers a solid theoretical foundation to guide the future development of more effective and generalizable reasoning agents.

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. ...

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.

Chain-of-Thought (CoT) reasoning has significantly advanced state-of-the-art AI capabilities. However, recent studies have shown that CoT reasoning is not always faithful when models face an explicit bias in their prompts, i.e., the CoT can give an incorrect picture of how models arrive at conclusions. We go further and show that unfaithful CoT can also occur on realistic prompts with no artificial bias. We find that when separately presented with the questions "Is X bigger than Y?" and "Is Y bigger than X?", models sometimes produce superficially coherent arguments to justify systematically answering Yes to both questions or No to both questions, despite such responses being logically contradictory. We show preliminary evidence that this is due to models' implicit biases towards Yes or No, thus labeling this unfaithfulness as Implicit Post-Hoc Rationalization. Our results reveal that several production models exhibit surprisingly high rates of post-hoc rationalization in our settings: GPT-4o-mini (13%) and Haiku 3.5 (7%). While frontier models are more faithful, especially thinking ones, none are entirely faithful: Gemini 2.5 Flash (2.17%), ChatGPT-4o (0.49%), DeepSeek R1 (0.37%), Gemini 2.5 Pro (0.14%), and Sonnet 3.7 with thinking (0.04%). We also investigate Unfaithful Illogical Shortcuts, where models use subtly illogical reasoning to try to make a speculative answer to hard maths problems seem rigorously proven. Our findings raise challenges for strategies for detecting undesired behavior in LLMs via the chain of thought.

Recent advances in agentic harness with orchestration frameworks that coordinate multiple agents with memory, skills, and tool use have achieved remarkable success in complex reasoning tasks. However, the underlying mechanism that truly drives performance remains obscured behind intricate system designs. In this paper, we propose HeavySkill, a perspective that views heavy thinking not only as a minimal execution unit in orchestration harness but also as an inner skill internalized within the model's parameters that drives the orchestrator to solve complex tasks. We identify this skill as a two-stage pipeline, i.e., parallel reasoning then summarization, which can operate beneath any agentic harness. We present a systematic empirical study of HeavySkill across diverse domains. Our results show that this inner skill consistently outperforms traditional Best-of-N (BoN) strategies; notably, stronger LLMs can even approach Pass@N performance. Crucially, we demonstrate that the depth and width of heavy thinking, as a learnable skill, can be further scaled via reinforcement learning, offering a promising path toward self-evolving LLMs that internalize complex reasoning without relying on brittle orchestration layers.

Human beings naturally utilize multiple reasoning modalities to learn and solve logical problems, i.e., different representational formats such as natural language, code, and symbolic logic. In contrast, most existing LLM-based approaches operate with a single reasoning modality during training, typically natural language. Although some methods explored modality selection or augmentation at inference time, the training process remains modality-blind, limiting synergy among modalities. To fill in this gap, we propose Mixture-of-Thought (MoT), a framework that enables LLMs to reason across three complementary modalities: natural language, code, and a newly introduced symbolic modality, truth-table, which systematically enumerates logical cases and partially mitigates key failure modes in natural language reasoning. MoT adopts a two-phase design: (1) self-evolving MoT training, which jointly learns from filtered, self-generated rationales across modalities; and (2) MoT inference, which fully leverages the synergy of three modalities to produce better predictions. Experiments on logical reasoning benchmarks including FOLIO and ProofWriter demonstrate that our MoT framework consistently and significantly outperforms strong LLM baselines with single-modality chain-of-thought approaches, achieving up to +11.7pp average accuracy gain. Further analyses show that our MoT framework benefits both training and inference stages; that it is particularly effective on harder logical reasoning problems; and that different modalities contribute complementary strengths, with truth-table reasoning helping to overcome key bottlenecks in natural language inference.

Chain-of-Thought (CoT) prompting enables large language models to solve complex reasoning problems by generating intermediate steps. However, confined by its inherent single-pass and sequential generation process, CoT heavily relies on the initial decisions, causing errors in early steps to accumulate and impact the final answers. In contrast, humans adopt recursive thinking when tackling complex reasoning problems, i.e., iteratively breaking the original problem into approachable sub-problems and aggregating their answers to resolve the original one. Inspired by the human cognitive process, we propose SOCRATIC QUESTIONING, a divide-and-conquer style algorithm that mimics the recursive thinking process. Specifically, SOCRATIC QUESTIONING leverages large language models to raise and answer sub-questions until collecting enough information to tackle the original question. Unlike CoT, SOCRATIC QUESTIONING explicitly navigates the thinking space, stimulates effective recursive thinking, and is more robust towards errors in the thinking process. Extensive experiments on several complex reasoning tasks, including MMLU, MATH, LogiQA, and visual question-answering demonstrate significant performance improvements over the state-of-the-art prompting methods, such as CoT, and Tree-of-Thought. The qualitative analysis clearly shows that the intermediate reasoning steps elicited by SOCRATIC QUESTIONING are similar to humans' recursively thinking process of complex reasoning problems.

The drive for predictable LLM reasoning in their integration with compound systems has popularized structured outputs, yet concerns remain about performance trade-offs compared to unconstrained natural language. At the same time, training on unconstrained Chain of Thought (CoT) traces has brought about a new class of strong reasoning models that nevertheless present novel compute budget and faithfulness challenges. This paper introduces iSelf-Discover, an instance-level adaptation of the Self-Discover framework, and using it compares dynamically generated structured JSON reasoning with its unstructured counterpart. Our empirical evaluation across diverse benchmarks using state-of-the-art open-source models supports a consistent advantage for unstructured reasoning. Notably, on the complex MATH benchmark, unstructured plans achieved relative performance improvements of up to 18.90\% over structured approaches. Zero-shot unstructured iSelf-Discover variants are also shown to outperform their five-shot structured counterparts, underscoring the significance of this gap, even when structured plans are dynamically generated to ensure reasoning precedes the final answer. We further demonstrate that the optimal granularity of plan generation (instance-level vs. task-level) is context-dependent. These findings invite re-evaluation of the reliance on structured formats for complex problem-solving and how compound systems should be organized.

Complex reasoning problems often involve implicit spatial, geometric, and structural relationships that are not explicitly encoded in text. While recent reasoning models have achieved strong performance across many domains, purely text-based reasoning struggles to represent global structural constraints in complex settings. In this paper, we introduce FIGR, which integrates active visual thinking into multi-turn reasoning via end-to-end reinforcement learning. FIGR externalizes intermediate structural hypotheses by constructing visual representations during problem solving. By adaptively regulating when and how visual reasoning should be invoked, FIGR enables more stable and coherent reasoning over global structural properties that are difficult to capture from text alone. Experiments on challenging mathematical reasoning benchmarks demonstrate that FIGR outperforms strong text-only chain-of-thought baselines. In particular, FIGR improves the base model by 13.12% on AIME 2025 and 11.00% on BeyondAIME, highlighting the effectiveness of figure-guided multimodal reasoning in enhancing the stability and reliability of complex reasoning.

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.

Reasoning-specialized language models show large performance gains over base models, yet the internal changes responsible for improved multi-step reasoning remain poorly understood. It is unclear whether reasoning fine-tuning improves local token-level competence or globally reorganizes how models structure inference over time. We address this question by modeling Chain-of-Thought reasoning as a switching dynamical system (SDS), in which internal representations evolve under discrete latent policy states. Our framework combines time-aware contrastive representation learning with discrete regime discovery to recover latent policies from activation trajectories. Across four benchmarks and model scales from 1.5B to 32B parameters, reasoning-fine-tuned models exhibit richer latent-policy organization than their base counterparts, characterized by more differentiated transition structure and model-dependent changes in state utilization, persistence, and mixing. The recovered regimes exhibit functional specialization aligned with distinct reasoning stages, and extensive controls confirm that their structure is not explained by correctness, representation learning, or modeling priors, but depends on the coherent temporal organization of reasoning trajectories. Causal interventions further show that the regimes are functionally meaningful: state-swap ablations reduce one-step predictive fit, while transplanting reasoning dynamics into base models improves performance on challenging reasoning problems. Finally, SDS-guided pruning of failure-prone reasoning prefixes outperforms self-consistency in 11 of 12 model-dataset settings, with gains of up to 12.5 percentage points. Together, our results suggest that reasoning fine-tuning globally reorganizes latent dynamics, offering a new lens for mechanistic analysis and process-level control of reasoning models.

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.

The development of artificial intelligence systems with advanced reasoning capabilities represents a persistent and long-standing research question. Traditionally, the primary strategy to address this challenge involved the adoption of symbolic approaches, where knowledge was explicitly represented by means of symbols and explicitly programmed rules. However, with the advent of machine learning, there has been a paradigm shift towards systems that can autonomously learn from data, requiring minimal human guidance. In light of this shift, in latest years, there has been increasing interest and efforts at endowing neural networks with the ability to reason, bridging the gap between data-driven learning and logical reasoning. Within this context, Neural Algorithmic Reasoning (NAR) stands out as a promising research field, aiming to integrate the structured and rule-based reasoning of algorithms with the adaptive learning capabilities of neural networks, typically by tasking neural models to mimic classical algorithms. In this dissertation, we provide theoretical and practical contributions to this area of research. We explore the connections between neural networks and tropical algebra, deriving powerful architectures that are aligned with algorithm execution. Furthermore, we discuss and show the ability of such neural reasoners to learn and manipulate complex algorithmic and combinatorial optimization concepts, such as the principle of strong duality. Finally, in our empirical efforts, we validate the real-world utility of NAR networks across different practical scenarios. This includes tasks as diverse as planning problems, large-scale edge classification tasks and the learning of polynomial-time approximate algorithms for NP-hard combinatorial problems. Through this exploration, we aim to showcase the potential integrating algorithmic reasoning in machine learning models.

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

Recent progress on long-horizon agentic tasks has been driven largely by scaling up individual agents through stronger models, better tools, and more effective scaffolding. In contrast, much less is understood about scaling out: whether multiple peer agents, all targeting the same task, can become an additional source of capability without relying on explicit role specialization or workflow orchestration. We study this question and propose AgentFugue, a collective reasoning framework built around a shared reasoning hub. As peer agents explore the same task in parallel, the hub records concise notes on what each agent has established, attempted, or ruled out, and enables each agent to selectively access what other agents have discovered in a form useful for its current search. This design turns otherwise isolated trajectories into a connected ecology of reusable intermediate reasoning without requiring centralized planning. We instantiate the hub as a plug-in communication layer, trained with supervised fine-tuning and end-to-end reinforcement learning. Across the challenging long-horizon settings we study, AgentFugue improves over strong baselines. Our results suggest that collective reasoning can turn scaling out peer agent systems into a distinct source of capability gains, rather than merely a way of spending more compute.

Large Language model (LLM)-based Multi-Agent Systems (MAS) are prone to cascading risks, where early-stage interactions remain semantically fluent and policy-compliant, yet the underlying interaction dynamics begin to distort in ways that amplify latent instability or misalignment. Traditional auditing methods that focus on per-message semantic content are inherently reactive and lagging, failing to capture these early structural precursors. In this paper, we propose a principled framework for cascading-risk detection grounded in semantic--geometric co-evolution. We model MAS interactions as dynamic graphs and introduce Ollivier--Ricci Curvature (ORC) -- a discrete geometric measure -- to characterize information redundancy and bottleneck formation in communication topologies. By coupling semantic flow signals with graph geometry, the framework learns the normal co-evolutionary dynamics of trusted collaboration and treats deviations from this coupled manifold as early-warning signals. Experiments on a suite of cascading-risk scenarios aligned with the risk category demonstrate that curvature anomalies systematically precede explicit semantic violations by several interaction turns, enabling proactive intervention. Furthermore, the local nature of Ricci curvature provides principled interpretability for root-cause attribution, identifying specific agents or links that precipitate the collapse of trustworthy collaboration.

Chain-of-Thought (CoT) empowers Large Language Models (LLMs) to tackle complex problems, but remains constrained by the computational cost and reasoning path collapse when grounded in discrete token spaces. Recent latent reasoning approaches attempt to optimize efficiency by performing reasoning within continuous hidden states. However, these methods typically operate as opaque end-to-end mappings from explicit reasoning steps to latent states, and often require a pre-defined number of latent steps during inference. In this work, we introduce PLaT (Planning with Latent Thoughts), a framework that reformulates latent reasoning as planning by fundamentally decouple reasoning from verbalization. We model reasoning as a deterministic trajectory of latent planning states, while a separate Decoder grounds these thoughts into text when necessary. This decoupling allows the model to dynamically determine when to terminate reasoning rather than relying on fixed hyperparameters. Empirical results on mathematical benchmarks reveal a distinct trade-off: while PLaT achieves lower greedy accuracy than baselines, it demonstrates superior scalability in terms of reasoning diversity. This indicates that PLaT learns a robust, broader solution space, offering a transparent and scalable foundation for inference-time search.

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.

Recent studies on transformer-based language models show that they can answer questions by reasoning over knowledge provided as part of the context (i.e., in-context reasoning). However, since the available knowledge is often not filtered for a particular question, in-context reasoning can be sensitive to distractor facts, additional content that is irrelevant to a question but that may be relevant for a different question (i.e., not necessarily random noise). In these situations, the model fails to distinguish the knowledge that is necessary to answer the question, leading to spurious reasoning and degraded performance. This reasoning failure contrasts with the model's apparent ability to distinguish its contextual knowledge from all the knowledge it has memorized during pre-training. Following this observation, we propose teaching the model to reason more robustly by folding the provided contextual knowledge into the model's parameters before presenting it with a question. Our method, RECKONING, is a bi-level learning algorithm that teaches language models to reason by updating their parametric knowledge through back-propagation, allowing them to then answer questions using the updated parameters. During training, the inner loop rapidly adapts a copy of the model weights to encode contextual knowledge into its parameters. In the outer loop, the model learns to use the updated weights to reproduce and answer reasoning questions about the memorized knowledge. Our experiments on two multi-hop reasoning datasets show that RECKONING's performance improves over the in-context reasoning baseline (by up to 4.5%). We also find that compared to in-context reasoning, RECKONING generalizes better to longer reasoning chains unseen during training, is more robust to distractors in the context, and is more computationally efficient when multiple questions are asked about the same knowledge.

Recent research has shown that rationales, or step-by-step chains of thought, can be used to improve performance in multi-step reasoning tasks. We reconsider rationale-augmented prompting for few-shot in-context learning, where (input -> output) prompts are expanded to (input, rationale -> output) prompts. For rationale-augmented prompting we demonstrate how existing approaches, which rely on manual prompt engineering, are subject to sub-optimal rationales that may harm performance. To mitigate this brittleness, we propose a unified framework of rationale-augmented ensembles, where we identify rationale sampling in the output space as the key component to robustly improve performance. This framework is general and can easily be extended to common natural language processing tasks, even those that do not traditionally leverage intermediate steps, such as question answering, word sense disambiguation, and sentiment analysis. We demonstrate that rationale-augmented ensembles achieve more accurate and interpretable results than existing prompting approaches--including standard prompting without rationales and rationale-based chain-of-thought prompting--while simultaneously improving interpretability of model predictions through the associated rationales.

Recent progress in large language models has led to the emergence of reasoning models, which have shown strong performance on complex tasks through specialized fine-tuning procedures. While these methods reliably improve pass@1 accuracy, prior works have observed that they show a coverage shrinkage behavior, where pass@k degrades relative to the base model. In this paper, we investigate the reasoning shrinkage arise under SFT-based post-training. We hypothesize that this behavior is driven by properties of the fine-tuning data, specifically related to decision points or "forks in the road" scenarios where model faces indecipherable patterns with multiple valid reasoning paths. To test this hypothesis, we design controlled case studies that simulate such decision-point settings, spanning indecipherable nodes in graph branching, and reasoning modes. By tracking post-training dynamics in these settings, we find that the shrinkage phenomenon is tightly correlated with the prevalence of decision-point scenarios in the training data. We also demonstrate that this shrinkage behavior can be partially mitigated through targeted data synthesis design of decision-points, and a more systematic diversity-encouraging decoding mechanism. Our findings identify data-centric factors as a key driver of shrinkage in reasoning models and highlight diversity-aware designs as an effective lever for controlling it.