LLM Reasoning

Process rewards have been widely used in deep reinforcement learning to improve training efficiency, reduce variance, and prevent reward hacking. In LLM reasoning, existing works also explore various solutions for learning effective process reward models (PRM) with or without the help of an expert policy. However, existing methods either rely on strong assumptions about the expert policies (e.g., requiring their reward functions) or suffer intrinsic limitations (e.g., entropy collapse), resulting in weak PRMs or limited generalizability. In this paper, we introduce rePIRL, an inverse RL-inspired framework that learns effective PRMs with minimal assumptions about expert policies. Specifically, we design a dual learning process that updates the policy and the PRM interchangeably. Our learning algorithm has customized techniques to address the challenges of scaling traditional inverse RL to LLMs. We theoretically show that our proposed learning framework can unify both online and offline PRM learning methods, justifying that rePIRL can learn PRMs with minimal assumptions. Empirical evaluations on standardized math and coding reasoning datasets demonstrate the effectiveness of rePIRL over existing methods. We further show the application of our trained PRM in test-time training, test-time scaling, and providing an early signal for training hard problems. Finally, we validate our training recipe and key design choices via a detailed ablation study.

Recent studies increasingly explore Large Language Models (LLMs) as a new paradigm for recommendation systems due to their scalability and world knowledge. However, existing work has three key limitations: (1) most efforts focus on retrieval and ranking, while the reranking phase, critical for refining final recommendations, is largely overlooked; (2) LLMs are typically used in zero-shot or supervised fine-tuning settings, leaving their reasoning abilities, especially those enhanced through reinforcement learning (RL) and high-quality reasoning data, underexploited; (3) items are commonly represented by non-semantic IDs, creating major scalability challenges in industrial systems with billions of identifiers. To address these gaps, we propose the Generative Reasoning Reranker (GR2), an end-to-end framework with a three-stage training pipeline tailored for reranking. First, a pretrained LLM is mid-trained on semantic IDs encoded from non-semantic IDs via a tokenizer achieving $\ge$99% uniqueness. Next, a stronger larger-scale LLM generates high-quality reasoning traces through carefully designed prompting and rejection sampling, which are used for supervised fine-tuning to impart foundational reasoning skills. Finally, we apply Decoupled Clip and Dynamic sAmpling Policy Optimization (DAPO), enabling scalable RL supervision with verifiable rewards designed specifically for reranking. Experiments on two real-world datasets demonstrate GR2's effectiveness: it surpasses the state-of-the-art OneRec-Think by 2.4% in Recall@5 and 1.3% in NDCG@5. Ablations confirm that advanced reasoning traces yield substantial gains across metrics. We further find that RL reward design is crucial in reranking: LLMs tend to exploit reward hacking by preserving item order, motivating conditional verifiable rewards to mitigate this behavior and optimize reranking performance.

Chain-of-thought (CoT) prompting is widely used as a reasoning aid and is often treated as a transparency mechanism. Yet behavioral gains under CoT do not imply that the model's internal computation causally depends on the emitted reasoning text, i.e. models may produce fluent rationales while routing decision-critical computation through latent pathways. We introduce a causal, layerwise audit of CoT faithfulness based on activation patching. Our key metric, the CoT Mediation Index (CMI), isolates CoT-specific causal influence by comparing performance degradation from patching CoT-token hidden states against matched control patches. Across multiple model families (Phi, Qwen, DialoGPT) and scales, we find that CoT-specific influence is typically depth-localized into narrow ''reasoning windows,'' and we identify bypass regimes where CMI is near-zero despite plausible CoT text. We further observe that models tuned explicitly for reasoning tend to exhibit stronger and more structured mediation than larger untuned counterparts, while Mixture-of-Experts models show more distributed mediation consistent with routing-based computation. Overall, our results show that CoT faithfulness varies substantially across models and tasks and cannot be inferred from behavior alone, motivating causal, layerwise audits when using CoT as a transparency signal.

Large Language Models (LLMs) have achieved significant breakthroughs across various domains, but they can still produce unreliable or misleading outputs. For responsible LLM applications, uncertainty quantification techniques are used to estimate a model's uncertainty about its outputs, indicating the likelihood that those outputs may be problematic. For LLM reasoning tasks, it is essential to estimate uncertainty not only in the final answer but also in the intermediate reasoning process, particularly to identify where uncertainty arises. Such information may enable more fine-grained and targeted interventions during inference. In this study, we investigate which metrics can effectively localize uncertain places within an LLM reasoning trajectory. Our study reveals that uncertain intermediate continuations are more likely to occur at tokens that are highly sensitive to perturbations in the embeddings of preceding tokens. In our experiments, we show that such perturbation-based metrics achieve stronger performance in localizing uncertain intermediate steps than baseline methods, including probability-based, sampling-based, and Bayesian-based approaches. Meanwhile, our proposed metrics also enjoy good simplicity and efficiency.

Latent reasoning reduces the token-generation cost of chain-of-thought reasoning by replacing explicit intermediate tokens with continuous latent transitions. However, existing latent reasoning methods usually rely on dense and entangled transitions, making their reasoning trajectories difficult to inspect or intervene on. We introduce LSTR (Latent Sparse Transcoder Reasoning), a framework that turns sparse transcoders from post-hoc diagnostic tools into in-loop, intervenable transition components for latent reasoning. At each latent step, a Latent Transition Transcoder (LTT) combines a linear skip path with a Top-k sparse innovation path, exposing a small set of active sparse features. Under matched compression settings, LSTR offers a mechanistically inspectable alternative to dense latent reasoning. On GSM8K-Aug, ablating only a few top-active sparse features reduces accuracy by up to 16.5%, whereas analogous interventions have much smaller effects in dense latent baselines. These results indicate that the active sparse features are causally involved in the latent transition process, rather than merely post-hoc descriptors. Additional experiments on mathematical benchmarks and StrategyQA suggest that sparse latent transitions can preserve the compression benefits of latent reasoning while making the resulting trajectories more inspectable and intervenable.

Large language model reasoning is often treated as a monolithic capability, relying on binary preference supervision that fails to capture partial progress or fine-grained reasoning quality. We introduce continuous utility direct preference optimization (CU-DPO), a framework that aligns models to a portfolio of prompt-based cognitive strategies by replacing binary labels with continuous scores that capture fine-grained reasoning quality. We prove that learning with K strategies yields a Theta(K log K) improvement in sample complexity over binary preferences and that DPO converges to the entropy-regularized utility-maximizing policy. To exploit this signal, we propose a two-stage pipeline: (i) strategy selection, which optimizes the model to choose the best strategy via best-vs-all comparisons, and (ii) execution refinement, which trains correct execution using margin-stratified pairs. The framework is domain-agnostic: any task admitting cognitively distinct solution strategies and a decomposable continuous utility signal can be incorporated into the portfolio. On mathematical reasoning benchmarks, CU-DPO improves strategy selection accuracy from 35-46% to 68-78% across seven base models, yielding downstream reasoning gains of up to +6.6 points on in-distribution datasets with effective out-of-distribution transfer. CU-DPO demonstrates consistent gains on code generation and causal reasoning benchmarks, confirming generalization beyond the mathematical domain.

Chain-of-Thought (CoT) empowers Large Language Models (LLMs) to tackle complex problems, but remains constrained by the computational cost and early token commitments in discrete reasoning traces. Recent latent reasoning approaches attempt to optimize efficiency by performing reasoning within continuous hidden states. However, many such methods optimize latent states end to end without a trained interface for intermediate textual readout, and several representative configurations use a pre-defined number of latent steps during inference. In this work, we introduce \textbf{PLaT} (\textbf{P}lanning with \textbf{La}tent \textbf{T}houghts), a framework that decouples latent planning from verbalization. The Planner deterministically evolves latent planning states, while an independent Decoder provides textual readouts when needed. Answer-aware textual stopping allows the latent rollout to use a problem-dependent number of groups rather than a pre-specified chain length. PLaT achieves competitive coverage at larger $k$ in several mathematical settings, with lower Pass@1: on Llama-1B GSM8K, it reaches 80.59% Pass@128 versus CODI's 72.37%. These results support PLaT as a candidate-generation interface supplying multiple textual readouts for downstream verification or reranking.

Large language models (LLMs) exhibit failure modes on seemingly trivial tasks. We propose a formalisation of LLM interaction using a deterministic multi-tape Turing machine, where each tape represents a distinct component: input characters, tokens, vocabulary, model parameters, activations, probability distributions, and output text. The model enables precise localisation of failure modes to specific pipeline stages, revealing, e.g., how tokenisation obscures character-level structure needed for counting tasks. The model clarifies why techniques like chain-of-thought prompting help, by externalising computation on the output tape, while also revealing their fundamental limitations. This approach provides a rigorous, falsifiable alternative to geometric metaphors and complements empirical scaling laws with principled error analysis.

Large language models (LLMs) have demonstrated promising capabilities in Text-Attributed Graph (TAG) understanding. Recent studies typically focus on verbalizing the graph structures via handcrafted prompts, feeding the target node and its neighborhood context into LLMs. However, constrained by the context window, existing methods mainly resort to random sampling, often implemented via dropping node/edge randomly, which inevitably introduces noise and cause reasoning instability. We argue that graphs inherently contain rich structural and semantic information, and that their effective exploitation can unlock potential gains in LLMs reasoning performance. To this end, we propose Homophily-aware Structural and Semantic Compression for LLMs (HS2C), a framework centered on exploiting graph homophily. Structurally, guided by the principle of Structural Entropy minimization, we perform a global hierarchical partition that decodes the graph's essential topology. This partition identifies naturally cohesive, homophilic communities, while discarding stochastic connectivity noise. Semantically, we deliver the detected structural homophily to the LLM, empowering it to perform differentiated semantic aggregation based on predefined community type. This process compresses redundant background contexts into concise community-level consensus, selectively preserving semantically homophilic information aligned with the target nodes. Extensive experiments on 10 node-level benchmarks across LLMs of varying sizes and families demonstrate that, by feeding LLMs with structurally and semantically compressed inputs, HS2C simultaneously enhances the compression rate and downstream inference accuracy, validating its superiority and scalability. Extensions to 7 diverse graph-level benchmarks further consolidate HS2C's task generalizability.

Chain-of-Thought (CoT) prompting often improves the reasoning performance of large language models (LLMs), but the internal signal that triggers this behavior remains poorly understood. Leveraging the sparse features captured by Sparse Autoencoders (SAEs), we propose a systematic framework to analyze and intervene on the internal representations of LLMs, identifying a small set of latent features that are linked to reasoning behavior and can be causally tested through targeted intervention. Across multiple model families and reasoning benchmarks, we show that steering one or a small number of reasoning-related latent features can substantially induce reasoning behavior without explicit CoT prompting, achieving accuracy comparable to CoT. We further show that the identified features are not tied to particular wording patterns or verbosity, and confirm their causal role in reasoning through suppression experiments that impair performance even under CoT prompting. These results suggest that CoT prompting activates specific latent features to trigger reasoning, and that targeted intervention on these features offers an alternative pathway to elicit efficient reasoning behavior without explicit CoT prompting. Code is available at https://github.com/Zhenghao-He/LatentCoT.

Speculative decoding (SD) accelerates large language model (LLM) inference by using a lightweight draft model to propose tokens and a stronger target model to verify them. However, standard SD is mainly designed for acceleration, and its output quality is typically constrained by the target model. In this work, we propose Entropy-Aware Speculative Decoding (EASD), a lightweight and training-free extension of SD that improves reasoning quality through token-level entropy-guided rejection. EASD detects cases where both draft and target models exhibit high uncertainty while strongly overlapping in their top predictions. In such uncertain-agreement cases, EASD rejects the aligned token and resamples from the target distribution, preventing low-confidence errors from propagating. Experiments on challenging reasoning benchmarks show that EASD consistently improves accuracy over standard SD and reward-guided variants while maintaining comparable inference efficiency. Notably, EASD can surpass the standalone performance of the target model, suggesting that speculative decoding can serve not only as an acceleration method but also as an effective mechanism for improving reasoning quality. The code is available at https://github.com/ECNU-Text-Computing/EASD.

Language-processing systems that optimize for a single resolved output risk losing ambiguity. With incomplete context, competing interpretations may be compressed prematurely. We specify Non-Resolution Reasoning (NRR) as an explicit retention-commitment interface for preserving context-indexed alternatives until evidence supports commitment. NRR organizes context-indexed alternatives, independently active weights, declared retention and commitment operations, and non-destructive output projection around three principles: Context-indexed Non-Identity, Approximate Identity, and Non-Resolution. It specifies a retained state and candidate operator vocabulary, and proposes Multi-Vector Embeddings, Non-Collapsing Attention, and Contextual Identity Tracking as implementable architectural realizations. In a reproducible synthetic two-turn task, one gated Multi-Vector-Embedding instantiation maintains high output entropy before disambiguating context arrives ($H = 0.91$ bits, near the $1.0$-bit maximum), while a controlled single-embedding baseline has low entropy ($H = 0.15$ bits); both tested systems resolve correctly after context arrives. Thus, high pre-context output uncertainty and accurate later resolution can coexist in the tested gated configuration. This result does not validate the full NRR architecture or matched-parameter superiority; the specification, proposed components, and demonstrated behavior remain distinct contribution layers. NRR targets premature commitment, not commitment itself: alternatives can remain available while evidence is incomplete, and commitment occurs at explicit output or action gates. The question is not whether AI should resolve ambiguity, but when, how, and under whose control. Implementation: https://github.com/kei-saito-research/nrr-core. Series hub: https://github.com/kei-saito-research/nrr-series-hub.

LLMs have shown strong performance in data-rich domains such as programming, but their reliability in engineering tasks remains limited. Circuit analysis is particularly challenging because it requires both multimodal understanding and precise mathematical reasoning. This paper presents an enhanced end-to-end circuit problem-solving framework using Gemini 2.5 Pro as the backbone model for scalable engineering-education applications. We systematically evaluate Gemini 2.5 Pro on undergraduate circuit-analysis problems and identify two major failure modes: circuit-recognition hallucinations, especially source-polarity errors, and reasoning-process hallucinations, such as incorrect current-direction assumptions. To reduce recognition errors, we integrate a fine-tuned YOLO detector with OpenCV-based processing to isolate voltage and current sources for polarity re-identification. To mitigate reasoning errors, we introduce an ngspice-driven verification loop that supports iterative refinement with optional human feedback. On 83 problems, the proposed pipeline achieves 97.59% accuracy, compared with 79.52% for baseline Gemini. Across four hand-drawn diagram variations, accuracy improves from 60.61%--71.21% to 89.39%--92.42%, with statistically significant gains (p<0.005). On 43 problems from a different textbook, accuracy increases from 58.14% to 83.72%, further supporting cross-textbook generalizability. Error analysis shows that circuit recognition remains the dominant source of residual failures, particularly under varying diagram representations. Overall, the framework substantially improves the robustness, scalability, and generalizability of LLM-based circuit problem solving for engineering education and practical circuit analysis.

Egocentric video understanding requires procedural reasoning under partial observability and continuously shifting viewpoints. Current multimodal large language models (MLLMs) struggle with this setting, often generating plausible but visually inconsistent or weakly grounded responses. We introduce $\textbf{EgoVITA}$, a framework that decomposes egocentric video reasoning into a structured $\textit{plan-then-verify}$ process. The model first generates an $\textbf{egocentric plan}$: a causal sequence of anticipated actions from a first-person perspective. This plan is then evaluated by an $\textbf{exocentric verification}$ stage that uses third-person reasoning over the same video to verify its spatiotemporal and logical consistency, without exocentric video input. This decomposition enables cross-perspective feedback without requiring paired ego-exo supervision. To train this reasoning process, we adopt Group Relative Policy Optimization (GRPO) with two dense reward signals: one that grounds anticipated actions in subsequent visual observations and another that reinforces consistent third-person verification. $\textbf{EgoVITA}$ achieves state-of-the-art performance on egocentric reasoning benchmarks, outperforming Qwen2.5-VL-7B by $\mathbf{+7.7}$ on EgoBlind and $\mathbf{+4.4}$ on EgoOrient, while maintaining strong generalization on exocentric video tasks with only $52k$ training samples.

While recent safety guardrails effectively suppress overtly biased outputs, subtler forms of social bias emerge during complex logical reasoning tasks that evade current evaluation benchmarks. To fill this gap, we introduce a new evaluation framework, PRIME (Puzzle Reasoning for Implicit Biases in Model Evaluation), that uses logic grid puzzles to systematically probe the influence of social stereotypes on logical reasoning and decision making in LLMs. Our use of logic puzzles enables automatic generation and verification, as well as variability in complexity and biased settings. PRIME includes stereotypical, anti-stereotypical, and neutral puzzle variants generated from a shared puzzle structure, allowing for controlled and fine-grained comparisons. We evaluate multiple model families across puzzle sizes and test the effectiveness of prompt-based mitigation strategies. Focusing our experiments on gender stereotypes, our findings highlight that models consistently reason more accurately when solutions align with stereotypical associations. This demonstrates the significance of PRIME for diagnosing and quantifying social biases perpetuated in the deductive reasoning of LLMs, where fairness is critical.

Long Chain-of-Thought (CoT) traces can improve reasoning accuracy, but repeatedly generating them is costly for smaller or latency-constrained language models. This paper studies a practical alternative: produce a rich rationale once with a capable \emph{thinking} model, compress it, and reuse the compressed trace as context for a cheaper \emph{answering} model. We introduce CoT-X, an adaptive framework for cross-model CoT transfer. CoT-X segments reasoning traces into semantic units, scores their diagnostic and logical importance, selects budget-feasible evidence paths, and reconstructs a coherent compressed rationale for the answering model. On $7,501$ Japanese medical licensing questions spanning $10$ specialties, CoT-X improves accuracy over direct truncation by up to $40.5\%$ under the same token budget, with the largest gains at $64$--$256$ tokens. Across $64$ thinking--answering pairs from eight DeepSeek-R1 and Qwen3 models (1.5B--32B parameters), reasoning transfer is most reliable within a model family, yet remains effective across families once compression normalizes the trace. A Gaussian Process Bayesian optimization layer finds near-optimal model--budget configurations with $15$ evaluations rather than an exhaustive search over all $64$ pairs, reducing evaluation cost by $84\%$. These results show that reasoning quality, token budget, and model compatibility can be optimized jointly, making CoT-style reasoning more practical under realistic deployment constraints.

Most current large language models (LLMs) support a wide variety of languages in addition to English, including high-resource languages (e.g. German, Chinese, French), as well as low-resource ones (e.g. Swahili, Telugu). In addition, they have shown impressive capabilities in different domains, like coding, science and math. In this paper, taking math as an example domain, we study the performance of different LLMs across languages. Experimental results show that there exists a non-negligible and consistent gap in the performance of the models across languages. Interestingly, and somewhat against expectations, the gap exists for both high- and low-resource languages. These results should impact further research into cross-lingual capability generalization for next generation LLMs. Or they would, if it weren't for the fact that they are distorted by data quality issues. By analyzing one of the standard multilingual math benchmarks (MGSM), we determine that several translation errors are present in the data. Furthermore, the lack of standardized answer extraction from LLM outputs further influences the final results. We propose a method for semi-automatic quality assurance to address the first issue at scale, and give recommendations to address the second one. Combining these two approaches we show that the aforementioned language gap mostly disappears, leading to completely different conclusions from our research. We additionally release the corrected dataset to the community (https://github.com/google-research-datasets/MGSM-Rev2).

Hallucination remains one of the key obstacles to the reliable deployment of large language models (LLMs). Although various mitigation approaches have been proposed, existing studies often analyze different technical paradigms independently, lacking a unified perspective to understand the underlying mechanisms of different approaches and their correspondence with different types of hallucinations. This survey adopts a capability enhancement perspective to systematically examine hallucination mitigation approaches, focusing on Retrieval-Augmented Generation (RAG), reasoning enhancement, and their integration within agentic systems. Based on their primary mitigation mechanisms, we categorize hallucinations into knowledge-based hallucinations and logic-based hallucinations, analyze how RAG and reasoning enhancement methods respectively improve knowledge acquisition and reasoning reliability, and further discuss the integration mechanisms of retrieval and reasoning capabilities in Agentic Systems for mitigating composite hallucinations. By considering the applicability, mitigation mechanisms, and limitations of different approaches, this survey establishes a unified analytical framework connecting hallucination types, key capability dimensions, and technical paradigms.

Large reasoning models (LRMs) often consume excessive tokens, inflating computational cost and latency. More broadly, in goal reaching sequential decision problems we often want to reach the goal quickly, and LRM reasoning can be viewed through this lens. We challenge the assumption that longer responses improve accuracy. By penalizing reasoning tokens using a discounted reinforcement learning setup (interpretable as a small token cost) and analyzing Blackwell optimality in restricted policy classes, we encourage concise yet accurate reasoning, analogous to preferring shorter successful trajectories in a stochastic shortest path problem. Experiments confirm our theoretical results that this approach shortens chains of thought while preserving accuracy.

Large Language Models (LLMs) can propose rules in natural language, sidestepping the need for a predefined predicate space in traditional rule learning. Yet many LLM-based approaches ignore interactions among rules, and the opportunity to couple LLMs with probabilistic rule learning for robust inference remains underexplored. We present RLIE, a unified framework that integrates LLMs with probabilistic modeling to learn a set of weighted rules. RLIE has four stages: (1) Rule generation, where an LLM proposes and filters candidates; (2) Logistic regression, which learns probabilistic weights for global selection and calibration; (3) Iterative refinement, which updates the rule set using prediction errors; and (4) Evaluation, which compares the weighted rule set as a direct classifier with methods that inject rules into an LLM. We evaluate multiple inference strategies on real-world datasets. Applying rules directly with their learned weights yields superior performance, whereas prompting LLMs with the rules, weights, and logistic-model outputs surprisingly degrades accuracy. This supports the view that LLMs excel at semantic generation and interpretation but are less reliable for precise probabilistic integration. RLIE clarifies the potential and limitations of LLMs for inductive reasoning and couples them with classic probabilistic rule combination methods to enable more reliable neuro-symbolic reasoning.

Can a language model improve reasoning by learning from its own imperfect responses, without rewards or teacher-provided solutions? We present Self-evolving Post-Training (SePT), a simple method that alternates temperature-controlled self-generation with next-token likelihood training. Each round uses the updated model to generate new training responses, with one response per prompt by default and no correctness filtering. Across six mathematical benchmarks, SePT improves a temperature-selected no-training baseline by 11.4 and 6.7 AVG points on Qwen2.5-Math-7B and Qwen2.5-7B, respectively, where AVG averages Pass@1, Pass@8 and Pass@32 across benchmarks. We analyze how sampling temperature shapes the learning signal and investigate the value of the resulting responses. Responses from a SePT-trained model improve a student initialized from the original weights, while their reasoning prefixes help an unchanged model complete solutions, even when matched in length to prefixes from a colder initial model. Comparing next-token predictions at identical contexts also reveals changes in token rankings that decoding-temperature adjustment cannot reproduce. Further evaluations across nine starting models, general reasoning and code generation examine broader applicability. Together, these results show that reward-free self-training can improve both a model's predictions and the supervision it provides. Our code is available at https://github.com/ElementQi/SePT.

Large language models (LLMs) still struggle with strategic persuasion, largely because existing approaches either neglect information asymmetry or rely on unrealistic pre-commitment assumptions. We introduce a type-induced commitment-communication mechanism that grounds Bayesian Persuasion (BP) in natural language dialogue without pre-commitment: the persuader narrates their potential types (e.g., honest vs. dishonest) to dynamically construct an information schema, enabling the persuadee to perform Bayesian belief updates within the conversation itself. We implement two variants: Semi-Formal-Natural-Language (SFNL) and Fully-Natural-Language (FNL), evaluating them against strong baselines across multiple LLMs and human judges. BP strategies consistently outperform baselines: SFNL excels in logical credibility, while FNL shows superior robustness and emotional resonance. We verify that gains stem from genuine Bayesian reasoning rather than superficial formatting, and we further show that supervised fine-tuning enables small models to match the persuasive performance of much larger ones.

Hybrid thinking enables LLMs to switch between reasoning and direct answering, offering a balance between efficiency and reasoning capability. Yet our experiments reveal that current hybrid thinking LLMs only achieve partial mode separation: reasoning behaviors often leak into the no-think mode. To understand and mitigate this, we analyze the factors influencing controllability and identify four that matter most: (1) larger data scale, (2) using think and no-think answers from different questions rather than the same question, (3) a moderate increase in no-think data number, and (4) a two-phase strategy that first trains reasoning ability and then applies hybrid think training. Building on these findings, we propose a practical recipe that, compared to standard training, can maintain accuracy in both modes while significantly reducing no-think output length (from 1085 to 585 on MATH500) and occurrences of reasoning-supportive tokens such as "wait" (from 5917 to 522 on MATH500). Our findings highlight the limitations of current hybrid thinking and offer directions for strengthening its controllability. The code is available at: https://github.com/SR-A-W/demystifying-hybrid-thinking

Recent language models exhibit significant logical reasoning abilities, yet the mechanisms supporting deductive inference remain poorly understood. This paper studies small transformer-based language models trained from scratch on multi-step deductive tasks, focusing on the distinction between horizontal reasoning, where intermediate steps are generated autoregressively, and vertical reasoning, where inference unfolds implicitly across layers before the first output token is produced. We analyze two synthetic tasks: logical consequence over chains of symbolic implications and root-to-leaf navigation in binary trees. Mechanistic interpretability reveals that Chain-of-Thought supervision enables models to learn rule-based inference rather than statistical shortcuts. In the horizontal setting, a shallow attention-only model develops interpretable circuits for rule completion, rule chaining, and final decision making, largely implemented through induction-head-like mechanisms. We further introduce a truncated pseudoinverse method to decode the information carried by queries, keys, and values. For vertical reasoning, Chain-of-Thought appears to act less as explicit step-by-step guidance and more as a form of curriculum learning, helping the model acquire increasingly complex reasoning patterns. Without Chain-of-Thought, models tend to memorize or exploit dataset biases. These results provide a low-level account of how transformers can implement deductive reasoning and suggest how Chain-of-Thought may serve different functions in horizontal and vertical reasoning.

Organic reaction mechanisms describe the step-wise elementary processes by which reactants transform into intermediates and products, and are fundamental to understanding chemical reactivity and guiding molecular and reaction de-sign. While large language models (LLMs) have shown promise on chemical tasks such as synthesis design, it remains unclear to what extent this reflects genuine chemical reasoning capabilities: the ability to generate chemically valid intermediates, maintain consistency across reaction steps, and follow logically coherent multi-step pathways. To investigate this, we introduce oMeBench, the first large-scale, expert-curated benchmark for organic mechanism reasoning, comprising over 10,000 annotated mechanistic steps with reaction type labels, intermediate structures, and difficulty ratings. To enable fine-grained evaluation, we further propose oMeS, a dynamic scoring framework that jointly assesses step-level logical consistency and chemical structural similarity. Systematic evaluation of state-of-the-art LLMs reveals that while current models exhibit promising chemical intuition, they struggle to produce correct and consistent reasoning across multi-step mechanisms. Notably, combining prompting strategies with fine-tuning enables smaller-scale models to achieve performance comparable to closed-source frontier models. We hope oMeBench will serve as a rigorous foundation for advancing AI systems toward genuine chemical reasoning.

Many LLMs plan before they act, yet planning and execution are often still entangled in one long generation trace, enforced only through prompts, or split across separate components. We argue that these two stages call for different computation: planning benefits from diversity and breadth, whereas execution demands precision and faithful adherence to a chosen strategy. Treating them as a single undifferentiated chain wastes tokens on routine derivation and makes it costly to explore alternative strategies at test time. We present the \textbf{Explore-Execute Chain (E\textsuperscript{2}C)}, which keeps both stages in one model but separates them structurally: a stochastic \textit{Exploration} phase drafts a concise high-level plan, and a deterministic \textit{Execution} phase carries it out. Causal SFT and RL train this split so that exploration stays informative and execution remains plan-faithful. Once plans are short yet decisive, extra inference compute can be directed to exploration rather than to repeatedly decoding full solutions. On AIME'2024 at $K{=}32$, \textbf{E\textsuperscript{2}C-ReAct Loop} reaches 53.3% accuracy with only 12.4k tokens, outperforming Tree-of-Thoughts ($N{=}32$: 50.0%, 71.3k). The same structure also supports lightweight domain adaptation: \textbf{Exploration-Focused SFT (EF-SFT)} updates only the planning phase, uses 3.5% of the tokens required by standard SFT, and improves medical benchmark accuracy by up to 14.5%.

Given the prohibitive cost of pre-training large language models, it is essential to leverage smaller proxy models to optimize datasets before scaling up. However, this approach becomes challenging for reasoning capabilities, which exhibit emergent behavior that only appear reliably at larger model sizes, often exceeding 7B parameters. To address this, we introduce rBridge, showing that small proxies ($\leq$1B) can effectively predict large-model reasoning by aligning more closely with (1) the pre-training objective and (2) the target task. rBridge achieves this by weighting negative log-likelihood with task alignment, using reasoning traces from frontier models as gold labels. In our experiments, rBridge (i) reduces dataset ranking costs by over 100x relative to the best baseline, (ii) achieves the strongest correlation across six reasoning benchmarks at 1B to 32B scale, and (iii) zero-shot transfers predictive relationships across pre-training datasets at 1B to 7B scale. These findings indicate that rBridge offers a practical path for exploring reasoning-oriented pre-training at lower cost.

Large language models (LLMs) show strong reasoning via chain-of-thought (CoT) prompting, but the process is opaque, which makes verification, debugging, and control difficult in high-stakes settings. We present Vis-CoT, a human-in-the-loop framework that converts linear CoT text into an interactive reasoning graph. Users can visualize the logical flow, identify flawed steps, and intervene by pruning incorrect paths and grafting new, user-defined premises. This shifts interaction from passive observation to active collaboration, steering models toward more accurate and trustworthy conclusions. Across GSM8K and StrategyQA, Vis-CoT improves final-answer accuracy by up to 24 percentage points over non-interactive baselines. A user study also shows large gains in perceived usability and trust. Vis-CoT points to a practical path for more reliable, understandable, and collaborative reasoning by combining LLMs with targeted human oversight.

Best-of-n sampling improves the accuracy of large language models (LLMs) and large reasoning models (LRMs) by generating multiple candidate solutions and selecting the one with the highest reward. The key challenge for reasoning tasks is designing a scoring function that can identify correct reasoning chains without access to ground-truth answers. We propose Probabilistic Confidence Selection And Ranking (PiCSAR): a simple, training-free method that scores each candidate generation using the joint log-likelihood of the reasoning and final answer. The joint log-likelihood of the reasoning and final answer naturally decomposes into reasoning confidence and answer confidence. PiCSAR achieves substantial gains across diverse benchmarks (+10.18 on MATH500, +9.81 on AIME2025), outperforming baselines with at least 2x fewer samples in 16 out of 20 comparisons. Our analysis reveals that correct reasoning chains exhibit significantly higher reasoning and answer confidence, justifying the effectiveness of PiCSAR.

Large Language Models (LLMs) have demonstrated remarkable progress in reasoning across diverse domains. However, effective reasoning in real-world tasks requires adapting the reasoning strategy to the demands of the problem, ranging from fast, intuitive responses to deliberate, step-by-step reasoning and tool-augmented thinking. Drawing inspiration from cognitive psychology, we propose a novel taxonomy of LLM reasoning strategies along two knowledge boundaries: a fast/slow boundary separating intuitive from deliberative processes, and an internal/external boundary distinguishing reasoning grounded in the model's parameters from reasoning augmented by external tools. We systematically survey recent work on adaptive reasoning in LLMs and categorize methods based on key decision factors. We conclude by highlighting open challenges and future directions toward more adaptive, efficient, and reliable LLMs.