Large Language Model Reasoning

Autoregressive multimodal large language models (MLLMs) suffer from error snowballing: a single incorrect inference early in a chainof-thought (CoT) trace corrupts all downstream reasoning. We find that in state-of-the-art open-source MLLMs, once the first error occurs, the reasoning cascades into failure across all remaining steps in 65% of such cases (a metric we term the snowball rate). Existing mitigations-sampling multiple chains, post-hoc self-verification, or full program synthesis-either lack symbolic grounding, catch errors too late, or sacrifice the flexibility of natural language reasoning. We propose Constraint-Anchored Reasoning Traces (CART), a neuro-symbolic framework that trains MLLMs to interleave natural language reasoning steps with symbolic constraint assertions: lightweight, machine-checkable statements about visual content (e.g., count(red_objects) = 3). A dual-pronged Constraint Propagation Module-combining a learned neural grounding head with Boolean Constraint Propagation-continuously verifies these anchors against extracted visual features and checks their mutual logical consistency. When a contradiction is detected, a backtrack controller halts generation and reverts to the last consistent checkpoint, preventing error propagation. A variable-frequency emission mechanism allows the model to adaptively control anchor density, avoiding trace bloat. We construct 218K training instances by augmenting GQA, CLEVR-CoGenT, and VCR with ground-truth constraint annotations derived from scene graphs, and fine-tune open-source MLLMs (LLaVA-NeXT, Qwen2-VL) via LoRA. On five benchmarks, CART reduces the snowball rate from 0.65 to 0.14, improves GQA accuracy by +4.6 percentage points over trainingonly baselines, and achieves 89.1 F1 on POPE-all with at most 18% inference overhead.

Reinforcement learning (RL) has become central to improving large language models (LLMs) on complex reasoning tasks, yet RL post-training is largely studied in isolation from the pretraining that precedes it. As a result, two basic questions remain open: (1) how do pretraining choices (model size, data) shape the returns to RL compute, and (2) what does RL actually do to the model? These questions are difficult to study in the standard LLM setting: pretraining corpora are vast and uncontrolled, making it hard to attribute behaviors to pretraining versus RL, and systematic compute sweeps across both stages are prohibitively expensive. To address these challenges, we use chess as a controlled testbed for studying reasoning across the full pretraining-to-post-training pipeline. We follow the standard LLM training pipeline by pretraining language models from 5M to 1B parameters on human chess games, supervised fine-tuning on synthetic reasoning traces, and running RL on chess puzzles with verifiable rewards. Using this framework, we find that the post-RL performance at given RL compute level is well-predicted from the pretraining loss, and slope of the RL reward curves improves approximately linearly with the pretraining tokens. Beyond scaling, we find that RL does not simply sharpen the SFT policy: on easy puzzles it amplifies correct moves the SFT policy already preferred, while on hard puzzles it surfaces correct moves that were nearly absent under SFT. We further test whether our findings transfer beyond chess by training a 1B language model on math-domain text, where the same predictive pattern emerges: longer-pretrained checkpoints reach higher post-RL performance and improve faster under RL. In sum, we provide a quantitative account of the pretraining-to-RL interface and a controlled testbed for studying the science of reasoning across the full pretraining-to-post-training pipeline.

Reasoning language models (RLMs) have demonstrated impressive performance in domains such as mathematics and coding. These domains permit reliable verification of model outputs, which is important for enabling the reinforcement learning that drives RLM performance gains. However, training RLMs on domains that lack reliable verifiers remains challenging. Meanwhile, for both verifiable and unverifiable domains, large amounts of unused supervised fine-tuning data with human-written solutions exist. In this work, we show that these data can be used efficiently to further improve RLM performance. For this, we first use classic instruction tuning, supervised fine-tuning without reasoning traces, on the RLM. Next, we merge our instruction-tuned model with the original reasoning model, recovering its reasoning behavior on the target domain. Our extensive evaluation demonstrates that our technique improves RLM performance in both verifiable and hard-to-verify domains, including coding and text summarization, while preserving RLM capabilities across other domains. Importantly, our method is highly cost-effective, enabling such improvements for less than USD $3.

Existing LLM-based theorem provers have achieved impressive results on formal mathematics benchmarks, yet they remain confined to acting as autonomous agents that prove a stated proposition. In this paper, we propose MathCoPilot, a human-in-the-loop system that embodies a new human--AI symbiotic paradigm for mathematical research, in which the mathematician steers the high-level mathematical direction while AI agents carry out the detailed formalization and proof work under continuous human guidance. MathCoPilot unifies three core capabilities: (1) an interactive workbench where the mathematician and AI agents collaborate through a living proof blueprint that decomposes a proof into navigable steps the human can directly inspect, direct, and refine; (2) automated proving skill orchestration with adaptive knowledge base search and Lean-integrated iterative verification; and (3) topic-driven paper retrieval and automated formalization into a verified Lean knowledge base. Using MathCoPilot, we systematically compare four state-of-the-art LLMs, including Gemini3.1Pro, GPT-5.4, and ClaudeOpus4.7, on a FormalMATH subset and on two real PDE theorems requiring deep domain expertise, evaluating their ability to produce verified Lean~4 proofs and to identify errors in deliberately incorrect proofs. Our results show that while current models can handle undergraduate-level problems with high success rates under favorable autoformalization conditions, substantial challenges remain for domain-specific theorems requiring genuine mathematical understanding.

A standard recipe for distilling the reasoning ability of large language models (LLMs) is to sample chains of thought from the model, keep those that reach the correct final answer, and fine-tune on the survivors. When sampling fails, a common fix shows the generator the gold answer and asks it to write a chain that reaches that answer. We show that this second step degrades the training data in a way that correctness filtering cannot catch. We run a controlled experiment that fixes the generator, the problem set, and the correctness filter, and varies only whether the chain is generated under answer-conditioning, the gold answer shown with a request to reach it. Training a strong instruction-tuned reasoning model on its own answer-conditioned chains sharply lowers its verifiable-reasoning accuracy. The loss grows with difficulty, reaching as much as about 27 points on the hardest competition problems. The mechanism is legible in the chains themselves, which rationalize backward from the shown answer instead of deriving it, with the early final-answer statement as the measurable symptom. The harm is a property of the data rather than the generator, read off unlabeled generations before any fine-tuning, ordering the penalty across eight thinking models from four families, and transferring across teacher families. A prompt ablation localizes it to the rationalize-toward instruction rather than the answer's bare visibility. The practical takeaway is to generate answer-blind, because no correctness filter can see this damage in the data.

While Large Language Models (LLMs) excel in many general NLP tasks, their formal reasoning capabilities are often compromised by content effects, demonstrating a measurable bias towards real-world plausibility. In this paper, we present our system for SemEval-2026 Task 11, which evaluates the ability of models to disentangle formal logic from content across 12 languages with and without distractor premises. We address this challenge using mDeBERTa-v3 networks fine-tuned on a synthetic, rule-based dataset of syllogistic schemes to avoid the semantic noise of LLM-augmented data. To explicitly decouple plausibility from logical structure, our training pipeline employs a multi-objective loss function combining Adaptive Group Distributionally Robust Optimization (DRO), a scheduled differentiable bias penalty, and KL-Divergence consistency regularization. Our system achieved #1 ranks and perfect Ranking Scores (100.0) with 0.00% bias and 100.0% accuracy on Subtask 1 (English), Subtask 2 (Noisy English), and Subtask 3 (Multilingual). On the highly complex Subtask 4 (Noisy Multilingual), the system achieved the 6th rank with 89.06% Accuracy and F1-score, alongside a limited 2.89% Bias and a 37.78 Ranking Score. Our dataset generation engine and codebase are publicly available to facilitate future work on robust logical reasoning.

The emergence of Chain-of-Thought (CoT) reasoning has significantly enhanced the ability of large language models (LLMs) to tackle complex, multi-step tasks. However, when errors occur, current interaction approaches typically involve re-generating another response that may make mistakes again, or users laboriously flag the faulty step in follow-up turns that may get responses <You are right, I made a mistake here> followed by similar errors recurring. To address this issue, we propose an efficient human intervention mechanism for precisely correcting reasoning errors in LLMs, termed Deep Interaction. Our approach enables direct editing of the original response, allowing erroneous parts to be corrected while preserving accurate reasoning steps. We refine the edited CoT into a distilled prompt, which then steers the LLM along the corrected reasoning path. Experimental results show that our method achieves over a 25% improvement in correction success rate and reduces token usage by approximately 40% on STEM tasks reasoning compared to baseline approaches.

Reaction mechanisms consist of the step-by-step sequences of elementary reactions that explain chemical transformations. Learning the mechanism logic is therefore essential for enhancing the fundamental chemical intelligence of large language models (LLMs). The stepwise deduction of reaction mechanism aligns naturally with the reasoning paradigms of reasoning LLMs. However, current chemical LLMs primarily emphasize coarse-grained name reactions for product prediction and retrosynthesis, often leading to physical inconsistencies and hallucinations. In contrast, specialized small-scale generative models for mechanism inference typically suffer from restricted generalization capacity across diverse chemical spaces. To overcome these limitations, we built a novel, large-scale reasoning dataset of reaction mechanisms. Furthermore, we established the FukuyamaBench, a difficult benchmark derived from Fukuyama's Advanced Organic Reaction Mechanism book, to rigorously evaluate model performance on hierarchical mechanism reasoning. Our fine-tuned Qwen3-30B-A3B achieves 8.3% exact pathway match on FukuyamaBench Set~A, surpassing the specialized FlowER model (5.1%), demonstrating that mechanism-aware training substantially enhances chemical reasoning in language models.

Reinforcement learning with verifiable rewards (RLVR) optimizes LLMs using sparse verifiable final-answer rewards. This sparse anchor reliably verifies whether a trajectory succeeds but provides no direct feedback on the reasoning path that produced it. Before success, prerequisite progress on hard problems receives no reward signal; after success, outcome rewards cannot distinguish well-organized correct trajectories from redundant or locally flawed ones. We introduce SCOPE-RL (Scaffolded Chain Optimization with Process Efficiency), a two-stage framework that densifies this anchor while retaining the GRPO update: Adaptive Scaffolded RL adds prefix-decomposed verifiable rewards on answer-hidden sub-question chains before success, and Quality-Aware Process RL applies correctness-gated process-shape rewards to refine correct trajectories after success. An expert-validated Step-Quality Evaluation Protocol evaluates useful-step density, error localization, and token efficiency beyond final-answer accuracy. On Qwen3-8B-Instruct trained on DAPO-Math and Big-Math, SCOPE-RL improves average accuracy by up to 11.2 pp and reduces reasoning tokens by up to 27.1% over outcome-only GRPO; the gains hold under GSPO and on Qwen3-0.6B-Instruct, indicating that reward-signal densification is complementary to policy-update-level RLVR advances. Code and data are available at https://github.com/tokencraft-lab/SCOPE-RL.

Table-based reasoning with large language models (LLMs), which requires reasoning based on natural language questions and structured tabular data, has gained widespread attention. However, a series of issues still constrain the application of this task. The previous approaches suffered from significant performance degradation when faced with large tables due to the difficulty of long text modeling and the limitation of input length for LLMs. The text-to-SQL approach is used to efficiently extract key information from tables and generate smaller sub-tables. However, tabular data, especially web tables, often lack the necessary structure and consistency, making them unsuitable for performing mathematical logic operations using SQL queries. We propose the ProgramTab framework, which guides LLMs employing in-context learning to perform tabular data preprocessing with Python code, as well as the momentous contents extraction with row and column extraction and SQL generation. The experiment results on table reasoning datasets demonstrate that the ProgramTab framework effectively deals with table-based reasoning tasks and outperforms all LLM-based baselines.

We introduce Self-Verified Reasoner (SVR-R1), a multi-turn RL framework that turns a model's own verification into a learning signal for multimodal reasoning. For each query, the model proposes an answer using the same weights, and issues a binary self-verdict (Yes/No). A 'No' triggers a second-chance rethink; a 'Yes,' or a turn cap, finalizes the output for computing the outcome-based reward. SVR-R1 is implemented with GRPO and an asynchronous multi-turn rollout framework and needs no external supervision or auxiliary critics. We evaluate SVR-R1 on vision-language reasoning benchmarks and show that it improves accuracy by a large margin over strong standard GRPO baselines. Training dynamics show decreasing reliance on verification-fewer verification turns, yet higher test accuracy-indicating that the gap between verification and generation narrows as the policy internalizes self-correction and chooses the most confident answer via our framework. SVR-R1 bridges the less explored intersection of inference-time self-refinement and RL training for VLMs, offering a simple yet effective recipe for bootstrapping multimodal reasoning. We will open-source \textbf{SVR-R1} to facilitate future research in VLMs.

Evaluating the multi-hop reasoning capabilities of large language models remains a significant challenge. Although current models achieve strong results on existing multi-hop question answering datasets, such performance often masks two critical vulnerabilities: (1) reliance on internal parametric knowledge rather than adherence to the provided context, and (2) exploitation of dataset shortcuts, such as single-document cues or type-matching, that diminish the need for genuine evidence aggregation across multiple documents. We introduce CRiT-QA (Counterfactual Reasoning with Traps), a dataset explicitly designed to address both limitations. To neutralize reliance on memorized knowledge and enforce strict context dependency, CRiT-QA transforms factual reasoning chains with counterfactual entities. Furthermore, it injects multi-anchor distractor chains, plausible but incorrect reasoning paths that diverge at different hops. These traps require models to follow the entire reasoning process rather than exploiting shallow heuristics. Our experiments show that LLMs exhibit substantial performance degradation on CRiT-QA compared to standard datasets, exposing their vulnerability to counterfactual conditions and distractor traps. CRiT-QA thus serves as a rigorous diagnostic tool for evaluating genuine multi-hop reasoning and provides a foundation for developing more reliable, evidence-grounded LLMs.

Despite advances in Emotional Intelligence (EI), Large Language Models (LLMs) still significantly underperform humans in complex emotional reasoning. This gap originates partly from the limited incorporation of individual differences, particularly personality traits, which are fundamental to human emotional inference. To address this, we propose PTEI, a novel framework for integrating Personality Traits into Emotional Intelligence tasks using LLMs. In PTEI, MBTI and OCEAN personality traits are first extracted directly from the given emotional scenarios and then utilized as contextual knowledge within personality-aware prompts, guiding LLMs to accurately infer emotions and their underlying causes. To ensure optimal contextual grounding, we employ Contrastive Learning to construct an optimized retrieval system that surfaces emotionally and personally aligned scenarios, enhancing reasoning quality. Extensive experiments on established EI benchmarks show that PTEI enhances the Emotional Understanding (EU) capabilities of various LLMs, with the strongest improvement observed in GPT models. Combining PTEI with Chain-of-Thought (CoT) reasoning yields an additional 4 percent increase in accuracy. These findings underscore PTEI's contribution toward advancing AI systems with more sophisticated social and psychological grounding.

Selecting the correct answer from a pool of candidate reasoning chains is the engine of test-time scaling, yet the standard selectors each carry a cost: self-consistency inherits the errors of the single model it resamples, and trained reward models need labeled data and transfer poorly off-distribution. We study a third signal, free at inference time: cross-model consensus, the degree to which independently trained models, each solving the problem once, agree on a final answer. We treat the panel as an LLM-jury, in which the structure of agreement, not any model's score of another, is the verification signal. Across seven benchmarks it selects correct answers better than self-consistency and far better than a model scoring its own candidates: on competition math it closes the entire gap to an oracle selector, while self-scoring closes almost none. The mechanism is error decorrelation: independently trained models err differently, so their wrong answers scatter while the correct one accumulates agreement. We make this precise with a parameter-free law, derived in closed form, that predicts consensus accuracy from three measured panel statistics to a mean absolute error of $0.03$ and exposes the method's ceiling: a shared-error floor where models share a misconception, near zero on math but non-trivial on science. Against four trained verifiers spanning discriminative, outcome, and generative reward models, the free LLM-jury matches the strongest inside their math training domain and is the top selector outside it. Cross-model consensus is thus a verifier we can characterize in advance: a law that says when to trust it, and a floor that marks where it cannot.

We present a practical pipeline for recovering source code from stripped binary functions by combining reverse engineering, anchor-based source code retrieval, and large language model reasoning. Our binary-to-source-code retrieval method attempts to identify the source function from a source code database, rather than generating approximate decompiled pseudocode. It extracts anchors such as strings, constants, external calls, and available function names using Ghidra, retrieves candidate files via an inverted-index search database, narrows candidates to likely function snippets, and re-ranks them with a large language model (LLM) based on disassembly, decompiled code, and source metadata. Confident matches can also serve as anchors in later passes. In an evaluation backed by our high-fidelity source code database on a stripped, optimized tcpdump binary, our proposed binary-to-source matching method achieves 95.2% assembly instruction coverage. Experiments on a GitHub-based retrieval database showed lower performance with 35.5% instruction coverage on average, mainly due to retrieval misses. These results show that source-level binary recovery excels with high-quality databases and remains a useful tool in noisy environments.

Multimodal Large Language Models (MLLMs) often follow a fixed Think-then-Answer paradigm, which is inefficient in heterogeneous multitask settings because simple inputs may not require explicit reasoning while difficult ones can benefit substantially from it. Learning when to think is also unstable during post-training, where imbalanced rollouts can drive the model toward always-thinking or always-direct behavior. We propose Switch-Reasoner, a GRPO-based framework that learns to adaptively select reasoning modes for MLLMs. It treats thinking as a virtual tool invocation and allows the model to either answer directly or invoke explicit reasoning before answering. To stabilize this decision, we introduce a dual-level regulation mechanism that balances the overall use of Thinking Mode and Direct Mode while providing sample-level supervision based on the relative benefit of the two choices. Experiments on 11 multimodal tasks show that Switch-Reasoner reduces unnecessary reasoning while maintaining strong performance, achieving a better accuracy-efficiency trade-off.

LLMs often struggle to balance compositionality with knowledgeability, a challenge we define as Composition-Knowledge Dichotomy. To address this, we propose Concretized Proposition Prompting (CPP), a framework that explicitly concretizes propositions relevant to questions. The results demonstrate that CPP significantly enhances reasoning performance, particularly in medical benchmarks where precise knowledge is paramount, while being competitive on math benchmarks where deductive reasoning is prioritized. Additional experiments reveal that CPP is scalable to various foundation models and parameter sizes, being a fundamental paradigm that bridges the gap between composition- and knowledge-based approaches. Consequently, CPP resolves the composition-knowledge dichotomy by providing a solid foundation for logically organized and factually grounded reasoning.

Large-Language Models (LLMs) can be prone to flawed and unfaithful reasoning that decoding strategies like Self-Consistency (SC) fail to detect as they evaluate only final-answer agreement while ignoring the logical validity of intermediate steps. This raises three fundamental questions: How can we reliably quantify uncertainty in LLM reasoning? Can semantic, structural, and causal awareness select more faithful reasoning compared to naïve majority voting? and How robust is reasoning topology under adversarial conditions? To address these questions, we introduce GRAPHEVAL, a graph-based reasoning framework that re-frames uncertainty quantification (UQ) as a holistic reasoning fidelity problem. We propose a novel UQ metric, Graph Reasoning Coherence Score (GRCS), that quantifies semantic-structural consensus of the reasoning space and captures pathological mode collapse and confident hallucinations. We find that GRCS is the only metric that is consistently negatively correlated with reasoning faithfulness across both more capable and smaller models. Additionally, we introduce Graph Self-Consistency (GSC), a medoid-based decoding strategy that trades nominal accuracy for reasoning fidelity, exposing the degree to which SC is inflated by unfaithful lucky guesses in smaller models, while preserving or improving accuracy in more capable ones. Finally, through adversarial medoid ablation, we demonstrate that the GSC-selected path acts as a "load-bearing path" and forcing models away from it degrades reasoning faithfulness and, in targeted cases, causes drops in accuracy.

Large language models (LLMs) increasingly improve their reasoning at test time via additional computation, yet most existing works treat each problem in isolation. When problems arrive sequentially, accumulating reusable experience across them can further improve performance. Existing memory-based methods either store whole-solution templates that generalize poorly to novel problems or use heuristic step-level selection that is not optimized for final-answer correctness. Learning selection policies requires large-scale training data and fixed action spaces, making such approaches unsuitable for test-time settings where memory expands incrementally and only limited supervision is available. We propose MILES (Modular Instruction Memory with LEarnable Selection for self-improving LLM reasoning), a framework that dynamically expands step-wise memory and applies correctness-optimized memory composition under realistic test-time constraints. MILES maintains modular memory units consisting of asymmetric pairs of sub-goal embeddings and sub-instructions, each associated with a learnable selection head. This memory structure enables a coarse-to-fine retrieval mechanism: The coarse level enables memory expansion and collects supervision for training selection heads from confident samples, while the fine stage applies learned selection heads to rerank coarse-level candidates and guide reasoning for uncertain samples. MILES consistently matches or outperforms prior methods while achieving superior accuracy-efficiency tradeoffs. Extensive experiments demonstrate its effectiveness, robustness, and transferability.

Training large language models (LLMs) with extended reasoning has enabled in-context search, in which models iteratively generate, critique, and revise solution attempts. We provide a theoretical analysis of in-context search by modeling it as approximate inference over reasoning traces, where the base model defines a prior and self-reflection provides feedback for posterior updates, and study the resulting inference-time sampling complexity - the number of sequential attempts needed to achieve high success probability. We show that when reflections reliably localize early mistakes, in-context search can yield exponential improvements over the base model, solving problems with exponentially small zero-shot pass rates using only a polynomial number of sequential attempts, whereas when this property fails, conditioning on past attempts offers no asymptotic benefit over parallel sampling. We further show that these gains are robust and learnable: approximate posterior updates suffice, and cross-entropy training on search rollouts recovers the required behavior with polynomial sample complexity. Finally, we show that under a stagewise abstraction of reinforcement learning with verifiable rewards, the optimal policy extension implements the same posterior reweighting rule. We validate key qualitative predictions of the theory on real large reasoning models.

Persistent memory has enabled large language model (LLM) agents to store factual knowledge, prior decisions, reasoning histories, tool usage information, and context. While this has improved the agent's functionality and continuity across tasks, it has also introduced a new attack surface: the agent's own reasoning history. In this paper, we introduce the Forged Amplifying Rationale Memory Attack (FARMA), which poisons an agent's remembered reasoning rather than its factual knowledge. It inserts forged reasoning traces using evasive language that bypasses keyword-based defenses, then amplifies them through self-referential reinforcement that defeats consensus-based defenses. To address FARMA, we introduce SENTINEL, a layered defense pipeline to detect forged reasoning entries. Its central component is the Reasoning Guard that structurally analyzes candidate entries for forgery using five weighted signals. We evaluate FARMA and SENTINEL across multiple agents and different LLM models with 50 trials and show that FARMA achieves an attack success rate of up to 100% under baseline conditions and is capable of defeating defense mechanisms like keyword filter and A-MemGuard. Our evaluation also shows that SENTINEL reduces FARMA's attack success rate to as low as 0% with no false positives observed across 326 benign agent traces. Our work demonstrates the need to protect not only an agent's retrieved content but also the integrity of its reasoning history.

Although LLMs have made significant progress in mathematical reasoning, determining whether a mathematical problem is solvable remains a fundamental yet challenging capability. While recent studies have probed internal representations of model solvability beliefs, verbalization has primarily been studied behaviorally rather than as an internal representation, limiting its analysis and manipulation. We address this gap by separately probing representations of solvability knowledge and verbalization, allowing us to disentangle the two within model hidden states. Across multiple LLMs, we show that knowledge and verbalization are encoded as distinct, linearly decodable representations and that fabrication is primarily associated with changes in verbalization rather than the underlying knowledge. Prompting with unsolvability cues reduces fabrication primarily by shifting verbalization, while activation steering demonstrates that these representations can be echanistically manipulated to improve model abstention.

Large language model (LLM) tutors often produce fluent step-by-step explanations, but a correct and pedagogically formatted response does not guarantee that the answer was derived from the student-facing problem. In realistic tutoring systems, the model may also have access to teacher notes, answer keys, rubrics, or retrieved solution artifacts. We study whether such private answer information can make tutor explanations answer-driven: the final answer is behaviorally available before the written explanation has justified it. Using Truncated Reasoning AUC Evaluation (TRACE), which probes how early a chain-of-thought prefix can pass a verifier, we evaluate 1000 GSM8K test problems under three paired tutoring contexts: question-only, correct answer-key, and wrong answer-key. At fixed fractions of each generated explanation, we force the model to answer immediately and verify the response against the gold numeric answer. With Qwen2.5-3B-Instruct, answer-key access raises median TRACE AUC from 0.375 to 0.900 and makes the gold answer available at the first 10% prefix in 997 of 1000 cases. The effect remains strong on the 746 examples where both question-only and answer-key explanations end with the correct answer. These results support truncated CoT auditing as a lightweight process-level diagnostic for answer-driven reasoning in math tutoring explanations.

Diffusion large language models (dLLMs) generate text by iteratively denoising a masked sequence, offering a parallel alternative to autoregressive models, but eliciting strong reasoning through post-training remains difficult: supervised fine-tuning is off-policy and suffers from exposure bias, while reinforcement learning gives only sparse, sequence-level rewards and is hard to apply without tractable sequence likelihoods. On-policy self-distillation (OPSD) offers a promising alternative, using one model as both student and teacher to provide dense, token-level, on-policy supervision, but its effectiveness hinges on giving the teacher privileged information (PI) - typically an instance-specific ground-truth reference unavailable at inference - so the student ends up distilling a weak PI-free consensus policy that yields little improvement on dLLM reasoning. We introduce dOPSD, which instead derives the teacher's privilege directly from the student's own denoising trajectory, evaluating masked positions using later, more-decoded steps of that same trajectory rather than an external label, so the teacher's advantage emerges from the model's own decoding process; on Dream and LLaDA, dOPSD improves both in-domain math reasoning and out-of-domain code generation, outperforming supervised and on-policy baselines.

AI reasoning has become a central focus in contemporary artificial intelligence, largely driven by the success of large language models. However, mathematical research, which is characterized by non-linear derivation paths, rigorous logical requirements, and protracted exploration cycles, poses severe challenges for existing reasoning systems. To overcome these limitations, we present the MechMath Agent Team (MMAT), which is a large language model driven agent designed to serve as a co-pilot throughout the full cycle of mathematical research. We design a tripartite Harness Architecture that decouples system responsibilities into Control, Execution, and Augmentation planes, thereby reconciling rigorous logical control with the agility demanded by open-ended research. Building upon this framework, we instantiate three specialized agents: a Knowledge Base Manager, a Natural Language Prover, and a Formal Language Prover, all operating in a closed loop to produce formally certified mathematical proofs. We evaluate MMAT on open problems in Number Theory, Algebraic Complexity Theory, Differential Algebra, Operator Algebra, and Inequalities. Across a two-month deployment, 11 problems have been solved, demonstrating its capacity to act as a co-pilot throughout the entire research cycle. The contributions are threefold: a general decoupled Harness Architecture for multi-agent mathematical reasoning, its concrete instantiation in the MMAT system, and empirical validation on a diverse suite of open problems.

Interpretability methods aim to reveal the features represented inside large language models (LLMs). Many existing methods begin with labeled examples of a human-defined concept that may reflect human biases, and then identify how that concept is represented within the model, for example in its activation space or through other decomposition methods. We introduce \emph{Mining via Activation Geometry} (MAG), a simple unsupervised framework for extracting reasoning features from model activations by prepending the same natural-language instruction $Q$ to every input $p$, where $Q$ defines the reasoning feature of interest, such as Can this object be found in the desert?'' or Is this prompt malicious?'' We measure how the instruction changes the model's internal representation using $m(Q \mid p) - m(p)$ at a single readout point. We explore eight different MAGs. The extracted reasoning features predict the models' own world understanding and judgment, can be approximated into a single activation direction, we found that some features are more linearly represented and some less, this linear representation, which is vector steering, can change the LLMs' decisions through activation steering by injecting reasoning features. Finally, we use the same method to select the best training datasets for prompt-injection classifier probes: while similarity between ordinary activations is almost unrelated to downstream performance, RFD-based similarity achieves $94.7\%$ Top-1 and $100\%$ Top-2 accuracy.

Recent reasoning-centric Large Language Models (LLMs) have made significant strides, yet they predominantly operate on a passive-inference pattern that assumes complete information. In contrast, real-world clinical intelligence is inherently an iterative investigative process requiring strategic evidence acquisition. To bridge this gap, we formalize medical diagnosis as an Iterative Evidence-Seeking Task. We leverage Reinforcement Learning with Verifiable Rewards (RLVR) to elicit intrinsic reasoning within a closed-loop environment, guided by a novel suite of rewards that enforce diagnostic precision and examination consistency. To facilitate this, we introduce the Retrieval-Augmented Generation-based Examination Simulator (RAGES), a high-fidelity clinical oracle that provides realistic, knowledge-grounded follow-up evidence. Empirical results across diverse datasets demonstrate that our framework enables LLMs to transition from passive responders to autonomous assistants. Notably, our model demonstrates comparable performance to larger and reasoning-enhanced baselines, while RAGES proves superior to vanilla LLMs in generating biologically plausible clinical feedback.

Understanding and reasoning over long contexts has become a key requirement for deploying large language models (LLMs) in realistic applications. Although recent LLMs support increasingly long context windows, they often fail to use relevant evidence that is already present in the input, revealing a gap between context access and effective context utilization. In this work, we propose Recursive Evidence Replay as LLM Harness for Long-Context Reasoning (RECONTEXT), a training-free inference method for improving long-context reasoning. RECONTEXT uses model-internal relevance signals to construct a query-conditioned evidence pool and replays it before final generation while preserving the full original context. This recursive selection process separates evidence organization from answer generation without training, external memory, or context pruning. We also provide a theoretical analysis based on associative memory, which characterizes the context as a memory store, the question as a retrieval cue, attention as cue-trace association, and replay as trace reactivation. Experiments on eight long-context datasets with 128K context length show that RECONTEXT consistently improves evidence utilization across Qwen3-4B, Qwen3-8B, and Llama3-8B, achieving the best average rank on all three backbones. Code is available at https://github.com/Yanjun-Zhao/ReContext.

Long-form TV dramas present a formidable challenge for comprehensive video understanding, where deciphering complex storyline often relies on \textbf{speaker recognition}, the task of accurately attributing each spoken utterance to its respective character. In this paper, we advance this field through two primary contributions. (1) We introduce \textbf{DramaSR-532K}, a large-scale benchmark comprising 532K annotated dialogue lines across more than 900 unique characters, necessitating the integration of auditory, linguistic, and visual cues for speaker recognition. (2) We propose \textbf{DramaSR-LRM}, a robust approach built upon a large reasoning model (LRM). DramaSR-LRM is designed to autonomously aggregate contextual evidence via multimodal tool-use, synthesizing diverse inputs to achieve high-fidelity attribution. Experimental results demonstrate that DramaSR-LRM significantly outperforms existing baselines, particularly on short utterances where acoustic biometrics are inherently unreliable. \textit{All the data and code will be made publicly available at the project page: https://www.github.com/198808xc/DramaSR-LRM.}

Personalization changes what a model says to a user; we show that it can also change the reasoning trajectory used to justify the response. Modern LLMs personalize interactions by storing user attributes, preferences, and prior context, then injecting this information into future prompts. We study whether such memory reshapes reasoning on open-ended questions where no single ground-truth answer exists. To quantify this effect, we introduce DRIFTLENS, a ground-truth-free framework that maps each expressed reasoning step to a value category and measures divergence between a question's no-memory trajectory and its trajectory under injected user-attribute memory. We first validate that DRIFTLENS distinguishes content-free pragmatic noise from substantive reasoning changes. Across four LLMs and 10 user-attribute categories, including age, occupation, and disability, user-attribute memory induces medium-to-large reasoning drift above each model's pragmatic-noise floor, even when final answers remain fluent, on-topic, and plausible. We then evaluate GRPO- and DPO-based post-training methods for reducing drift. Both reduce drift, but neither uniformly dominates; effects on downstream capability, helpfulness, and instruction following are model-and reward-dependent. These results suggest that memory-induced reasoning drift is a measurable and only partly mitigated failure mode of personalized language models.

Reasoning Language Models (RLMs) have significantly improved performance on complex tasks by extending the reasoning chain. However, these chains are prone to containing factual errors, particularly in knowledge-intensive tasks. To address this issue, we propose CheckRLM, a framework that improves the reliability of the reasoning process through Retrieval-Augmented Generation (RAG) by timely checking and correcting factual errors. Specifically, CheckRLM extracts factual claims from the reasoning chain to identify and localize subtle knowledge inconsistencies during inference. Upon detection of errors, a refinement mechanism performs minimal-cost yet precise corrections by leveraging external knowledge, ensuring coherence between the reasoning chain and correct knowledge. Extensive experiments demonstrate that CheckRLM substantially outperforms existing baselines, exhibiting a strong capability to mitigate error accumulation in long-horizon reasoning with lower costs. The code and data are available at https://github.com/AI9Stars/CheckRLM.

Long-context reasoning requires models to locate, revise, and synthesize evidence distributed across lengthy inputs. Existing long-context RL methods usually reward final answers or static evidence extraction, offering little feedback on how intermediate actions change the model's evidence state. We propose Maven, a reinforcement learning framework with an editable evidence memory. Maven defines an answer-conditioned evidence-state value and rewards action-level state transitions: add actions are credited by marginal gain and hindsight contribution, link actions by evidence synergy, and drop actions by improved answer support after removing misleading evidence. These rewards are assigned to the corresponding action spans in GRPO. Across Llama and Qwen models on LongBench v2, LongReason, and RULER, Maven outperforms outcome-only RL and evidence-identification baselines, producing more sufficient evidence sets and lower distractor retention. Our results show that long-context RL benefits from optimizing stateful evidence navigation rather than one-shot evidence extraction.

Faithful reasoning is essential in medicine, where clinical decisions require transparent justification grounded in reliable evidence. Current medical LLMs either lack active access to evidence or use retrieved evidence without supervising how it should be appraised and applied during reasoning. To address this, we formalize evidence-based medicine principles as process-level criteria and introduce FaithMed, a framework that combines clinician-designed, automatically refined rubrics with reinforcement learning using step-level process reward assignment and advantage grouping. Across seven medical benchmarks, FaithMed improves over agentic-search baselines (+9% on average) and outcome-only RL (+5.8%), while raising average evidence-based medicine rubric scores over agentic-search Qwen3 baselines (+15.5%). This work demonstrates that explicit step-level supervision can improve both task success and the faithfulness of the reasoning process. Code is available at https://github.com/cxcscmu/FaithMed.

While inference-time scaling has improved the reasoning abilities of large language models (LLMs), the need to generate long chains-of-thought (CoTs) is a computational bottleneck. Thus, in contrast to sequential scaling methods like CoT, recent parallel scaling techniques instead use fork and join (FJ) primitives to divide work across multiple LLM threads. However, in the fork-join paradigm, threads are typically transient and do not communicate pointwise with one another which limits scalability. To tackle this, we introduce Message Passing Language Models (MPLMs), a framework for LLM reasoning in which threads communicate directly via lightweight send and receive primitives. MPLMs enable efficient scaling through two key mechanisms: (1) reduced communication costs, achieved by avoiding redundant context sharing, and (2) preemption, which allows threads to terminate early based on partial information from their peers. We demonstrate the promise of MPLMs on 3 classes of tasks. First, on Sudoku puzzles, we show that MPLMs require an asymptotically smaller context than both serial CoT and parallel FJ. We then fine-tune a single model to solve 25 x 25 puzzles that remain challenging for standard CoT and FJ approaches, as well as frontier reasoning models without tools. Second, on 3-SAT puzzles, the capability of preemption allows termination of unpromising branches, which results in improved efficiency. Finally, we show that appropriately prompted large pre-trained models follow the MPLM protocol, achieving competitive results on long-context question answering relative to popular fork-join approaches.

Large Language Models (LLMs) represent one of the most significant advances in AI and natural language processing in recent years. Still, many pressing questions about their mechanisms, capabilities, and relationship to human cognition remain highly debated. This chapter aims to outline our current understanding of LLMs by discussing recent evidence on emerging capabilities and their mechanistic implementation within processing layers. We begin with a concise overview of the Transformer architecture, emphasizing how the attention mechanism enables training on massive datasets, allowing LLMs to function as generalist rather than specialized models. Next, we examine emergent LLM capabilities that appear to resemble aspects of human cognition, including symbolic reasoning, theory of mind, and deception strategies. Several studies provide evidence that LLMs can solve tasks previously thought to require human-like cognition. Other studies reveal insightful failure cases that shed light on the differences between human and LLM cognition. Alongside these findings, we review explainable AI approaches ranging from neuron activation analysis to circuit tracing. In the final section, we address current debates concerning what LLMs genuinely understand versus what they merely appear to understand. Prominent arguments against AI anthropomorphism point to the simplicity of LLM training objectives, claiming that LLM behavior is better explained by pattern memorization of training data than by genuine cognition. We argue that this standpoint is guided by misconceptions about optimization processes and cognitive capacity, and advocate for a more nuanced discussion of LLM cognition that neither dismisses the differences between humans and LLMs nor precludes the possibility of AI cognition through overly simplistic reductionist arguments.

Large reasoning models (LRMs) have achieved strong reasoning capabilities in English, yet their performance degrades significantly when required to reason in other languages. A natural solution is to transfer the model's English reasoning ability to target languages. However, existing transfer approaches typically rely on distilled target-language reasoning traces from stronger LRMs or online supervision from external judge models, which are costly and difficult to scale. In this paper, we propose PCS (Progressive Code-Switching), a more efficient transfer framework that requires only lightweight translation without any stronger model for distillation or judging. PCS first constructs code-switched reasoning traces by translating a subset of English reasoning steps into the target language, and uses them to initialize the model's code-switching ability via supervised fine-tuning. It then applies reinforcement learning with a step-level language consistency curriculum, progressively raising the target-language ratio until the model reasons entirely in the target language. This progressive design provides a smooth transfer path that avoids the instability and performance degradation commonly observed when directly enforcing target-language reasoning. Experiments on multiple benchmarks and five typologically diverse languages show that PCS substantially narrows the performance gap between target-language and English reasoning, yielding more language-consistent reasoning while maintaining competitive accuracy.

Metacognition is a critical component of intelligence that describes the ability to monitor and regulate one's own cognitive processes. Yet LLMs exhibit systemic deficiencies in key metacognitive faculties: they hallucinate with high confidence, fail to recognize knowledge boundaries, and misrepresent their internal uncertainty--undermining trustworthiness and reliability. Since monitoring task performance and adapting behavior accordingly are central to metacognition, we posit that models capable of accurately judging their own performance are better positioned to improve it. We operationalize this idea via two novel mechanisms: reinforcement learning with metacognitive feedback (RLMF), a paradigm to refine completion rankings during preference optimization based on the quality of a model's self-judgments of performance, and metacognitive data selection, which uses similar self-judgments to identify high-value training examples, outperforming naive active learning. We apply these innovations to the problem of faithful calibration (FC), a task that is itself fundamentally metacognitive: the goal is to align expressed with intrinsic uncertainty, difficult even for frontier LLMs. We adopt a two-stage, decoupled approach, first using these methods to calibrate the faithfulness of models' self-reported confidence scores, then mapping to natural, context-adaptable linguistic uncertainty via targeted output editing. Extensive experiments show RLMF achieves generalizable, state-of-the-art FC on diverse tasks while preserving accuracy. Further, RLMF surpasses standard RL by up to 63% while enhancing models' ability to assess and express their own capability limits. This positions RLMF as a promising paradigm to enhance LLM metacognition toward improved abilities and alignment, and suggests metacognitive performance as an effective RL signal to overcome limits of prior intrinsic feedback methods.

Despite recent progress, the reasoning capabilities of large multimodal language models (MLLMs) remain fundamentally constrained by static supervision, where fixed prompts, rules, or reward models provide non-adaptive guidance throughout training. Such static signals are often sufficient to enforce output formats, but fail to shape the underlying reasoning process, leading to brittle generalization and performance saturation in complex decision-making tasks. We propose Evo-PI, a principle-centric learning framework that treats reasoning principles as explicit, language-based supervision signals that can be generated, evaluated, and iteratively evolved. Instead of relying on fixed rewards, Evo-PI enables a co-evolutionary loop in which principles guide model reasoning, while model behaviors in turn refine the principles that supervise them. This dynamic alignment mechanism allows supervision to progressively adapt to the model's reasoning deficiencies. We instantiate Evo-PI in medical visual question answering as a high-stakes testbed requiring structured visual-textual reasoning. Across eight benchmarks and multiple model backbones, Evo-PI consistently improves reasoning accuracy, achieving gains of up to 24.6%. Our results suggest that evolving principle-guided supervision offers a scalable and general paradigm for training expert-aligned reasoning in MLLMs. Code is available at https://github.com/zhengxianda/Evo_PI.

Reinforcement learning (RL) has become a powerful tool for propelling Large Language Models (LLMs) beyond imitation-based training towards more robust reasoning capabilities. Among existing approaches, RL with Verifiable Rewards (RLVR) has emerged as a pivotal paradigm for advancing LLM reasoning. Despite its empirical success, recent studies have offered different insights. One line of inquiry advocates prioritizing high-entropy token positions during training, while another perspective cautions against allowing low-probability tokens to dominate gradient updates. Notably, although high-entropy tokens are usually correlated with low probability, both paradigms empirically yield substantial performance gains. In this work, we argue that evaluating sampled-token probability or entropy in isolation is insufficient to capture the policy optimization dynamics. To resolve this tension, we introduce the Relative Surprisal Index (RSI), a principled, information-theoretic metric that naturally couples the token's entropy with the probability of the selected token. We show that, under mild conditions, RSI is related to the local ratio between the first-order variations of the logit-gradient norm and predictive entropy under a selected-logit perturbation. Building on RSI, we propose RSI Selection (RSI-S), an entropy-adaptive token filtering method that retains tokens within a stable RSI interval. RSI-S successfully reconciles previous contradictory paradigms and filters out both redundant low-surprisal tokens and unstable high-surprisal tail tokens. Empirical evaluations show that RSI-S achieves higher avg@32 accuracy across different model scales (Qwen2.5-1.5B, 3B, and 7B) on AIME and AMC benchmarks: RSI-S improves avg@32 accuracy by 2--3 percentage points over GRPO. Overall, RSI offers a promising perspective for RLVR improvement.

Parallel thinking has enjoyed great success for boosting LLM performance on reasoning tasks without the need for any re-training. However, existing methods follow a think-first-then-decide paradigm, i.e., they first sample multiple reasoning paths, which inevitably leads to overgeneration, then prune or stop unnecessary paths to compensate. In contrast, decide-first-then-think, i.e., first identifying points that are likely to lead to desirable generations, has been underexplored so far. Following this paradigm, we propose Fork-think with confidence, that first identifies forking points using model confidence in a single seeding path, then triggers thinking, sampling multiple continuations and aggregating them for the final response. Our experiments across three models and three reasoning benchmarks show that Fork-think reduces the token consumption by up to 30% and run-time by up to 57%, while performing comparable to or better than parallel thinking. Our analysis reveals that Fork-think is able to identify forking points that are meaningful with respect to the downstream task and that sampling at later positions can lead to substantially better generations. Finally, we demonstrate how combining Fork-think with existing mechanisms such as early stopping and weighted voting can further boost the performance and perform comparably to existing state-of-the-art methods, without requiring any warm-up or offline training. Our results establish pre-determined forking as a promising research direction for efficient LLM reasoning.

Human reasoning is inherently multimodal: when problems become difficult, we rarely think in words alone. We often externalize our reasoning by sketching diagrams or drawing grids to understand the underlying conceptual structure and avoid mistakes. Building on this premise, our research investigates: (a) whether grounding multi-hop textual-spatial stories into geometry-aware modalities, such as layouts or grids, improves reasoning compared to natural language-based inference; and (b) whether a model can decide when to rely on natural language reasoning and when to switch to a structured modality. We address these questions by introducing a switching metric based on trustworthiness and complexity signals, which estimates when grounding a spatial story into structure is likely to improve performance. This takes a first step toward principled modality selection in Large Language Model (LLM) reasoning. Across our settings, switching from natural language-based reasoning to a grid-based representation improves LLM performance by up to 42%, highlighting the importance of modality choice in shaping reasoning outcomes.

Large language models (LLMs) are typically deployed in multi-turn conversations, where each turn provides new evidence that should reduce epistemic uncertainty about their environment. Acting rationally then requires inferring the unobserved quantities that govern it and updating beliefs about them as evidence accumulates. Yet most evaluations only score the model's final-turn answer in a single-turn format, leaving this process unexamined. We ask how closely LLMs' belief updates match those of a rational Bayesian reasoner in multi-turn settings, and introduce BayesBench, a suite of simulation environments that probe this across three progressively complex tasks: (i) Bayesian estimation, where the model infers an unknown parameter from sequential evidence; (ii) Bayesian prediction, where the model turns inferred beliefs about a latent variable into outcome forecasts; and (iii) latent-framed Bayesian prediction, where observations are filtered through a user-persona framing, requiring joint inference over the latent state and the persona. Across seven LLMs (3B--70B), scaling improves latent inference and evidence accumulation, with updates occasionally matching the Bayesian posterior. However, these gains do not reliably carry over to downstream prediction, exposing a gap between inferring latent structure and using it to rationally update beliefs about the target outcome.

Reinforcement Learning with Verifiable Rewards (RLVR) is a powerful paradigm for improving the reasoning capabilities of large language models (LLMs). However, existing RLVR methods typically rely on on-policy optimization from scratch, resulting in high sampling costs and inefficient utilization of accumulated experience. As model capabilities and policy behaviors evolve during training, recent attempts to reuse experience via fixed reasoning trajectories further suffer from policy mismatch. Motivated by these limitations, we argue that experience in RLVR should not be reused as fixed reasoning trajectories, but instead expressed in a policy-adaptive manner. In this work, we propose Experience-Augmented Policy Optimization (EAPO), which leverages a prior RL-optimized policy as an action-level experience prior and selectively injects experience at critical decision points during rollout. To ensure stable and unbiased learning from experience-augmented rollouts, EAPO further incorporates an adapted importance sampling scheme. Experiments on using Qwen-2.5-math 7b and Qwen-3-8B on five different benchmarks demonstrate that EAPO consistently improves reasoning performance over state-of-the-art RLVR methods.

Knowledge graphs can guide large language models (LLMs) reasoning, but the graph seen by a system is usually a retrieved, linked, temporally scoped, and incomplete evidence state rather than a complete account of truth. We develop a theoretical perspective on grounding observable LLM trajectories under such incomplete graph evidence.The evidence state induces entity anchors, typed relation residuals, path energies, and support regions, while the language model supplies a prior over candidate trajectories. We show that, under open-world incompleteness, no hard rule based only on the observed state can both reject every false unsupported trajectory and retain every true-but-unobserved one.We then characterize soft grounding as a KL-regularized deformation of the LLM prior: finite slack preserves support for unsupported but non-contradicted trajectories, whereas hard conditioning appears as an infinite-penalty limit.The framework also yields stability bounds under evidence perturbations and clarifies the constraint regimes appropriate for GraphRAG, KGQA, graph agents, constrained decoding, and faithful generation. The claims are evidence-relative: KG compatibility is treated as declared support, not factual truth.

Chain-of-thought (CoT) prompting improves LLM reasoning, but the source is contested: do the intermediate steps help because they carry useful semantic content, or because conditioning on more tokens buys extra computation before the model commits to an answer? We bring two lines of evidence to bear. First, in distribution: we repeatedly sample each model on the same question and pair a shorter with a longer of its own natural generations that follow the same reasoning plan, so nothing is rewritten and both traces are genuinely in-distribution. Across 25 models the extra tokens leave accuracy essentially unchanged for every independently-trained reasoner, and a blind analysis of the surplus tokens shows that what gain exists elsewhere tracks validation- and checking-content, not verbosity per se. Second, as a controlled intervention, we ask whether two traces expressing the same semantic content (the same facts, operations, and intermediate values, verified through directed acyclic graph equivalence) produce different outcomes when one is more verbose, using a dual-validator design across four targets and eight benchmarks with number-redacted completion and stratified bootstrap confidence intervals. Verbose traces do improve accuracy (25 of 32 benchmark-target cells are positive under at least one validator), but the effects are modest (typically 1-4 points) and depend on the quality of the verbose prose, not merely its length. Under maximum numerical redaction the effect is amplified (median 3.24x across four arithmetic benchmarks), and length-matched non-reasoning filler recovers none of it. Both lines converge: what matters is what the extra tokens do (the reasoning and validation content they carry), not how many there are, a picture neither a pure forward-pass-compute nor a pure semantic-content account fully explains.

Distilling historical trajectories into reusable experience to enhance future problem-solving has become a focal point of recent LLM research. However, existing methods predominantly operate at the task level, leveraging general summaries or rules under the assumption that analogous tasks share universal solution patterns. This approach often fails in complex reasoning, which typically falters at local bottlenecks that require precise, state-specific guidance rather than broad heuristics. We introduce HippoSpark, a state-level experience system that performs on-demand retrieval tailored to the immediate needs of the current reasoning state. Across mathematical, scientific, and programming benchmarks, HippoSpark consistently outperforms both standard prompting and task-level experience baselines. Our findings reveal that the most effective experience systems are those that provide actionable guidance at critical bottlenecks rather than serving as generic task-level context. Our code is available at https://github.com/DanlingMeng/HippoSpark.

Chain-of-Thought (CoT) improves large language models (LLMs) on difficult reasoning tasks, but it often incurs long natural-language rationales that are poorly aligned with efficient machine reasoning. We propose Communicative Language Symbolism Routing (CLSR), a test-time framework in which multiple LLM agents autonomously invent, evolve, and share compact Language Symbolism Frameworks (LSFs), while a latent-free router adaptively selects and composes these languages per query to optimize the accuracy-token trade-off. Unlike prompt optimization that refines surface instructions, CLSR treats each LSF as a reusable symbolic protocol with compact symbols, usage rules, and a message-passing contract, and improves it through an evolutionary loop driven by correctness and token cost. At inference time, the router may invoke a single low-cost LSF call, ensemble multiple LSFs, or execute a multi-round LSF composition protocol on harder queries. Across challenging benchmarks, CLSR reduces latency-oriented generated token completion by $3\sim 6\times$ compared to standard CoT while maintaining accuracy. We further derive an information-theoretic lower bound on token cost under arbitrary symbolism and show that, under an interpreter-realizability premise, multi-round LSF protocols conditionally subsume program-execution pipelines. Code is publicly available (https://github.com/pzqpzq/LSF_MDia).

Group Relative Policy Optimization (GRPO) is a default recipe for process-supervised reinforcement learning of LLM reasoners, and dense process supervision -- via learned process reward models (PRMs) or on-policy-distillation KL signals -- is a common way to densify its otherwise weak outcome reward. Layering such a step-level signal on top of GRPO's group-standardized advantage, however, exposes three structural pathologies: \emph{channel contamination} between the pooled process, outcome, and format streams at group standardization; \emph{resolution mismatch} between the granularity of the process signal and the granularity of the logical decisions being credited; and a \emph{cumulative trap} by which GRPO's return-to-go sum surfaces either length inflation or truncated exploration depending on the sign regime of the signal. We propose \textbf{PASS} (\emph{Process Advantage Signal Shaping}), a compact middleware that sits between any scalar step-level process signal and GRPO's clipped surrogate and addresses the three pathologies in turn: \emph{Advantage Fusion} standardizes the three streams independently within each group, \emph{Chunk-by-Value} derives value-homogeneous chunks from the signal itself and broadcasts credit within each chunk, and \emph{Divide-Length} converts the cumulative objective into an average-value-density score. We validate PASS across two domains and two process-signal paradigms -- a learned PRM on mathematical reasoning and an on-policy-distillation KL signal (with a generalized variant) on multi-hop question answering -- and under two group-standardization operators. In every regime PASS delivers a consistent pass@1 gain over the corresponding GRPO baseline.

We introduce the Complexity Ceiling Benchmark (CCB), a controlled evaluation of how language-model reasoning decays as the number of required sequential steps grows. CCB fixes the semantic content of a task and varies only its depth N in {5,...,50} across three structurally distinct regimes: grounded spatial state-tracking, abstract symbolic pointer manipulation, and transitive relational inference. Across 6,000 trials over five frontier and open-weight LLMs we find a consistent pattern of geometric per-step decay with widely separated domain ceilings: on the first two regimes the strongest models retain pd>0.92 across N=50; on the third every model collapses by N=5, with the best model's 50%-success horizon at H0.5~4.7 steps despite pd=0.863. A trace-level metric (TFBC) shows that 14.5% of correct answers across the benchmark are reached via incorrect intermediate reasoning. Forced verbose state-tracking does not move the ceiling (McNemar p=1.000), and the mean step at which reasoning first diverges, k*, predicts within-domain accuracy better than parameter count. CCB and the geometric decay model together reduce a model's long-horizon reasoning profile to one interpretable number per task family.

Large language models (LLMs) demonstrate broad reasoning abilities but struggle with accuracy and reliability in specialized domains such as travel, where reasoning depends on precise definitions, rules, and expert-defined conceptual frameworks, and where confident but unfounded outputs arise from a reasoning failure in which the model has not internalized the underlying domain graph rather than from missing domain knowledge alone. We propose a modular pipeline for building a travel-domain reasoning LLM grounded in an expert-designed knowledge graph (KG). Our pipeline integrates a travel KG that encodes domain entities and their relationships, a bottom-up construction procedure that walks the KG to produce multi-hop question answer (QA) pairs, a supervised fine-tuning stage that embeds the domain knowledge into a reasoning-capable LLM using the generated QA pairs as auditable reasoning traces, and a travel-domain benchmark dataset that measures the fine-tuned model's accuracy and calibration. We evaluate our approach using Qwen3-4B with LoRA adaptation. Our reasoning model achieves an $82.4\%$ exact match on the benchmark. This performance significantly outperforms the pretrained Qwen3-4B baseline at $22.4\%$. A calibration analysis decomposes the residual $17.57\%$ of errors into two distinct failure modes: an over-confident multi-label decoder that predicts both correct answers plus one spurious option on most dual-answer mistakes, and a smaller reasoning failure on single-answer questions where the supporting facts are present in the KG but the model fails to reconstruct the correct multi-hop path. This split confirms that explicit KG-grounded reasoning substantially improves the accuracy and uncertainty interpretation of LLMs in specialized domains, and isolates per-option calibration and trace-length-aware decoding as the next axes of improvement.

Open-ended scientific discovery with large language models (LLMs) increasingly operates as a long-horizon loop of hypothesis search and verification, where a reward signal guides which hypotheses to test next. A notable recent example is AutoDiscovery, which uses "Bayesian surprise" - the belief shift an LLM undergoes after observing evidence for a hypothesis - as both a discovery metric and a reward for search. We first observe that AutoDiscovery treats surprisal as a static quantity, while surprisal in human reasoning is non-stationary - it is defined relative to beliefs that evolve with experience, a prerequisite for continual scientific discovery. We address this mismatch with evidence-informed LLM beliefs: priors updated with evidence from previous hypotheses to compute non-stationary surprisal for new hypotheses. We compare in-context belief-updating mechanisms and find that embedding-based retrieval-augmented generation over prior discoveries best anticipates eventual posteriors, identifying 37.5% of static surprisals as spurious. We then modify search to avoid these spurious rewards and prioritize hypotheses that remain surprising under non-stationary beliefs. Concretely, we introduce two complementary changes to the original search procedure: belief-update filtering and diversity maximization. Across five discovery domains, our method increases accumulated non-stationary surprisal by 30.62% on average compared to the original search procedure, demonstrating that continual scientific discovery with LLMs requires not only better belief measurement but also search procedures that avoid redundancy and encourage diversity.

We present ThinkProbe, a framework for structural analysis of LLM reasoning traces. ThinkProbe converts each trace into a Thought Graph a directed graph with cycles, 8 node types, and 6 edge types and derives a 19-metric five-dimensional cognitive profile (5D-CP: Breadth, Depth, Structure, Metacognitive, Efficiency) through a fully non-generative pipeline combining rule-based segmentation and discriminative semantic linking. Applied to 4{,}200 traces from 7 native reasoning models across 200 open-ended questions and 10 cognitive domains, ThinkProbe reveals that reasoning structure is a stable, model-level property: between-model variance exceeds between-domain variance by up to fourfold across four of five cognitive dimensions, with Structure showing genuine sensitivity to question domain, exposing qualitatively distinct cognitive profiles invisible to accuracy-based evaluation.

Recent artificial intelligence (AI) systems have shown remarkable progress in mathematical reasoning. Many existing approaches, including large language models (LLMs), draw on human prior knowledge in the form of mathematical text, code, or theorem libraries. Although these approaches are highly effective in practice, it remains an open question whether an agent can autonomously discover useful theorems without such human priors. We study this question in a formal axiomatic system by developing an agent that starts from axioms and inference rules alone and gradually grows a library of useful theorems. Concretely, we propose a self-supervised theorem-discovery algorithm that alternates between proof search and useful-theorem extraction, building a theorem library whose entries are reused as lemmas for subsequent proof search. Experiments show that the agent discovers tens of thousands of theorems and finds proofs for human-written benchmark problems, suggesting that its discoveries include theorems meaningful from a human mathematical perspective. Furthermore, the discovered theorems improve LLM proof performance when provided as prompt lemmas, indicating that they can serve as external knowledge for LLM reasoning. Our results provide evidence that useful theorems can emerge from proof search without relying on human-provided theorem libraries. More broadly, they suggest a path toward self-evolving AI systems for mathematics whose discoveries remain formally verifiable.

Current approaches to enhance Large Language Model (LLM) reasoning, such as Chain-of-Thought and "Wait" prompts, primarily encourage models to think more, yet often fail to guide them toward Truth. While Representation Editing (RepE) offers a intrinsic control, its application to dynamic reasoning trajectories remains underexplored. In this work, we bridge this gap by investigating the geometry of truth within unfolding reasoning chains. We uncover three critical insights: (1) Truth is encoded at the sentence level and is entangled with latent reasoning patterns; (2) Effective intervention follows an Uncertainty Principle and a Decay Effect, requiring localization to early, high-entropy forks; (3) Naive steering vectors suffer from noise, risking collateral damage to correct trajectories. Based on these findings, we propose DynaSteer, a dynamic RepE framework. DynaSteer employs pattern clustering to disentangle reasoning manifolds and utilizes Fisher-LDA to project purified truth. By dynamically monitoring lookahead entropy, it selectively steers and rolls back trajectories only when necessary. Comprehensive experimental results on several MATH benchmark verify the effectiveness of DynaSteer, and experiments on out-of-domain coding tasks further confirm its generalization ability. Our code is publicly available at https://github.com/tianlwang/DynaSteer.

Predicting human item difficulty is central to educational assessment, where reliable estimates support fairness and effective test construction. Existing methods often depend on costly human calibration or item-level textual representations, providing limited evidence about the cognitive processes that make items difficult. We argue that difficulty should be viewed not only as a property of item text, but also as an observable consequence of the problem-solving burden an item induces. Large Reasoning Models (LRMs) offer scalable process evidence through reasoning traces, but such evidence must be structured to support interpretable modeling. To this end, we introduce Epi2Diff (Episode to Difficulty), a framework that maps LRM reasoning traces into cognitively grounded episode sequences. These episodes group trace segments into functional problem-solving states, enabling difficulty to be modeled through reasoning scale, effort allocation, and state transitions. Epi2Diff extracts compact episode-dynamic features and combines them with semantic item representations for human difficulty prediction. Experiments on four real-world human difficulty datasets show that Epi2Diff consistently outperforms strong baselines, including fine-tuned small language models, LLM in-context learning, and supervised LLM adaptation. On SAT-derived classification benchmarks, Epi2Diff achieves an 8.1% average relative gain over supervised LLM fine-tuning baselines. Further analyses show that harder items induce more effortful, iterative, and implementation-centered episode dynamics, rather than merely longer responses. These results demonstrate that cognitive episodes in LRM reasoning traces provide a predictive and interpretable process representation for human item difficulty, offering a new lens for educational measurement with reasoning models.

Reinforcement learning with verifiable rewards (RLVR) has significantly improved the reasoning capability of large language models, reaching expert or even superhuman performance in domains such as competition math. However, whether weaker agents and humans can actually harness this capability is far less certain, with RLVR documented to drift reasoning toward idiosyncratic patterns such as poor readability and language mixing. Tandem training is a recently introduced paradigm that targets this compatibility problem: a trained, stronger senior co-generates each rollout with a frozen, weaker junior, and the two are rewarded as a team, so the senior is pushed to reason in ways the junior can follow. Yet this paradigm has so far been demonstrated only in proof-of-concept settings, leaving open whether it scales to the long chains of thought of the modern RLVR pipeline. In this work, we propose Tandem Reinforcement Learning (TRL), which carries the tandem training paradigm into RLVR. In TRL, the senior and a frozen junior alternate stochastically to co-generate the reasoning, the resulting generation is rewarded, and the standard GRPO loss is applied to the senior. Training Qwen3-4B-Instruct on competition math, we find that TRL matches vanilla GRPO on solo reasoning capability while three properties emerge together from the same rollout structure: stronger handoff robustness with the junior, reduced distributional drift from the junior, and a chain-of-thought more legible to the junior. Our results demonstrate a promising route for RLVR with practical payoffs in multi-model communication and human compatibility.

Translation cascades for reasoning translate the query from another language to English, reason in English, and translate the answer back to the original language. This is a competitive approach to multilingual reasoning, but structurally lossy, since each stage discards information later stages may need, including cues for cultural grounding, register, and disambiguation. We examine the benefits of a simple and training-free intervention: a context-aware translation cascade, which additionally provides the original question, the English translated question, and the reasoning trace to the context of the final translation module. We evaluate gains across nine multilingual benchmarks including various task types, three backbone models, and 285 high-, mid-, and low-resource languages, and demonstrate strong gains for open-ended generation across models and resource regimes. We show that the original language question carries most of the beneficial context. Our study emphasizes the need to better design information flow in machine translation cascades for mitigating error propagation, and provides a simple and actionable default strategy: preserve the original user question until the end of the pipeline.

Successful forecasting involves identifying patterns between historical and future states of the world which generalize to future observations. We apply LLMs to a variety of forecasting tasks and inspect their internal states using sparse autoencoders to understand whether they appear to rely on time-specific pieces of knowledge versus generalizable patterns. Our analyses identify features associated with both time-aware reasoning and look-ahead-biased reasoning. We then apply the LLMs to an entirely different domain and intervene on these features. We find that amplifying time-awareness features substantially reduces look-ahead bias on forecasting prompts while preserving general reasoning performance. In contrast, steering the candidate look-ahead-bias features does not produce an effect. These results suggest that interpretable temporal features can be used to causally shift LLMs toward more historically grounded reasoning.

Humans flexibly adapt their reasoning strategies to the requirements of a given problem. Large language models (LLMs) have performed well on many cognitive tasks, however, it is unclear whether this accuracy is a result of pattern matching from training data or flexible reasoning. Here, we introduce a novel paradigm to test this question: the riddle riddle paradigm. Riddle riddles are word problems written to mimic popular riddles, but altered so their answers only require literal interpretations. Identifying correct answers requires looking past the structure of each question and flexibly apply different reasoning strategies based on the content. If LLMs respond to surface features, such as form, a riddle-like structure should cause models to use an inventive reasoning strategy even when a literal interpretation suffices. Alternatively, if LLMs reason based on content, they should flexibly switch strategies when appropriate. Across two experiments with nine state-of-the-art LLMs and 100 human participants, we show humans and LLMs fail on this paradigm in opposite directions. LLMs were far more accurate on genuine riddles than on riddle riddles (84.9% vs. 50.7%); whereas humans showed the reverse effect (50.5% vs. 80.5%). Error analysis shows that 90.8% of LLM errors on riddle riddles (the condition where they show diminished performance) were due to inappropriate use of inventive reasoning while only 57.6% of human errors on genuine riddles were due to overextending literal reasoning. Thus, while both groups make mistakes, reasoning mistakes are made more often by LLMs than by humans. Overall, LLMs' strong performance on genuine riddles may reflect memory retrieval rather than flexible strategy selection, and without stimuli designed to elicit this contrast, it becomes easy to conflate LLM-generated outputs that look like reasoning with genuine reasoning.

Chain-of-thought (CoT) reasoning is widely used in language-model agents, but prior work has shown that verbalized CoT is not always faithful and may instead reflect post-hoc reasoning, which means the model already knows the answer before reasoning. We therefore ask what CoT training is actually improving: is the model getting better at changing its action through generated reasoning, or is it getting better at predicting the action directly from the prompt? We study this question by comparing \emph{prompt actions} (predicting action without CoT) with CoT actions (predicting action with CoT). Across checkpoints, prompt-action quality improves substantially. While interacting with the environment, the relative advantage of CoT actions over prompt actions remains similar, showing that CoT training does not widen the advantage of CoT reasoning, and it helps to improve the quality of prompt actions. We further find that later checkpoints are less likely to revise the action in response to CoT, suggesting greater reliance on the prompt. Motivated by these patterns, we selectively mask action-token supervision on a fraction of training examples. This intervention improves out-of-domain generalization.