Large Language Model Reasoning

Autoregressive chain-of-thought (CoT) reasoning in large language models (LLMs) is fundamentally forward-directed: each step conditions only on prior tokens. This unidirectional inductive bias renders even capable models susceptible to error snowballing, wherein a single logical or arithmetic mistake in an early step irreversibly corrupts the entire reasoning chain. We introduce Teleological Reasoning Infilling (\TRI{}), a training framework that endows decoder-only transformers with a native \emph{goal-conditioned bridging} capability. The key insight is to reframe erroneous reasoning segments as fill-in-the-middle (FIM) tasks: given a verified prefix premise $P$, a verified downstream milestone $S$, and the original query $Q$, the model must synthesise the logical bridge $M$ that connects $P$ to $S$ rigorously and completely. To achieve this with standard causal architectures, we introduce a Prefix-Suffix-Middle (PSM) sequence rearrangement with three non-overlapping sentinel tokens, enabling $M$ to attend to both $P$ and $S$ without any structural modification to the self-attention mechanism. Training proceeds in two stages: (i) Supervised Fine-Tuning (SFT) on symbolically verified $(P, S, M)$ triples extracted from formal mathematics corpora, and (ii) Direct Preference Optimisation (DPO) with a deterministic symbolic verifier (Lean 4 / Python) as the sole reward oracle, eliminating LLM-judge sycophancy. At inference, TRI operates as a surgical repair module within a dual-system loop: a causal draft model generates an initial trace, the verifier pinpoints failures, and TRI infills only the damaged segment, leaving verified sections intact. Comprehensive experiments on three benchmarks demonstrate that TRI achieves state-of-the-art performance across all tasks, while reducing per-problem token expenditure by 31.2%.

Multi-party dialogue is a critical setting for studying collaborative reasoning and decision-making, yet existing datasets rarely focus on structured, in-depth complex reasoning tasks. We introduce DeliChess, a novel dataset of group deliberation dialogues in which participants collaboratively solve multiple-choice chess puzzles. Each group first completes the puzzle individually, then engages in a multi-party discussion before submitting a revised collective answer. The dataset includes 107 dialogues with full transcripts, pre- and post-discussion choices, and metadata on puzzle difficulty and move quality. We evaluate performance using three metrics based on chess engine evaluations, and find that deliberation significantly improves group accuracy. We further analyse the role of probing utterances (i.e., messages that elicit proposals, justifications, or strategic reflection) using a classifier trained on prior deliberation data. While probing makes group performance more variable after discussion, it does not consistently lead to better performance. Our dataset offers a rich testbed for modelling group reasoning, dialogue dynamics, and the resolution of differing perspectives and opinions in a well-defined strategic domain.

End-to-end ASR systems typically use fixed-depth acoustic encoders at inference, making it difficult to trade additional test-time computation for improved recognition without training a larger model. A natural approach is to reuse a shared Transformer block recurrently, but we find that naive looping does not fully exploit additional recurrent compute. We introduce LARM, a depth-conditioned looped Transformer that turns recurrent encoder depth into a controllable test-time compute axis. LARM combines sparse CTC checkpoints, supervision-clock embeddings, FiLM depth conditioning, and delayed soft-posterior feedback. These components structure the loop into recognition checkpoints separated by latent refinement phases and allow shared weights to specialize across recurrent steps. On LibriSpeech, LARM improves WER as the number of inference loops increases and achieves performance competitive with deeper unshared-parameter baselines. Our results show that test-time compute scaling can extend beyond autoregressive language-model reasoning to continuous non-autoregressive speech recognition.

Reinforcement learning (RL) for large language models usually supervises reasoning with scalar outcome rewards, such as binary correctness. Such rewards provide an optimization direction but rarely explain how a model should revise its mistaken reasoning, which can encourage shortcut learning and brittle policies. We propose \textbf{SocraticPO} (Socratic Policy Optimization), a policy-optimization framework that augments RL rollouts with Socratic-style natural-language guidance. During rollout, the student first answers independently; if the answer is incorrect, a teacher diagnoses the attempt and provides concise corrective guidance, after which the student continues under the expanded context. Crucially, this guidance is paired with reward decay: correct answers obtained after teacher intervention only receive decayed rewards, preventing the policy from treating teacher help as a free path to reward. Since SocraticPO only modifies the rollout process while leaving the standard expected-reward objective intact, it can be plugged into existing policy-gradient backends such as Reinforce++. Moreover, because the teacher provides only text-level guidance, SocraticPO can leverage stronger black-box teacher models without requiring access to logits or distribution matching. On undergraduate-level scientific reasoning benchmarks from SciKnowEval, SocraticPO improves over strong RL and self-distillation baselines. Ablations show that both targeted guidance and reward decay are necessary, with reward decay mitigating reliance on assisted correction.

Mobile agents are increasingly expected to operate everyday applications from screenshots and language goals, where reliable control requires reasoning over screen affordances, multi-step navigation, and future state changes. However, many agents externalize this computation as long textual chains of thought, which slows interaction, increases supervision cost, and complicates deployment. We introduce MIRAGE, a framework that learns continuous latent reasoning representations from visible textual reasoning traces. MIRAGE transfers explicit reasoning into compact hidden states, enabling the agent to reason internally without decoding long rationales. It also incorporates a generative world-model objective: latent reasoning vectors are aligned with future screenshots, encouraging the agent to anticipate upcoming interface states before acting. This turns hidden computation into both a compressed thought representation and a forward-looking model of environment dynamics. At inference time, MIRAGE reasons in continuous latent space, reducing token generation while improving execution efficiency. On AndroidWorld, MIRAGE matches explicit chain-of-thought supervised fine-tuning in the 4B ablation with a 3-5x lower decoded-token budget and improves a comparable instruction-tuned baseline by 10.2 points; on AndroidControl, it improves action grounding while generating over 75% fewer tokens.

Public benchmarks enable fair and reproducible evaluation of LLM reasoning, but they become fragile for deep research agents that actively search the web during inference. Such agents may retrieve public benchmark metadata, question context, or even ground-truth answers via web search. This gives rise to Search-Time Contamination (STC), where external retrieval bypasses intended reasoning and inflates measured performance. We systematically study STC in deep research agent evaluation. We define three contamination types with increasing severity, namely Benchmark Metadata Leakage, Question-Context Leakage, and Explicit Answer Leakage, and develop detection algorithms to identify them and quantify their impact on agent performance. Evaluating modern deep research agents on six public benchmarks, we find that STC is widespread and can inflate performance by up to 4%. Our findings show that existing evaluations may overestimate true reasoning ability. We therefore advocate contamination-aware practices, including isolated sandboxes, transparent search trajectories, and controlled benchmark access.

Reinforcement learning with verifiable rewards (RLVR) significantly advances LLM reasoning, yet it faces a dilemma: standard supervised scaling is throttled by high annotation costs, while unsupervised alternatives suffer from severe model collapse. Recent semi-supervised RLVR methods address this by using a small labeled set to guide unlabeled data, achieving a promising trade-off between training efficacy and annotation cost. However, they suffer from a severe data-efficiency bottleneck due to the reliance on coarse performance heuristics, leaving a vast majority of valuable instances underutilized. To this end, we propose GeoMin, which models global feature distributions on labeled data to decode the structural discrepancy between correct and incorrect rollouts, thereby establishing a robust prior to assess the reliability of self-reward signals and fully unleash the potential of unlabeled data. Empirically, GeoMin outperforms the strongest baselines by +4.1% and even surpasses fully supervised models with only 10% of the annotations, demonstrating remarkable data efficiency.

Speech Large Language Models (SLLMs) underperform their text counterparts on complex reasoning. We reveal that this gap is not a uniform cognitive deficit. Evaluating two architecturally diverse SLLMs, we show speech-to-text (S2T) matches or exceeds text-to-text (T2T) on spatial, syntactic, and factual tasks. Yet on logical tasks requiring entity tracking, S2T accuracy collapses to chance. We diagnose this as an entity binding failure: continuous speech features blur precise entity-property associations during implicit reasoning. To validate this diagnosis, we introduce Entity-Aware Chain-of-Thought (EA-CoT), a lightweight inference-time intervention forcing SLLMs to enumerate entities and bind them to claims before reasoning. EA-CoT bridges the gap, even when spoken names are misrecognized, yielding up to a 24.4 percentage-point accuracy gain. Ablations confirm the gains stem from explicit semantic binding, reframing the gap as an elicitation failure rather than a missing capability.

Post-training Small Language Models (SLMs) for reasoning typically follows an SFT-then-RL pipeline, yet existing work rarely considers what data should be learned at each stage. We argue that data strategy should be aligned with the distinct roles of SFT and RL: SFT is better suited for acquiring not-yet-mastered reasoning skills, while RL is better suited for consolidating skills that the model can already partially access. Based on this principle, we propose a difficulty-aware SFT-then-RL framework that organizes training data into stage-specific sets. For hard samples in the SFT stage, we introduce a Bridge mechanism that transforms raw teacher-generated reasoning traces into more learnable supervision for SLMs. For hard samples that remain unsolved during RL, we apply Critique Fine-Tuning by converting all-zero-reward failures into diagnostic, repair, and new reasoning trace supervision for the next SFT stage. Experiments on two SLMs across five reasoning benchmarks show that our method consistently improves over representative SFT, distillation, and RL baselines. Our results highlight the importance of coordinating data difficulty across SFT and RL for effective SLM reasoning post-training.

Large language models have shown strong performance in natural language generation and downstream reasoning tasks, but they still struggle with logical consistency, factual grounding, and interpretability in complex multi-step reasoning. To address these limitations, this paper proposes SGR, a stepwise reasoning enhancement framework that integrates large language models with external knowledge graphs through query-relevant subgraph generation. Given an input question, SGR first extracts key entities, relations, and constraints to construct a structured schema, then retrieves compact subgraphs from a knowledge graph using schema-guided querying. The generated subgraphs provide explicit relational evidence that guides the language model through step-by-step reasoning. In addition, SGR combines direct Cypher-based reasoning with collaborative reasoning integration, allowing candidate answers from multiple reasoning paths to be validated and aggregated according to both model confidence and graph consistency. Experiments on benchmark datasets including CWQ, WebQSP, GrailQA, and KQA Pro demonstrate that SGR improves reasoning accuracy and Hits@1 performance over standard prompting and several knowledge-enhanced baselines. Ablation studies further show that schema guidance and Neo4j-based retrieval are both crucial to the effectiveness of the framework. These results indicate that dynamically generated external subgraphs can improve the accuracy, robustness, and interpretability of LLM-based reasoning.

AI systems increasingly need to combine two demanding capabilities: navigating multi-session conversation history and performing deep reading comprehension within long documents. Yet no existing benchmark evaluates both simultaneously. We introduce MemoryDocDataSet, a synthetic benchmark of 50 micro-worlds and 1,000 QA pairs in which each instance comprises 3-5 personas, a temporal event graph spanning months of activity, 3-5 real long documents (20,000-50,000 tokens each sourced from the Caselaw Access Project), multi-session conversations grounded on those documents, and 20 question-answer pairs across five reasoning categories. The defining feature is the Hybrid source tag: questions requiring a system to first navigate conversation history to identify which document is relevant, then extract the answer from within that document. Hybrid questions account for 75.1% of the dataset. Dataset quality is characterised through a prompt-sensitivity self-consistency analysis using LLM-as-judge, yielding a median Cohen's $κ= 0.634$ across all 50 micro-worlds. We evaluate six baseline configurations spanning truncated context, long-context LLMs, retrieval-augmented generation (RAG), and memory systems. The best baseline (RAG-Both) achieves 0.358 overall F1 and 0.342 on Hybrid. Document-only retrieval (RAG-Doc) collapses to 0.267 on Hybrid despite achieving 0.453 on Doc-only questions, demonstrating a clear joint-retrieval gap that motivates architectures unifying conversational memory with long-document navigation. We release the dataset, generation pipeline, and all baseline implementations.

Recent large language models (LLMs) often appear to exhibit spatial reasoning ability; however, this capability is largely \emph{symbolic}, arising from pattern matching over spatial language rather than true \emph{geometric} reasoning over space. Because LLMs operate on discrete tokens, they lack native support for continuous spatial representations, explicit geometric computation, and structured spatial operators. To address this limitation, we introduce the \emph{Spatial Language Model (SLM)}, the first multimodal LLM that treats location information as a first-class modality and enables geometric spatial reasoning within the model's inference process. SLM directly operates on learned spatial representations rather than textual descriptions of spatial relations. To support effective training, we construct a \emph{Spatial Instruction Dataset} that aligns spatial representations, atomic geometric operations, and natural language instructions. We further propose a new benchmark named \emph{SpatialEval}, which is designed to evaluate spatial reasoning across attributes, distance, topology, and relative-position tasks. Extensive experiments show that SLM significantly outperforms existing LLM-based approaches that rely on symbolic reasoning via prompt engineering or textual abstraction, demonstrating the benefits of integrating geometric spatial representations for robust spatial reasoning. Our instruction dataset, evaluation benchmark, model training codes, and models' checkpoints can be found at: \hyperlink{https://github.com/chuchen2017/SLM}{https://github.com/chuchen2017/SLM}.

Low-Rank Adaptation (LoRA) is a popular parameter-efficient fine-tuning (PEFT) method that restricts weight updates to low-rank adapters, introducing a fixed low-rank inductive bias by optimizing in a low-dimensional subspace. In this work, we question whether a fixed-rank constraint is the most effective inductive bias for parameter-efficient fine-tuning. We introduce Learnable Rank LoRA (LR-LoRA), a PEFT method in which the adapter rank is learned during the training process. Instead of prescribing a uniform rank for all adapter layers, LR-LoRA allows the optimizer to determine the appropriate rank for each layer. Using this approach, we find substantial layer-wise variation in the learned ranks, with the attention and MLP layers in the transformer models exhibiting systematically different rank preferences. Across a range of language understanding and commonsense reasoning benchmarks, LR-LoRA achieves state-of-the-art performance in most settings and consistently outperforms strong PEFT baselines, demonstrating that a learnable rank provides a more flexible and effective inductive bias than fixed-rank adaptations.

Automatic generation of RTL code for digital hardware designs remains challenging due to long-horizon reasoning, multi-step dependencies, and strict correctness constraints in Verilog and VHDL. We present StepPRM-RTL, a novel framework that combines stepwise trajectory modeling, process-reward modeling (PRM), and retrieval-augmented fine-tuning (RAFT) to enhance both the functional correctness and reasoning fidelity of LLM-based RTL code generation. StepPRM-RTL constructs stepwise reasoning trajectories from canonical solutions, where each step contains a rationale and incremental code modification. A Process Reward Model (PRM) evaluates intermediate steps, providing dense feedback that guides reinforcement-style updates during RAFT fine-tuning. Monte Carlo Tree Search (MCTS) explores alternative reasoning paths, enriching the training dataset with high-quality trajectories. This integration of stepwise and outcome-aware rewards allows the model to learn both how and why to construct correct RTL, improving long-horizon reasoning beyond standard supervised or outcome-based training. Experimental evaluation on benchmark Verilog and VHDL datasets demonstrates that StepPRM-RTL outperforms the best prior methods by over 10% in functional correctness and reasoning fidelity metrics. Ablation studies confirm that the combination of PRM-guided rewards and stepwise trajectory exploration is key to its performance. StepPRM-RTL generalizes across RTL languages and provides a scalable framework for high-fidelity, interpretable code generation, establishing a new standard for LLM-assisted hardware design automation.

Large language models have made substantial progress on mathematical reasoning, but existing benchmarks typically evaluate well-specified problems with final answers, step-by-step solutions, or complete proofs. They do not capture collaborative open-problem solving: a setting in which participants propose partial arguments, identify gaps or errors in prior steps, repair flawed reasoning, and gradually synthesize incremental contributions into a proof. We introduce CrowdMath, a dataset of 164 expert-annotated progress chains from the MIT PRIMES--Art of Problem Solving (AoPS) CrowdMath program (2016-2025), a collaborative research initiative whose discussions have led to peer-reviewed publications. Each chain traces a multi-participant forum discussion from an open-problem statement to a completed proof. Posts are labeled by their functional roles in the evolving solution process, including partial progress, proof completion, erroneous reasoning, and error identification. We define evaluation tasks and benchmark six frontier models. Models achieve 83-88% accuracy on next-post prediction, suggesting that they can follow the local flow of mathematical discussion. However, they struggle to identify the functional significance of individual contributions with the best model achieving only 0.42 macro-F1 on post-role classification. CrowdMath exposes a gap between solving well-specified mathematical problems and understanding collaborative mathematical progress as it unfolds.

Reasoning models achieve strong performance on challenging tasks by generating explicit intermediate reasoning traces before producing a final answer. Yet the internal structure of representation space when reasoning remains poorly understood: how do a model's hidden representations differ during thinking versus the embeddings of the input prompt, and can this structure be exploited to elicit stronger reasoning at inference time? We show that both input embeddings and thinking embeddings (mean-pooled last-layer hidden states over the prompt and reasoning trace, respectively) exhibit extremely high conicity, with all vectors clustering tightly around a single mean direction. Crucially, these mean input and thinking directions are non-collinear, with thinking embeddings occupying a geometrically distinct region of embedding space across many different models and benchmark tasks. This observation motivates casting the input-to-thinking transition as a rotation problem admitting a closed-form solution via orthogonal Procrustes analysis. We propose Rotate2Think, a training-free method that estimates this rotation from a small set of correctly solved examples and injects the resulting synthetic thinking vector between thinking delimiters at inference time, providing a geometric primer at the onset of the reasoning trace. Evaluated across multiple benchmarks and model families, Rotate2Think improves accuracy in 30 of 32 model-benchmark configurations across mathematics, science, and code tasks, and generalizes zero-shot to multimodal reasoning on MATH-Vision.

Reliable uncertainty communication is critical to the trustworthiness of LLMs, yet faithful calibration (FC)--the alignment between models' intrinsic and (linguistically) expressed confidence--is a persistent failure mode. This challenge is key for large reasoning models (LRMs), whose extended reasoning traces are often interpreted by users as evidence of deliberation, competence, and confidence. Despite the importance of FC and wide usage of LRMs, the extent to which LRMs can faithfully express their confidence remains poorly understood. Moreover, the prevailing paradigm to measure FC does not generalize well to the long chain-of-thought outputs generated by LRMs, which tend to lack clear step boundaries, involve inconsistent step structure, and encode complex conditional dependencies throughout the trace--complicating estimation of intrinsic confidence. To address this challenge, we introduce a novel framework to systematically quantify FC of LRMs. Our framework analyzes linguistic decisiveness relative to three sources of internal uncertainty, based on token probabilities, hidden states, and sampled response consistency. We also devise a prefix-conditioned sampling approach to control for conditional and structural variation across traces. Applying our framework to a diverse suite of leading models, datasets, and prompts, we find that faithful confidence expression is a significant challenge for LRMs. Reasoning behaviors do not automatically translate to improved FC, and prompt interventions for non-reasoning models do not improve faithfulness in the reasoning setting. Different confidence estimators further produce divergent assessments of the same traces, revealing fragility in prior evaluation methodologies. Taken together, our work establishes FC as a distinct reliability and alignment target for LRMs, particularly as such systems are increasingly deployed in high-stakes contexts.

Large language models improve final-answer accuracy through extended chain-of-thought reasoning, but often spend tokens inefficiently and offer little inference-time control. Existing efficient reasoning methods control thinking length by shortening, early-stopping, or compressing traces, leaving how the model thinks implicit. In this paper, we propose Agentic Chain-of-Thought Steering (ACTS), which formulates reasoning steering as a Markov decision process where a controller agent adaptively steers a frozen reasoner during inference. At each step, the controller observes the reasoning trace and remaining thinking budget, then issues a steering action consisting of a reasoning strategy and a steering phrase that initiates the next reasoner step. This enables budget-aware strategy control for efficient reasoning while preserving the reasoner's generation continuity. We initialize the controller agent from our constructed synthetic steering trajectories with multi-budget augmentation, and further optimize it via reinforcement learning with budget-conditioned reward shaping. Experiments across multiple benchmarks show that ACTS matches full-thinking performance with substantial token savings, and enables controllable accuracy-efficiency trade-offs across different reasoners and tasks. The code is available at https://github.com/Andree-9/ACTS.

Reasoning models improve accuracy through extended chains of thought, but their long outputs create a memory and compute bottleneck. KV cache eviction methods reduce this cost by evicting unimportant key-value pairs from the cache, yet they often yield worse accuracy than selection-based sparse attention alternatives, which keep the full KV cache. We identify key factors crucial to KV cache eviction accuracy. First, a small fraction of value states have abnormally large magnitudes, and evicting them causes catastrophic failure where models enter repetitive reasoning loops. Second, introducing stochasticity during eviction improves accuracy by increasing cache diversity. Based on these findings, we propose Value-aware Stochastic KV Cache Eviction (VaSE), a training-free recipe that protects large-magnitude value states and promotes diverse eviction decisions. Across six reasoning tasks, Qwen3 models using VaSE with 4x KV cache compression yield higher average accuracies than SOTA selection method at the same sparsity, while outperforming the strongest eviction method by more than 4%. Overall, VaSE bridges the gap between efficiency and accuracy, supporting FlashAttention2 and enabling a static memory footprint for reasoning models.

AI agents can increasingly handle the mechanical tasks of financial analysis: retrieving documents, calculating formulas, updating spreadsheets. The harder, more valuable challenge is reasoning through the open-ended questions that define expert Analyst work. Existing benchmarks do not capture this class of problem, and those that attempt to evaluate open-ended reasoning rely on model-judged outputs that introduce noise and circularity. We present Hedge-Bench 1.0: a benchmark of 102 actual, on-the-job tasks grounded in the explicit reasoning traces of professional hedge fund analysts working with relevant information sources. This approach enables deterministic grading against verified expert steps. Frontier models and agents score below 16% on the benchmark. We publish the dataset and evaluation harness at github.com/Trata-Inc/trata-hedge-bench.

Large reasoning models (LRMs) are often evaluated using metrics such as final-answer accuracy or token count. However, identical scores on these metrics can hide fundamentally different reasoning structures. To address this limitation, we introduce a scalable LRM benchmark of logic puzzles and a pipeline that converts unstructured traces into verifiable reasoning graphs of claims and dependencies. This turns reasoning into a structured, measurable object whose topology can be quantitatively analyzed. Building on this, we define a reasoning efficiency metric that quantifies how concentrated the model's logical flow is. Our analysis on open-source reasoning models shows that structural measurements separate behaviors that token count and accuracy conflate, providing a practical tool for diagnosing failure modes and comparing how reasoning scales with puzzle difficulty.

Embodied chain-of-thought (CoT) aims to bridge linguistic reasoning and robotic control, but its effective form and integration strategy remain underexplored. In this paper, we revisit embodied CoT for vision-language-action (VLA) models at large scale. We construct the largest embodied CoT corpus to date, comprising 978,743 trajectories, 226.3M samples, and 2592.5 hours of robot data. Through extensive experiments, we find that effective embodied CoT should ground high-level semantic understanding into concrete action guidance, such as end-effector movement descriptions and image-space trajectories, while high-level reasoning alone brings only marginal gains. We further show that explicit CoT does not scale reliably when used as an autoregressive action prefix, as it suffers from compounding inference errors and unstable reasoning-action coupling. To address these limitations, we propose ERVLA, a VLA model that uses embodied CoT as representation-shaping supervision rather than mandatory test-time reasoning. ERVLA is trained with a reasoning-dropout strategy, enabling the model to absorb rich reasoning traces during training while predicting actions directly without CoT decoding during inference. This design improves scalability with increasing pre-training data and avoids autoregressive instability. ERVLA achieves state-of-the-art performance on LIBERO-Plus with an 86.9% success rate and reaches 53.2% success rate on VLABench, demonstrating strong out-of-distribution generalization. In real-robot experiments, ERVLA further outperforms competitive state-of-the-art baselines, especially on tasks requiring semantic disambiguation and long-horizon execution.

Large language models (LLMs) offer a promising approach to machine translation (MT) for extremely low-resource languages by incorporating linguistic resources through in-context learning. However, LLMs often struggle to apply grammatical information effectively during translation. Inspired by recent progress in chain-of-thought reasoning, we investigate whether low-resource MT can benefit from structured intermediate steps of linguistic analysis and grammatical reasoning. We propose a pipeline for automatically generating step-by-step linguistic reasoning traces from Universal Dependencies treebanks, dictionaries, and grammar-rule banks. We evaluate these traces in three settings: in-context learning (ICL), supervised fine-tuning (SFT), and reinforcement fine-tuning (RFT), on Xibe and Chintang as test cases. Our results show that linguistic reasoning traces are most effective as inference-time guidance: in ICL, reliable sentence-specific traces substantially improve translation performance across most models, languages, and metrics. In contrast, using the linguistic reasoning traces as training data yields smaller and less consistent gains, as models learn the trace format but often generate erroneous content. These findings suggest that LLMs can leverage grammatical information for low-resource MT when given reliable linguistic analyses, while learning to generate such analyses remains a major bottleneck.

Extended chain-of-thought (CoT) traces improve LLM reasoning but incur substantial computational and memory costs. While existing CoT compression methods mitigate this by condensing thought steps into compact representations via memory tokens and retaining only these representations at inference time, the loss of fine-grained information makes subsequent steps more error-prone. To alleviate this, we propose \textbf{HybridThinker}, where in addition to preserved these representations, thought steps are also temporarily retained to provide fine-grained details. However, we observe that naively keeping thought steps accessible to subsequent steps \emph{during training} lets the model bypass memory tokens by retrieving information directly from these steps, leaving the model's ability to compress and retrieve information through memory tokens insufficiently trained. We therefore introduce a hybrid training scheme, in which only some thought steps are directly accessible through attention to subsequent steps, while the other thought steps are masked, forcing the model to use memory tokens for compression and retrieval. Across 4 reasoning benchmarks, HybridThinker matches the uncompressed baseline, advancing the state of the art in CoT compression by 5.8 points on average accuracy with similar inference time. Ablation studies confirm that both temporary thought-step retention and the hybrid training scheme contribute to these gains.

Agentic reinforcement learning (RL) equips large language models (LLMs) with tool-use capabilities that substantially improve reasoning on complex tasks. However, integrating external tools often destabilizes training: over-reliance on tools can induce input distribution shift, while overly conservative tool use limits effective exploration. To address this issue, we propose a unified framework TAO-RL that couples tool-aware trajectory filtering with entropy-guided exploration for efficient policy optimization. Specifically, at the data level, TAO-RL filters rollout trajectories along two criteria: discarding those where all tool invocations fail to execute, and removing those where all rollouts are either correct or incorrect, as both cases yield degenerate advantage estimates that contribute no discriminative learning signal. This joint filtering retains data that are both tool-capable and informative, establishing a high-quality training distribution. At the algorithmic level, we introduce a tool-aware entropy-guided bonus that reshapes the advantage function at post-tool-call tokens, encouraging the policy to explore more diverse reasoning paths at critical decision points. These two components are mutually reinforcing: trajectory filtering establishes a clean and informative training foundation, while entropy-guided exploration drives stronger reasoning behaviors at critical tool-interaction junctures. Extensive experiments on 7 challenging reasoning benchmarks across 3 model scales demonstrate the superiority of TAO-RL over existing methods.

While Large Language Models (LLMs) have shown strong performance in generating formal proofs, their outputs often remain less readable, modular, maintainable, and reusable than proofs in mature formal mathematics libraries. We argue that this gap stems in part from the compile-first objective implicit in most proof-generation pipelines, which encourages monolithic or ad hoc proof scripts rather than library-quality artifacts. Existing approaches to proof-quality improvement often rely on explicit, computable optimization objectives. In practice, however, the most tractable and experimentally validated objectives are largely length-based, while higher-level qualities such as readability, modularity, maintainability, and reusability are difficult to reduce to reliable automatic metrics. Instead of optimizing proof improvement against a single proxy metric, we take a process-guided approach inspired by human proof-refactoring workflows. We propose an agentic framework $\textbf{Proof-Refactor}$ that decomposes proof refactoring into four phases: extracting candidate proof fragments, designing helper declarations, formally proving the extracted and designed components, and repairing the original proof using the verified components. On generated Lean proofs from PutnamBench and Putnam2025, Proof-Refactor improves rubric-based refactoring scores over a strong Claude Code refactoring baseline, with the largest gains in signature quality and human readability. These results suggest that process-guided refactoring can improve proof structure without treating proof length as the primary objective.

Long-horizon reasoning requires a system to commit to medium-horizon intent without becoming rigid: re-plan too often and computation never coheres into multi-step structure; commit too long and the plan goes stale. We study this stability-adaptivity tradeoff in the latent reasoning setting, where multi-step computation occurs inside hidden state rather than externalized token traces. We extend the Hierarchical Reasoning Model (HRM) with a feudal-style manager-worker interface: a slow high-level module periodically emits a normalized directional subgoal that persists for P low-level steps, biasing the worker's hidden-state updates and supplying an intrinsic cosine alignment loss. On ARC and ConceptARC, we find that subgoal persistence -- not subgoal injection alone -- is the central knob: moderate periods P in [3, 6] consistently outperform both very frequent (P=1) and very long horizons, with a clear minimum LM loss at P=3 (1.544 vs. 1.674 at P=1, 1.640 baseline; replicated over 5 seeds at mean 1.595, std 0.045). The intrinsic alignment weight lambda shows a complementary narrow optimum (lambda approximately 0.05). A controlled ablation at past-sweet-spot lambda isolates learned directional structure -- not architectural capacity or auxiliary loss alone -- as the source of interference when the alignment signal exceeds its optimum. Together these findings implicate a design principle for compositional planning in latent reasoning systems: medium-horizon intent must be coherent across enough computational steps for compositional structure to form.

Knowledge Graphs (KGs) are widely used to mitigate the limitations of Large Language Models (LLMs), such as outdated knowledge and hallucinations. Existing LLM-KG integration frameworks typically rely on predefined operators to retrieve factual knowledge from KGs and inject it into prompts for answer generation. This paradigm faces two critical bottlenecks: 1) Inflexibility: The predefined operators are limited in scope and thus lack sufficient compositional expressiveness to fully capture the complex semantics required by KG questions. 2) Unscalability: Direct injection of factual knowledge into prompts limits scalability in handling large-scale factual knowledge. To address these two bottlenecks, we propose Code-on-Graph (CoG), a programmatic reasoning framework for LLM-KG integration. Specifically, given the factual knowledge retrieved at each reasoning step, CoG first identifies the corresponding KG schemas and represents these schemas as Python classes, which serve as abstract interfaces to the retrieved facts. It then generates executable code grounded in these classes, with the retrieved facts instantiated as objects of the corresponding classes during execution. This design enables flexible code-based reasoning while avoiding the direct injection of large-scale factual knowledge into prompts. Experiments on WebQSP, CWQ, and GrailQA demonstrate that CoG outperforms prior state-of-the-art models by up to 10.5%.

Large Reasoning Models (LRMs) have demonstrated impressive capabilities in many tasks, yet they struggle with reliably following multiple instructions, either by failing to satisfy individual constraints or by struggling to balance competing constraints simultaneously. We formalize this challenge as the Constraint Adherence Problem (CAP). This paper introduces a novel framework that addresses CAP by representing instructions as a structured knowledge graph of constraints. Our approach, Constraint Relationship Graph Completion (CRGC), explicitly models relationships between constraints, identifies adherence challenges, and discovers ``bridge constraints'' that help the model better focus on and reconcile requirements. Bridge constraints act as auxiliary instructions that make primary constraints more salient and compatible. Unlike existing approaches that enhance instruction following through general training methods, CRGC specifically improves constraint satisfaction by leveraging the model's own knowledge to create better pathways for generation. Experiments across three popular instruction following datasets demonstrate that our approach reduces constraint violations by 39% compared to standard prompting while maintaining reasoning abilities of large reasoning models.

Test-time reinforcement learning has emerged as a promising paradigm for enhancing the complex reasoning abilities of large language models in a completely label-free manner. Despite existing studies focusing on Pass@1 performance, optimizing Pass@k remains under-explored yet critical in label-free settings, which measures generation coverage for sustained exploration. Optimizing Pass@k in label-free setting is highly non-trivial, as directly applying the Pass@k advantage designs effective for RLVR yields unsatisfactory performance. Through in-depth empirical analysis, we discover the root causes hindering performance: pseudo-label estimations for low-confidence samples have a high probability of being incorrect, while candidate answers for high-confidence samples suffer from severe diversity collapse. To overcome these hurdles, we propose TTRL-CoCoV (Test-Time Reinforcement Learning with Confidence-Conditioned Verification), a novel confidence-adaptive framework that expands Pass@k coverage and improves Pass@1 performance. Based on our key insight that verification capability generally leads generation capability, TTRL-CoCoV employs a confidence-conditioned mechanism: for high-confidence samples, it bootstraps verifier and applies an exploration-enhancing reward to prevent diversity collapse; for low-confidence samples, it delegates pseudo-label selection to the verifier to filter incorrect pseudo-labels; and for medium-confidence samples, it bypasses verification entirely. Extensive experiments demonstrate that TTRL-CoCoV outperforms the best competing methods across 6 widely-recognized benchmarks, achieves average absolute gains of +9.8% in Pass@1 and +18.7% in Pass@16 over TTRL, and even achieves absolute Pass@1 improvements of up to +5.0% across multiple reasoning benchmarks when compared against fully supervised RL methods. Our code repository: https://github.com/shanjf666/CoCoV.

Large language models achieve strong performance on arithmetic reasoning benchmarks, and one common response to arithmetic brittleness is to delegate computation to code. Yet models are still often used in settings where they must reason directly from natural language, and trustworthy models should solve small-number arithmetic word problems without external tools. Prior work shows that LLMs are sensitive to numerical variation: a model may solve an original problem but fail on structurally similar variants requiring the same reasoning procedure with different numbers. We ask whether this fragility persists under a stricter setting involving small, schema-preserving numeric changes that retain the original reasoning program and avoid large-number stress tests. We introduce an automatic algorithm for generating numeric-remapping attacks on arithmetic word problems. Unlike template-based perturbation methods requiring manual schemas or constraints, our approach derives problem-specific symbolic representations, generates constrained numeric remappings, recomputes gold answers, and realizes transformed questions through deterministic edits guided by LLM-generated edit plans. Stage-wise validation and a high-confidence audit retain reliable attacks, making the pipeline scalable with limited human intervention. We evaluate DeepSeek-R1 (70B), Gemma4 (31B), and GPT-OSS (120B) on GSM8K, MAWPS, and MultiArith. On GSM8K, completed runs show conditional accuracy drops of 12.16 to 25.82 percentage points. MAWPS and MultiArith are far more stable, with most attacked accuracies near or above 98%. These results show that numeric-remapping robustness depends strongly on dataset structure: GSM8K remains sensitive even when reasoning programs are preserved and answers are recomputed, while shorter, more regular datasets are more robust.

Reasoning segmentation aims to segment target objects described by complex language through joint visual-textual reasoning. Existing methods typically rely on either learned semantic tokens to bridge Multimodal Large Language Models (MLLMs) and segmentation models, suffering from difficult cross-modal alignment, or explicit spatial prompts such as bounding boxes, which may lose holistic response semantics. To address these limitations, we propose Attention-Guided and CoT-Enhanced Coarse-to-Refined Reasoning Segmentation, termed CR-Seg, a two-stage framework for coarse-to-refined reasoning segmentation. Specifically, we design an Extract Attention Maps and Points (EAP) module to extract attention maps for coarse target localization and select informative points, both of which are fed into SAM for mask refinement. To alleviate reasoning--answer inconsistency, we further introduce Global-to-Local Chain-of-Thought (GLCoT), which guides the model to reason progressively from global scene context to local target details. Extensive experiments on reasoning segmentation benchmarks demonstrate the effectiveness of CR-Seg.

Large Reasoning Models (LRMs) have achieved remarkable progress thanks to Reinforcement Learning with Verifiable Rewards (RLVR) on Chain-of-Thoughts (CoTs). However, since long CoTs naturally contain trial and errors and mainstream RLVR approaches choose outcome-correct CoT trajectories for memorization, the redundant explorations in long CoTs are inevitably reinforced, which results in the over-thinking issues of LRMs. Previous attempts to resolve this issue mainly give more advantage to shorter trajectories, yet their learning signals are still outcome-based and cannot reduce the memorization of redundant explorations in long CoTs. Therefore, we propose ThoughtFold, a framework that leverages fine-grained preference learning to mitigate redundant explorations for efficient reasoning. ThoughtFold employs an introspective strategy to identify redundancy within each correct trajectory, which yields a spectrum of candidate sub-trajectories. Leveraging this spectrum, we introduce a masked preference optimization objective that explicitly penalizes redundant explorations and encourages the model to directly bridge essential reasoning segments, effectively folding its reasoning chains into a more concise path. Extensive experiments show that ThoughtFold significantly enhances efficiency. It reduces the token usage of DeepSeek-R1-Distill-Qwen-7B by approximately 56% while maintaining state-of-the-art accuracy.

We introduce SagaQA, a long-form video benchmark for multi-hop reasoning over full-length TV series. Existing video reasoning benchmarks often emphasize local understanding of adjacent frames or clips. SagaQA addresses this gap by requiring high-level comprehension of extended multimodal narratives in entire TV shows. A distinguishing feature of SagaQA is the granularity of its reasoning steps. Our dataset necessitates long-range reasoning hops to connect information across completely different episodes. This requires models to reason over entire events and actions, demanding a deep understanding of the show's narration and progression at a multimodal level. Motivated by recent progress in agentic methods, we further study how different planning strategies handle such complex reasoning. We categorize these approaches into three classes-Parallel, Sequential, and Hybrid planners-and evaluate their ability to generate coherent and complete reasoning plans. Our results on SagaQA suggest that hybrid planners consistently produce higher-quality plans and exhibit stronger capabilities for complex, high-level narrative understanding in TV shows.

Chain-of-thought (CoT) reasoning has become a widely used mechanism for eliciting multi-step reasoning in large language models by generating intermediate reasoning steps at inference time. Yet the scaling behavior of generalization with CoT depth remains poorly understood. To address this question, we study a theoretically solvable model of CoT for in-context weight prediction in linear regression, where test-time reasoning is represented as an iterative refinement of the weight-parameter estimate. Using tools from random matrix theory under high-dimensional asymptotics, we derive an exact formula for the generalization error as a function of reasoning depth, pretraining data amount, and context length. Our analysis reveals a sharp phase transition separating exponential and polynomial improvement, saturation, and overthinking, and characterizes how the optimal reasoning depth scales. We further show that deeper reasoning is most effective with sufficiently rich pretraining and in-context information, whereas limited pretraining or context makes longer reasoning prone to error amplification or saturation. We also validate these predictions through experiments on fully learned linear attention and softmax attention models. Our results provide a unified theoretical account of how test-time CoT depth affects generalization.

Inference-time scaling has emerged as a critical avenue for enhancing Large Language Models' performance, yet real-world deployment is constrained by strict computational budgets. In this work, we formulate inference budget allocation as a global constrained optimization problem governed by economic principles. By modeling per-query reasoning utility with a shifted-surge function, we derive an optimal allocation policy based on a global shadow price that equilibrates marginal utility under resource scarcity. Based on this theory, we propose Constrained Latent-utility Equilibrium Allocation for Reasoning (CLEAR). It performs rational abandonment and reallocates resources from insolvent queries to solvable queries near their emergence thresholds. Extensive experiments on several reasoning tasks with different traffic streams demonstrate that CLEAR significantly improves the Pareto frontier of total token cost versus mean accuracy. In resource-scarce regimes, CLEAR achieves up to a 3x improvement in global accuracy compared to uniform allocation.

We propose ZX-Calculus (Knowledge Evolution Calculus), a conservative extension of Martin-Lof Dependent Type Theory (MLTT) integrating trace-indexed types, presheaf non-monotone semantics, and constructive AGM belief revision. A Coq mechanisation accompanies the paper (34 complete proofs; zero admits for the two central results). (I) Trace types. FinTrace(s0,sn) is an inductive family of typed execution traces. FinTrace and Star(Step) are isomorphic as path types but not judgementally equal; TraceElim exposes the event label e:Event explicitly, giving a more ergonomic interface for event-driven induction. We prove the Trace-Reachability Correspondence, Deterministic Replay, and a canonicity framework via reducibility candidates with a Transport Lemma (RC-elim deferred; all other Core results are Coq-verified). (II) Sheaf semantics. Trace-indexed propositions are contravariant sheaves over the free trace partial-order category Tf. A Separation Theorem (explicit countermodel) distinguishes proof-theoretic monotonicity from semantic non-monotonicity. The term model is an initial CwF (syntactic universal property, not classical completeness). (III) AGM belief revision. We give an explicit constructive partial meet contraction algorithm verified against (C1)-(C4). All eight AGM postulates (R1)-(R8) are theorems. Proofs of R7 and R8 use the Disjunctive Entrenchment Lemma, given a self-contained constructive derivation. (IV) Integration. B^AGM fails the sheaf composition law BP-comp for sequential revision (explicit countermodel, Coq-verified). We introduce Single-Step Revision Systems (SSRS), prove B^AGM is a valid SSRS (Coq-verified), and show this suffices for trace morphisms, retraction characterisation, and revision witnesses. The BP-comp failure reveals a fundamental tension between path-dependent belief revision and functor consistency, not previously identified.

Recent developments in Large Language Models (LLMs) have showcased impressive reasoning capabilities, with Reinforcement Learning with Verifiable Rewards (RLVR) being a promising enhancement strategy. However, existing reward mechanisms are constrained to the outcome-level correctness and lack explicit signals to guide the model to consider diverse solutions. In contrast, human problem solving typically involves evaluating multiple potential approaches and selecting the most reliable solution, a cognitive process that current RLVR frameworks do not explicitly incentivize. Inspired by this, we propose Hint-Guided Diversified Policy Optimization (HDPO), allowing the model to first list all potential candidate solution outlines as hints and then select the most reliable one for further reasoning. HDPO comprises two stages of Cold Start for Structured Reasoning and Hint-Guided Diversified Reinforcement Learning to incentivize the model to generate diverse and reliable solutions following the ``propose-select-think'' trajectory. Experimental results show that HDPO effectively boosts LLM reasoning and enhances the diversity of candidate solutions as well as the LLM's ability to identify reliable solutions.

Large reasoning models improve performance by generating extended chain-of-thought (CoT) reasoning, but this behavior becomes inefficient when applied to LLM agents. Current LLM agents often generate verbose textual reasoning at every decision step and allocate reasoning effort nearly uniformly across turns, leading to substantial inefficiency in multi-turn agentic trajectories. We propose Adaptive Latent Agentic Reasoning (ALAR), a dual-mode framework that uses compact latent reasoning for routine turns and selectively escalates to explicit chain-of-thought when deeper deliberation is needed. ALAR learns latent reasoning by using the agent's actions as supervision anchors and is further optimized to use latent reasoning when it is sufficient for task success and reserve explicit CoT for harder decisions. Experiments on agentic search and tool-use benchmarks show that ALAR maintains comparable or better task accuracy while substantially reducing generated tokens by up to 43.6% in search and 84.6% in tool use. These results demonstrate that ALAR improves the accuracy-efficiency trade-off of LLM agents by reducing unnecessary textual reasoning while preserving explicit deliberation for harder decision steps.

Large Reasoning Models (LRMs) improve performance by generating explicit intermediate reasoning traces through increased test-time compute, yet the assumption that longer reasoning is consistently beneficial remains under-examined. While recent evidence shows that additional reasoning can lead models to overthink, we ask: "Once a model has reached the correct answer, does further reasoning refine the solution, or deviate from it?" To study the dynamics after correctness, we introduce a prefix-level trajectory evaluation protocol grounded in reasoning sufficiency, defining the minimum reasoning budget required for a model to first generate the correct answer. This allows us to disentangle verbose overthinking, where additional reasoning is redundant but harmless, from harmful overthinking, where continued reasoning destabilizes an already-correct trajectory. Starting from multimodal benchmarks, we find that many instances considered reasoning-intensive require surprisingly little reasoning. Moreover, stopping at the first correct prefix improves accuracy over standard reasoning up to 21%, revealing that current models are limited not only by their ability to reason, but also by their inability to stop at the right time. Furthermore, while common efficiency strategies like early stopping substantially reduce verbose overthinking (up to 50%), they fail to mitigate harmful overthinking. Failure analysis reveals that correctness deviations are mainly driven by logical drift and visual reinterpretation. Finally, we show that our findings generalize to language-only reasoning benchmarks, highlighting harmful overthinking as a broader reliability risk. Code available at https://simonecaldarella.github.io/thinking-past-the-answer.

Large language models (LLMs) exhibit strong natural-language reasoning abilities for clinical decision support, but struggle to effectively model structured longitudinal electronic health records (EHRs). In contrast, EHR foundation models can learn predictive patient representations, yet lack interpretable language-based reasoning. To bridge this gap, we propose ChatHealthAI, a multimodal reasoning framework that aligns structured EHR representations from a pretrained EHR foundation model with the semantic space of a frozen LLM through a task-aware resampler. By integrating longitudinal patient representations with refined clinical event descriptions, ChatHealthAI enables clinically grounded natural-language reasoning while maintaining accurate patient prediction. We evaluated ChatHealthAI on three clinical predictive tasks from the EHRSHOT benchmark. Results show that ChatHealthAI improves reasoning quality and interpretability while preserving competitive predictive performance. These findings highlight the potential of integrating EHR foundation models with pretrained LLMs for interpretable clinical prediction.

Reasoning language models (RLMs) achieve strong performance on complex reasoning tasks, but still exhibit substantial multilingual reasoning gaps, largely due to language-understanding failures in non-English inputs. English translation can mitigate these failures by expressing non-English inputs in a form that RLMs can more reliably interpret, yet translating every input is unnecessary when the model can reason reliably from the original query. To address this challenge, we propose Luar, a Language Understanding Boundary-aware Reinforcement Learning framework that trains RLMs to selectively invoke translation when direct understanding is unreliable. Luar trains the model to choose between solving the original input directly and reasoning over its English translation, encouraging translation only when translator-augmented reasoning is expected to substantially outperform direct reasoning. Across multilingual reasoning benchmarks, Luar outperforms standard GRPO and other training-based baselines, with particularly large gains on low-resource languages. Further analysis shows that Luar avoids unnecessary translation in cases where direct reasoning is sufficient, while extending its translator-call behavior to unseen low-resource languages. Together, our work suggests a selective approach to multilingual reasoning: RLMs can learn to invoke translation only when their direct understanding is unreliable. The project will be made publicly available at https://github.com/deokhk/LUAR

The rapid development of LLMs has significantly advanced tabular question answering, but most systems cannot perform future-oriented numerical prediction. To address this gap, we introduce a novel task, Open-Domain Tabular Question Answering for Future Data Forecasting and Reasoning, and propose the first dataset to cover time-series forecasting and forecast-based reasoning scenarios using real estate data. This task poses challenges in retrieving precise historical data, overcoming the forecasting limitations of LLMs, and standardizing responses for diverse queries. To solve the above challenges, we propose TimeFore, an LLM agent-based framework that decomposes the problem into three collaborative roles: a Retriever autonomously generates SQL to fetch data, a Forecaster invokes external time-series models for higher accuracy, and an Analyzer synthesizes the results to construct a precise and consistent final answer. Extensive experiments demonstrate the effectiveness of our TimeFore.

Tool-augmented multimodal agents show strong benchmark gains, often taken as evidence that agents have learned to use tools. We argue that this interpretation can be premature: a tool-call trace alone does not show whether the tool supplied answer-critical information. We study two representative ``thinking with images'' agents, Thyme and DeepEyesV2, across real-world understanding, OCR, chart understanding, and mathematical reasoning. Each agent is compared with its Tool-Free counterpart and with a Pure-Text Reasoner trained from the same source pool without tool-calling trajectories. Tool access yields little consistent aggregate improvement, does not reliably reduce generated-token cost, and leaves only a small tool-only solved set: 93% of DeepEyesV2's tool-solved problems and 96% of Thyme's are also solved by at least one non-tool setting. Mechanism ablations further show that the full tool-use loop does not consistently outperform either the tool-call format or the returned execution result alone. In the settings we study, the analyzed agents appear to learn tool-calling patterns more reliably than tool-contributed capabilities, suggesting that evaluation should distinguish tool availability from whether tools actually expand what agents can solve.

Large language models solve complex problems by generating lengthy chains of explicit reasoning tokens. While effective, this makes reasoning expensive, length-sensitive, and constrained to (discrete) natural language. While latent reasoning offers a continuous alternative, determining useful structures for intermediate latent states is an open challenge. In this paper, we formulate latent reasoning as a geometric path-approximation problem within the model's pretrained token-embedding space. We introduce Geometric Latent Reasoning (GLR), which uses a lightweight transition head to predict iterative direction updates in embedding space. Using textual chain-of-thought traces as anchors, GLR learns to approximate discrete reasoning trajectories while permitting continuous deviations from exact token embeddings. Evaluations on mathematical reasoning benchmarks using Qwen3 models reveal an emergent phenomenon: geometric latent reasoning induces substantially shorter generations without an explicit length objective. By replacing early explicit reasoning with continuous latent steps, models often reach correct answers using substantially fewer total generation steps. These findings suggest that continuous trajectories act as compact intermediate reasoning states, exposing a new tradeoff between latent computation budget, output length, and accuracy.

Graphs have been used to enhance large language models (LLMs) for structured reasoning, mostly as external knowledge sources are provided to models at test time. In this paper, we take a different view: the value of graphs for LLMs lie not only in supplying information, but also in organizing reasoning. Inspired by how humans use graph-structured mind maps to organize branching and converging thoughts, we ask whether graphs can serve as an internal form of reasoning assistance. We study this question on multi-hop question answering tasks, where teacher-provided reasoning traces are rewritten as graph mind maps and used to guide a student model. Our experiments reveal a clear modality gap. When graph structures are flattened into text, their benefits become limited once direct answer hints are removed. Under this abstract guidance setting, both reasoning efficiency and answer quality degrade substantially. In contrast, visual graph guidance remains effective without direct answer clues, and its advantage persists after supervised fine-tuning and KL-based distillation. The above findings support the claim that graphs should be studied not only as external knowledge structures for LLMs, but also as visual scaffolds for organizing reasoning.

Post-training has become a primary driver of recent progress in large reasoning models, and reasoning data are often the key variable determining whether this stage succeeds. Work on post-training reasoning data has grown rapidly, yet this literature remains scattered across dataset papers, reinforcement-learning recipes, reward-model studies, benchmarks, and frontier system reports. This paper is the first primer to synthesize over 150 key public studies and system reports on post-training reasoning data. We organize the field around four questions: what data objects exist, what makes them useful, how they are constructed, and how they scale. Together, this organization provides an attribution framework for future reasoning-data releases and post-training recipes.

While Large Language Models (LLMs) achieve impressive performance on multi-step reasoning tasks, their reliability is persistently hindered by critical limitations such as unconstrained hallucinations and poor numerical computation. Fundamentally, these issues arise because standard models treat reasoning as a transient, one-off generation process rather than retaining and refining successful procedural logic. To address these challenges, we propose eMoT (evolving Memory-of-Thought), a unified framework that stabilizes multi-step reasoning by treating reasoning trajectories as dynamic, evolving memories rather than static templates. The framework primarily consists of three interconnected modules: (i) a memory corrosion mechanism that reinforces high-utility reasoning structures while gradually decaying less frequent ones; (ii) a symbolic anchoring engine that utilizes Python for deterministic computation, much like a human uses a calculator; and (iii) a consistency-driven refinement process that aligns neural inference with symbolic outcomes, reducing the accumulation of logical discrepancies. Across multiple reasoning benchmarks, eMoT improves accuracy and solution consistency over standard Chain-of-Thought and structured reasoning baselines.On the traditional task Game of 24, eMoT achieves 100% accuracy, surpassing the baseline by up to 17.6%. Evaluations on mathematical task GSM8K, ASDiv, SVAMP, and MGSM further show consistent gains in multi-step mathematical reasoning. In our evaluation, we achieve superior performance despite utilizing a lightweight backbone model with constrained baseline capabilities. Compared to alternative methods that rely on massively scaled models, our results demonstrate that the performance gains are fundamentally driven by the eMoT framework's reasoning control rather than sheer model size.

This paper investigates the entropy dynamics of Chain-of-Thought (CoT) and uncovers a consistent two-phase structure: an Uncertainty Region of exploration transitioning sharply to a Confidence Region of convergence. We demonstrate that the Confidence Region possesses two critical properties: 1) High Reliability -- answers in the confidence region become highly accurate and stable, and 2) High Redundancy -- models generate unnecessary tokens long after reaching the correct answer. These properties unlock more efficient and reliable inference strategies: 1) Early Exit leverages reliability and redundancy to terminate computation safely when returns diminish, and 2)Test-Time Scaling uses the Confidence Region signal to prioritize converged trajectories. To operationalize these insights, we formulate Confidence Region detection as a sequential change-point detection problem, being the first to apply classical change-point methods to monitor CoT reasoning. Using the Cumulative Sum (CUSUM) algorithm, a statistically optimal change-point detector, we develop a training-free framework for real-time inference control. Experiments show our approach establishes a superior Pareto-frontier for early exit. CUSUM achieves 63.06% accuracy with 11.1% token reduction, outperforming DEER and Dynasor by 3.28% and 4.36% in accuracy respectively. For test-time scaling, CUSUM-weighted voting consistently outperforms self-consistency.

Large Reasoning Models (LRMs) rely on long reasoning traces, making inference expensive. While low-bit quantization reduces per-token decoding cost, we show that aggressive 2-bit inference can fail to deliver end-to-end speedup because instability in the generation process inflates total token count. Instead of merely lowering answer accuracy, 2-bit quantization often produces much longer traces with repetitive loops, budget exhaustion, delayed commitment, and unclosed reasoning segments. We analyze full reasoning traces of Qwen3 reasoning models across mathematical and commonsense benchmarks and show that accuracy degradation is tightly linked to these process-level failures. To address them, we introduce two lightweight controls: FP16 planning, which gives the 2-bit model a short high-precision outline, and loop rescue, which detects repetitive traces and either commits to an earlier answer or falls back to FP16. On MATH-500, loop rescue improves Qwen3-8B accuracy from 17.2% to 74.2%, while planning plus loop rescue improves Qwen3-32B from 65.0% to 87.2%. Overall, our results show that extreme low-bit reasoning becomes practical when its failures are treated as controllable generation pathologies: with lightweight detection and selective FP16 support, 2-bit inference can recover accuracy while preserving real end-to-end speed. Our code is available at: https://github.com/brain-lab-research/quantized-reasoning.

Large language models achieve remarkable performance via extended chain-of-thought (CoT) reasoning, yet this lengthy process incurs substantial inference overhead. Existing CoT compression methods struggle with inflexible manual length budgets, computationally expensive multi-stage training pipelines, and fragile scalability restricted to small models. We propose HMPO (Hybrid Median-length Policy Optimization), a cost-effective, single-stage reinforcement learning framework. HMPO efficiently compresses CoT via three synergistic components: an adaptive median-based budget derived from successful rollouts to eliminate manual tuning, a cosine-decay token reward for smooth length penalization, and a multiplicative reward formulation that substantially mitigates trivial reward hacking by strictly prioritizing answer correctness. Trained exclusively on mathematical data, HMPO generalizes seamlessly across math, code, science, and instruction-following tasks. Extensive experiments scaling from 9B to 122B parameters across dense and Mixture-of-Experts (MoE) architectures demonstrate that HMPO achieves 19%--46% token compression with negligible accuracy degradation, all while drastically reducing training costs compared to existing multi-stage baselines.

Selecting the best response from multiple small-model samples using a stronger scorer is a simple inference-time strategy, but fails when the small model has already committed to incorrect reasoning paths. PRM guided search avoids this by scoring candidate continuations during generation, but requires a reward model trained with step-level labels. We propose Chunk-Level Guided Generation, a training-free alternative that uses an off-the-shelf large language model as a process scorer. At each step, a small model samples k fixed-length candidate chunks, while the larger model scores the candidates using likelihoods without generating any text. The selected chunk is committed before the next step, steering generation before errors can propagate. We instantiate this framework with two selection rules: Likelihood-Guided Selection (LGS), which selects the chunk with the highest length-normalized large-model log-probability, and Contrastive-Guided Selection (CGS), which subtracts the small model's log-probability to favor chunks where the large model's preference diverges from the small model's. We show that scoring variable-length reasoning steps with large-model likelihoods is unreliable due to a systematic length bias that persists even after length normalization, and that fixed-length chunks avoid this confound. On GSM8K, MATH, Minerva Math, AMC23, and AIME24 with Qwen2.5-1.5B guided by Qwen2.5-32B and Llama-3.2-1B guided by Llama-3.1-70B, CGS outperforms majority voting by up to 28 pp and, under matched guidance budgets, matches or outperforms Qwen2.5-Math-PRM-72B guided search on most benchmarks without reward-model training. With Qwen2.5-7B guided by Qwen2.5-72B, CGS reaches 81.8% on MATH and 63.6% on Minerva Math at k=16, surpassing majority voting by 4--6 pp. Finally, Chunk-Level Guided Generation produces substantially shorter reasoning traces than PRM guided search.

Test-time scaling has become a major way to improve large language model reasoning, but its orchestration has remained designer-engineered: a fixed sample budget, a fixed refinement loop, a fixed scoring rule, or a fixed search policy decides how compute is spent, leaving the model in charge of solving but not of orchestration. We introduce ATLAS, an agentic test-time scaling framework in which an LLM orchestrator owns the control loop end-to-end. Through a single action, explore, which dispatches a fresh independent solver on the original problem, the orchestrator decides whether to gather more evidence, when to stop, and how to synthesize the final answer; the action space is extensible, with each explore call optionally specifying solver, reasoning effort, or prompting strategy. We evaluate ATLAS on four benchmarks covering scientific question answering, code generation, and multimodal reasoning under a Claude Sonnet 4.6 backbone, where it reaches 56.00% on HLE-Verified, 82.29% on LiveCodeBench, 85.75% on GPQA-Diamond, and 23.71% on BabyVision while using far fewer API calls than fixed-workflow baselines. A multi-model extension, ATLAS-MM, that exposes solver choice as an additional action dimension further improves HLE-Verified to 60.00% and LiveCodeBench to 85.63%, with consistent gains on GPQA-Diamond and BabyVision. Ablations replacing the orchestrator's direct synthesis with a separate integrator degrade or fail to improve accuracy on three of four benchmarks, consistent with the role of stateful evidence management in producing the gains.

The effectiveness of Chain-of-Thought (CoT) prompting in Multimodal Large Language Models (MLLMs) remains uncertain: across several visual reasoning benchmarks, CoT prompting often degrades performance compared to direct prompting. In this paper, we provide a systematic analysis of CoT behavior in three modern MLLM families across model scales on datasets requiring step-wise visual evidence. Our analysis identifies two recurring failure modes: premature answer commitment and limited direct visual-token access during rationale generation. We further find that standard CoT-style Supervised Fine-Tuning (CoT-SFT) can mitigate these issues only partially, while often increasing reliance on textual priors and reducing counterfactual visual dependence. Motivated by these findings, we propose Attentive-CoT (Att-CoT), an attention-guided fine-tuning objective that encourages CoT trajectories to delay answer commitment while maintaining sustained visual-token access. Att-CoT can be plugged into any CoT-SFT training run without architectural changes. Experiments on three visual reasoning benchmarks across six MLLMs show that Att-CoT enhances CoT performance over standard fine-tuning.

Ensuring factuality and interpretability in RAG remains an open and urgent problem. We introduce Contrastive Evidence Rationale Attention (CERA), the first retrieval framework to employ subjectivity-based hard negative selection and inject an evidential inductive bias into contrastive learning through an auxiliary attention alignment loss. CERA fine-tunes a dense retriever using two training objectives: triplet-based contrastive learning and interpretable attention alignment, which supervises CLS-to-token attention using a part-of-speech-weighted masking distribution over human-annotated factual rationales as evidence signals. Experiments on a large corpus of clinical trial reports demonstrate that the subjectivity-based hard negative selection substantially improves retrieval effectiveness compared to both Contriever and hard negative selection baselines. Furthermore, rationale alignment improves faithfulness while maintaining competitive retrieval performance, supporting the hypothesis that attention can serve as a more faithful explanation of model behavior when guided by human rationales. Moving beyond topical similarity, CERA enables the retriever to identify the specific tokens that constitute supporting evidence, promoting more interpretable evidence selection in RAG systems.

Despite expanding their multilingual coverage, the advanced reasoning capabilities of LLMs remain largely confined to a few high-resource languages like English. To address this, we propose an unsupervised Reinforcement Learning (RL) approach to enhance multilingual reasoning by enforcing cross-lingual self-consistency: the principle that a model should produce the same final answer for equivalent problems in different languages. Existing methods are limited by the scarcity of multilingual reasoning data and show weak generalization to unseen languages. Our approach requires neither gold answers nor parallel data, and it achieves average gains of up to 21.7% on MGSM across 10 languages. In addition, our method demonstrates strong generalization, with an 18.2% mean improvement on MGSM languages unseen during training, and up to 6.2% gain on 3 out-of-distribution benchmarks. These results show the potential of consistency-based methods to improve the multilingual capabilities of LLMs without requiring supervised data.

Studies of human reasoning have shown that people are typically stronger at evaluating reasoning than producing it from scratch. In contrast, large reasoning models (LRMs) are trained to excel at producing long chains of reasoning to solve complex problems. How then do LRMs perform at evaluating reasons? We investigate this with the Valid-Answer-Invalid-Reasoning (VAIR) dataset: math problems and solutions with trivial reasoning flaws but valid answers, designed to isolate reasoning evaluation from the confound of reasoning production. Unlike humans, who we find are only 6% worse at grading than solving such problems, we find a substantial production-evaluation gap in LRMs: frontier models score as low as 48% when evaluating VAIR solutions, despite near-perfect solution production. Why this enigma? Through chain-of-thought (CoT) analysis, we find evidence of an answer confirmation bias: LRMs often produce then check for the correct answer instead of carefully verifying each step, fabricating rationalizations even when noticing anomalous reasoning. Linear probes corroborate this, showing that while LRM activations encode some representation of valid reasoning, they fail to robustly represent VAIR solutions as invalid. Causal patching of the final answer's representations causes LRM verdicts and activations to flip, demonstrating that answer validity is responsible for models' confirmation biases. These findings indicate an outstanding limitation in dominant approaches to reasoning training, which incentivize LRMs to produce and confirm reasoning towards correct answers, but not to robustly evaluate the underlying reasons.

Reinforcement learning with verifiable rewards (RLVR) has emerged as a powerful paradigm for enhancing the reasoning capabilities of large language models (LLMs). However, its effectiveness is substantially hindered by the prevalence of ineffective training data: many sampled prompts yield response groups that are either entirely correct or entirely incorrect, resulting in zero-variance rewards and limited learning signals. Recent state-of-the-art methods address this issue through extensive LLM rollouts to filter ineffective samples, but at the cost of considerable computational overhead. Alternative approaches, including predictive sampling and trajectory replay, aim to improve data efficiency but often remain insufficient and may introduce additional issues such as systematic bias or suboptimal constraints. To address these limitations, we propose Group Prioritized Off-Policy Optimization (POPO), a simple yet effective framework that fully exploits effective training batches without additional rollout overhead. POPO comprises two key components: prioritized group replay and decoupled off-policy optimization. The former replaces ineffective on-policy groups with effective off-policy groups via a recency-based replay mechanism that jointly considers sample quality and the degree of off-policiness. To further mitigate the off-policy gap, POPO employs decoupled importance sampling to correct off-policy bias while maintaining stable policy updates under consistent trust-region constraints. Empirical evaluations across diverse reasoning tasks, including mathematics, planning, and visual geometry, demonstrate that POPO substantially accelerates RL finetuning and achieves strong reasoning performance with significantly fewer rollouts.

Latent reasoning enables Large Language Models (LLMs) to perform multi-step inference within continuous hidden states, offering efficiency gains over explicit Chain-of-Thought (CoT). However, the opacity of these continuous thought vectors hinders their reliability and controllability. This paper bridges the gap between mechanistic interpretability and actionable control. We first present a systematic analysis using structural, causal, and geometric probes, revealing that latent vectors encode compressed, faithful representations of reasoning steps, with early vectors acting as critical causal hubs. Building on this, we operationalize these interpretability insights into a suite of training-free, decode-time interventions that refine the latent reasoning process by imposing the identified geometric and semantic priors. Extensive experiments across multiple model scales and diverse task domains demonstrate that our approaches consistently improve reasoning accuracy. Our interpretability-guided interventions consistently unlock latent capabilities and improve reasoning accuracy without any parameter updates.

Chain-of-Thought (CoT) has significantly enhanced LLM reasoning, yet often incurs substantial computational overhead due to "overthinking": generating excessively long rationales without commensurate accuracy gains. Existing efficiency methods typically apply uniform compression, which overlooks a critical observation that reasoning complexity is heterogeneous at two distinct granularity: across different problems and within individual reasoning steps. This motivates our principle of Thinking Economically: intelligently allocating computational resources based on intrinsic task and step demands rather than pursuing uniform brevity. We propose Hierarchical Adaptive Budgeter (HAB), a training framework that operationalizes this principle through coarse-to-fine budgeting. At the inter-step level, HAB predicts the optimal reasoning depth for each problem. At the intra-step level, HAB learns step-specific token budgeting signals from PPL-derived step comparisons and an adaptive Pareto optimization objective that captures the local quality-efficiency trade-off, while a Fisher Information-based pruner further provides fine-grained training-time guidance, thereby encouraging the generator to internalize more economical reasoning patterns. Experiments on GSM8K and MATH500 show that HAB not only surpasses standard CoT in accuracy but also reduces token usage, achieving a stronger performance-efficiency trade-off than the compared baselines.