Efficient Chain-Of-Thought Reasoning

We present an efficient method to distill reasoning capabilities into compact video-language models (VLMs) for video question answering (VideoQA). Our approach fine-tunes a 2B-parameter model using only $\sim$900 uncertainty-selected examples, each augmented with synthetic chain-of-thought (CoT) rationales generated by a 4B teacher. Despite its minimal compute cost - under two hours on a single A100 GPU - our method enables the 2B model to outperform VLMs up to 4$\times$ larger, and generalize across CinePile, ActivityNet-QA, and MLVU, approaching the performance of its own 4B teacher. A key finding is that placing CoT rationales after the answer - contrary to standard prompting - substantially improves reasoning in compact models. This insight challenges prevailing CoT conventions and reveals new alignment strategies under limited model capacity. Our findings offer a practical blueprint for training deployable, reasoning-rich VLMs suited for mobile and edge applications.

Recently, multimodal large-scale reasoning models have demonstrated remarkable capabilities in solving complex tasks through long Chains-of-Thought (M-CoT). However, excessively long reasoning trajectories incur substantial computational costs and significant KV-cache pressure. Existing CoT compression and alignment paradigms mainly rely on static rules or single-dimensional preferences, lacking fine-grained cross-modal constraints; as a result, they are prone to inducing visual laziness and hallucinatory reasoning. To address these issues, we propose Modality-Contrastive Preference Optimization (MCPO), a highly sample-efficient two-stage length-compression method that requires fewer than 900 training samples. In the compression stage, we introduce a step-level Normalized Cross-Modal Mutual Information (NCMI) pruning algorithm, which automatically identifies and removes visual-independent reasoning steps by comparing the reasoning discrepancies between with-image and no-image contexts. This significantly reduces redundancy and hallucinatory content in the reasoning chains. In the alignment stage, the model first undergoes supervised fine-tuning to achieve domain-adaptive initialization, followed by optimization using an asymmetric multimodal length-controlled preference loss. This objective adopts a highly nonlinear odds-ratio formulation that provides steep gradients in the with-image context to reinforce length constraints for preferred trajectories, while applying a scaled, flat-gradient linear difference in the no-image context to maintain modality consistency, thereby achieving stable cross-modal preference alignment. Extensive experiments on mainstream base models such as Qwen3-VL-Thinking show that our method can reduce CoT length by up to 69.5% and achieve up to 3.34x end-to-end inference speedup while preserving original accuracy.

Large language models often answer complex reasoning questions without revealing intermediate steps, raising whether they reason latently or complete patterns. We propose the Hidden CoT Detection Score (HCDS), a comparative behavioral and mechanistic signal measuring whether neutral-prompt behavior aligns more closely with explicit CoT or explicit no- CoT. Here, hidden CoT operationally denotes this neutral-prompt CoT-like alignment; HCDS does not directly observe or prove an unexposed reasoning trace. On GSM8K, HCDS is significantly positive for both Qwen3-4B variants (Thinking $+1.87$, $p = 1.2 \times 10^{-7}$; Instruct $+1.41$, $p = 1.9 \times 10^{-4}$), replicates across a different inference stack and quantization within $0.08$ ($+1.80$ and $+1.45$), and is not significantly positive in seven of eight length-adjusted calibration-control cells. The unadjusted score produces large positive scores on single-step arithmetic and numeric factual lookup. The variants also respond differently to no-CoT instructions: Instruct complies from the prompt alone, whereas Thinking continues reasoning and requires intervention. These findings show stronger, less prompt-conditional CoT-like behavior in the reasoning-tuned model, consistent with but not proof of latent reasoning. HCDS thus investigates latent reasoning without relying on models' self-reported traces.

Text-to-image generation has reached photorealistic quality, yet state-of-the-art systems remain unreliable at producing scientific diagrams, whose value depends not on appearance but on physical faithfulness: correct force directions, valid coordinate systems, consistent thermodynamic states, and equations matching the depicted scenario. Trained on web imagery with physically shallow captions, generic models produce diagrams that look plausible but are physically wrong, harmful in education and scientific communication. We present Princigram, a physics-faithful scientific-diagram generator, and its data pipeline. Our central advance is Structured Physical Chain-of-Thought (SP-CoT): a per-subdiscipline schema that decomposes a physics diagram into an explicit multi-step reasoning chain across six subdisciplines, from scene identification through force or process analysis to governing laws and synthesis. Unlike free-form chain-of-thought, SP-CoT follows a fixed schema with strict fidelity rules that separate visually grounded facts from physically inferred reasoning and type all mathematics symbolically; it serves both as dense training supervision and, at inference, as a structured "thinking" prompt. With it we curate and structurally annotate 4.3 million physics images, of which 115,037 carry expert-level annotation, and adapt a unified multimodal backbone. We further introduce VeriphyT2IBench, whose questions are derived from each held-out diagram's own structured annotation: each diagram becomes an item-specific bank of binary questions about its objects, forces, and states, so a judge model's score decomposes into named physical facts rather than one holistic number. On the physics subset of GenExam and on VeriphyT2IBench, Princigram shows that explicit physics-structured supervision improves the physical faithfulness of generated scientific diagrams.

Ultra-long egocentric video understanding requires reasoning over temporally sparse evidence distributed across hours or days, challenging current multimodal models with limited context and the grounding of key video segments. While Chain-of-Tool-Thought (CoTT) agent systems enable iterative retrieval and inspection, they suffer from error propagation due to rigid zoom-in strategies that lack recovery mechanisms. In this work, we address these challenges through SCOUT (Self-Checking Chain-Of-Tool-thought), a recovery-aware agentic framework introducing an adaptive policy that evaluates intermediate tool observations and dynamically trades off exploitation (zoom-in) and exploration (region switching), enabling robust multi-hop reasoning over extremely long horizons. However, training such multi-turn tool-using agents remains challenging, as existing RL methods rely on sparse outcome-level rewards and lack supervision over extended decision trajectories, resulting in suboptimal credit assignment for long-horizon reasoning. To address this, we develop UPS-GRPO, an uncertainty-prioritized policy optimization method that concentrates exploration on high-uncertainty post-tool states while preserving sample efficiency. We further introduce a turn-level advantage decomposition that integrates outcome rewards with tool-grounded temporal alignment rewards for improved credit assignment. Experiments show that SCOUT achieves state-of-the-art results on ultra-long egocentric benchmarks, while remaining competitive on shorter-horizon long-video settings.

The Tower of Hanoi is a simple planning puzzle that in prior work has proven challenging for large reasoning models (LRMs). Current models solve the standard formulation of the puzzle, but still struggle with the flat-to-flat variant (where initial and goal states are not restricted to have all rings on a single peg). This paper presents an in-depth study of how both small, in-house Transformers and large, third-party LRMs solve this task. To understand the failures mechanistically, we first train small Transformers from scratch on precomputed solution traces. Using a variety of interpretability techniques, we show that these Transformers develop an emergent world model: a linearly decodable, geometrically faithful representation of the puzzle's state space (the Sierpinski triangle), that is causally involved in solving the puzzles. Second, we return to the large LLMs and apply our techniques to two frontier reasoning models, Qwen3.6-27B and DeepSeek-R1-Distill-Qwen-32B, that attempt to solve the task through extended chain-of-thought. Surprisingly, we find that both models encode the Sierpinski world model near-perfectly at the end of the prompt, and yet fail at the majority of tasks when there are more than 3 rings. We locate the source of this failure in the decaying representation of the world model. We probe for the representation at different stages during planning, and establish causality by showing that performance can be improved by injecting the prompt-time representation at inference. The failure of the models is thus one of maintenance of the required representations, not their absence, and performance is at least partially recoverable. These results thus reframe the reported collapse in performance from prior work: current Large Reasoning Models build a world model, and then lose it.

World Action Models (WAMs) aim to construct a unified architecture capable of understanding world state evolution and guiding to generative motion planning. However, existing visual branches focus on predicting static visual observation, rather than reflecting potential transition information that captures the evolution of world states under motion interactions. This leads to representational entanglement between high-level physical condition evolution and low-level action trajectory generation within the Action Model, creating a structural bottleneck while weakening the predictive capability of world evolution modeling for action generation. We propose PILOT (Physical Inference for Latent Optimized Trajectories), whose core Representational Deduction (RD) bridges this gap by integrating motion thought-of-chain (CoT) guidance as a native model capability. Specifically, RD aims to encourage the action branch to explicitly model potential state transition tokens, which are retained as CoT in the reasoning space to guide fine-grained motion trajectory. Experiments demonstrate that RD not only significantly improves the success rate and generalization ability of WAMs in complex robotic manipulation tasks but also enhances the model's physical interpretability by decoupling high-level motion semantics from low-level trajectory details. Furthermore, the abundant state transition supervision signals introduced by RD effectively alleviate the sparse supervision in action generation, enabling it to serve as an efficient few-shot real-robot fine-tuning strategy and demonstrating superior scalability for migration to mainstream WAM architectures.

Creating sprint backlogs requires considerable effort, as items such as epics, user stories, and tasks can be missed or inconsistently specified. We propose a multimodal approach to support backlog generation from visual app mockups, an artifact available at early project stages. We evaluate three prompting strategies on GPT-4o: a zero-shot baseline, Compositional Chain-of-Thought (CCoT) for vision-language reasoning, and a persona-driven prompt. We study seven app development projects across two countries and interview developers about the results. Overall, we observed that the baseline prompt favours recall over precision, whereas CCoT is more balanced, achieving average F1 scores of 52-66% for epics and user stories. Tasks were more challenging to generate accurately. Precision gains were most consistent when adding architectural context, particularly for backend tasks (precision gains up to 35%). Interviews with developers revealed that up to 26% of false positives were still considered useful, reflecting the creative and open-ended nature of backlog creation. To capture this, we propose a new measure called Revised Recall, which complements ground-truth evaluation with developer assessments. Our findings suggest that hybrid prompting with architectural context can assist backlog generation from early mockups, though results vary by item type and developer oversight remains necessary.

Existing vision-language navigation methods often couple a VLM with waypoint decoders to produce multi-step action plans, but they typically lack an explicit closed-loop mechanism for tracking semantic progress, diagnosing execution failures, and recovering from error accumulation in long-horizon navigation. To address this gap, we propose ReflectVLN, an agentic VLN framework that organizes decision-making through bidirectionally interactive intention and execution agents. The intention agent performs subtask decomposition and reflection, generating executable subtask descriptions as corrective plans. Conditioned on these descriptions, the execution agent grounds them into short-horizon actions under current observations while monitoring sub-goal progress and detecting off-track behavior. Crucially, ReflectVLN enables closed-loop bidirectional communication: the execution agent emits progress and deviation signals to trigger reflection and subtask updates on demand, and the intention agent returns structured guidance that reconditions subsequent actions for recovery. To encourage temporally coherent decisions with interpretable intermediate rationales, we introduce Action Chain-of-Thought (Action-CoT), a path-conditioned dual-query training scheme for action generation. Experiments on standard VLN benchmarks show that ReflectVLN improves success rates and path efficiency under a constrained data budget, with favorable training cost and fewer high-level intention calls at inference time, while providing interpretable intermediate decisions for analysis and collaboration. Code is available at: https://github.com/AIprogrammer/ReflectVLN

Patent claim drafting is a challenging legal drafting task that requires technical expertise, precise linguistic control, strict adherence to formal conventions, and the preservation of complex logical relationships among claim elements. While Chain-of-Thought (CoT) prompting has been widely used to improve the reasoning capabilities of large language models (LLMs), recent evidence suggests that its benefits may be limited, or even negative, in highly structured or pattern-sensitive tasks. Therefore, this paper investigates whether CoT prompting benefits patent claim generation. We propose a task-specific CoT method for patent claim generation and evaluate its effectiveness through both automatic metrics and human expert assessment. Our results show that reasoning-enhanced prompting can improve claim quality. Moreover, we demonstrate a counter-intuitive but important empirical finding: implicit CoT, where reasoning is kept internal rather than explicitly verbalized, consistently outperforms explicit CoT. Through systematic analysis, we show that explicit CoT can introduce an unnecessary information bottleneck for claim generation. Verbalized reasoning may compromise the quality of final outputs through three specific mechanisms: abstraction of critical details, disruption of internalized generation patterns, and cascading error propagation. Our findings provide new insights into legal tasks and CoT applications.

Embodied Chain-of-Thought has emerged as a promising mechanism to enhance robot decision-making and interpretability in black-box Vision-Language Action (VLA) models. However, whether this verbalized Chain-of-Thought truthfully reflects the policy's underlying decision process remains poorly understood. We distinguish between functional reasoning, in which reasoning improves task performance, and faithful reasoning, in which reasoning truly reflects the policy's internal decision process. We argue that SoTA alignment strategies offer a necessary but insufficient notion of faithfulness, admitting reasoning whose intermediate steps can mask the causal links in action prediction through confounding factors (e.g., reasoning that is ungrounded in the environment and internally disconnected or inconsistent), restricting policy generalization. We study this gap through a human evaluation of a SoTA reasoning model for autonomous driving, revealing an inconsistent coupling between reasoning quality and downstream trajectory improvement. We then operationalize a behavioral surrogate for embodied faithfulness through a learned critic, Pinocchio, scoring observation grounding and stepwise coherence, and use this critic as a dense reward signal in post-training an embodied policy with reinforcement learning. Across withheld driving benchmarks, our post-trained planner improves faithfulness by 4% and 18% over SoTA alignment and trajectory error post-training baselines, respectively, while maintaining competitive downstream task performance. Finally, on a synthetic out-of-distribution test set, post-training for faithfulness improves policy responsiveness to rare counterfactual scenarios by 1.6x that of a SoTA policy, suggesting that faithful reasoning traces contribute to more robust, generalizable, and interpretable embodied intelligence. Project page: https://mjf-su.github.io/pinocchio/

Safety alignment in large language models is typically evaluated against direct, imperative harmful requests. We show that this alignment is highly conditioned on pragmatic register: models that refuse a direct request frequently comply when the same underlying objective is expressed through a different communicative stance. This suggests that current alignment policies are not invariant to semantic equivalence, but remain sensitive to how a request is pragmatically framed. We introduce Retroactive Chain-of-Thought (RetroCoT), a single-turn attack that reframes harmful requests as forensic reconstruction tasks. Rather than requesting harmful instructions directly, RetroCoT presupposes that the harmful outcome has already occurred and asks the model, acting as a forensic analyst, to reconstruct in reverse the causal chain that produced it. On AdvBench (n=50), RetroCoT achieves attach success rate of 58% on gpt-4o and 52% on gpt-4o-mini, compared with direct-request baselines of 0% and 4%, respectively. We further identify a pronounced generation gap: GPT-5-family models refuse RetroCoT entirely, explicitly identifying the reconstruction premise in their refusal rationales, consistent with explicit coverage of this reconstruction register. However, this robustness does not generalize across pragmatic forms. A single adversarial feedback turn presenting an existing forensic reconstruction response alongside evaluator critique raises ASR from 0% to 48% on GPT-5.4-mini and from 58% to 94% on GPT-4o; a control condition omitting the fabricated low score achieves 85% on GPT-5.4-mini, indicating that the operative element is pragmatic continuation within the established forensic frame rather than score manipulation. These results suggest that frontier-model alignment remains conditioned on pragmatic framing rather than semantic intent, and that new pragmatic registers can continue to expose a...

Frontier LLMs can perform multi-step reasoning over content-free filler tokens like dots or counting sequences, producing correct answers with no visible chain-of-thought (CoT). This is a limit case for behavioral oversight, where surface tokens carry no information about the underlying reasoning. But hidden from the output is not the same as hidden from us. On four task families (fact retrieval, parallel numeric composition, string manipulation, and in-context computation), two open-weights frontier models (DeepSeek V3, Kimi K2) compute over filler tokens in a structured, legible way: attention routes the question through the filler region to the answer, logit-lens readouts show retrieved facts emerging early and their composition crystallizing in late layers, and KV-cache transplants at filler positions causally swap outputs between examples. We introduce an unsupervised decoding pipeline that takes only hidden states as input and recovers intermediate values with 80-95% accuracy (best LLM judge) across both models and all four tasks, without ground-truth labels or training. Hidden computation that defeats behavioral CoT monitoring is, on these tasks, directly readable from the residual stream, suggesting monitorability is a property of the model's full computational trace, not just its surface tokens.

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.

Standard chain-of-thought on moral dilemmas exhibits two failure modes: stakeholder collapse (the trace names at most one party with a stake in the outcome) and uncertainty suppression (no explicit unknowns or hedges before committing to an action). We introduce narration-of-thought (NoT), a system prompt that structures chain-of-thought into five sections: protagonist, stakeholders, two-step consequences, uncertainty, then commitment. NoT adds no training, parameters, or fine-tuning. On 100 DailyDilemmas scenarios across four generators from three vendors, NoT cuts stakeholder collapse from up to 31% to under 1% and uncertainty suppression from up to 72% to 1-24% on every model. A matched-budget verbose-CoT control rules out token spend as the active ingredient; NoT retains Cliff's delta advantages of +0.79 to +0.90 on stakeholder count and +0.65 to +0.93 on uncertainty score for three of four generators, and a section ablation attributes each shift to its specific sub-instruction. Textual-gradient descent initialised at NoT improves the scaffold further; a cross-family training judge (different vendor from the generator) dominates an in-family one on every measured axis. Extended to a five-round multi-stakeholder debate protocol, the scaffold converts a 6% standoff into 95% full consensus on a calibration set and 100% combined convergence on a DailyDilemmas replication. The resulting traces externalise the stakeholders, consequences, and uncertainty grounding each commitment, providing an auditable substrate for dependable agentic deployment.

Recent LLMs demonstrate strong mathematical reasoning capabilities, but existing gains rely heavily on English-centric training resources and benchmarks. As a result, reasoning performance degrades substantially in low-resource languages such as Urdu, where reasoning-oriented datasets and adapted models remain scarce. Urdu lacks both reasoning-oriented resources and models adapted for multi-step mathematical problem solving, limiting the applicability of recent progress to Urdu-speaking users. We address this gap through Riazi-8B, an Urdu mathematical reasoning model developed through a two-step adaptation process comprising continued pre-training on Urdu Wikipedia and supervised fine-tuning on Urdu Chain-of-Thought data derived from GSM8K. We evaluate Riazi-8B on MGSM-Urdu against existing Urdu instruction-tuned models. Our results show consistent improvements in answer correctness, reasoning quality, response completeness, and Urdu generation. Our findings demonstrate that combining Urdu language adaptation with reasoning-focused fine-tuning is an effective strategy for extending mathematical reasoning capabilities to low-resource languages.

Test-time scaling improves language-model reasoning, but existing approaches often face a difficult trade-off: long chain-of-thought sampling remains single-threaded, while sentence- or solution-level search can be computationally expensive and hard to train end-to-end. We introduce Local Branch Routing (LBR), a token-level test-time scaling framework that expands a small local lookahead tree, forwards all sampled branches through the language model, and uses a lightweight router to select the depth-1 subtree to commit. By routing over the hidden states of candidate local futures, LBR allows each token decision to use evidence beyond the root next-token distribution while avoiding full solution-level search. The resulting prune-shift-grow decoding process preserves discrete branch identities and defines a tractable tree-trajectory likelihood: newly grown nodes are counted when first sampled, and router decisions are assigned explicit probabilities. This enables end-to-end reinforcement learning with verifiable rewards, jointly optimizing the base model and router under the same likelihood-ratio principle as discrete-token RLVR. On synthetic hierarchical-planning tasks, LBR shows that post-candidate hidden states provide useful routing evidence. On mathematical reasoning benchmarks, LBR improves both Pass@1 and Pass@32 over discrete chain-of-thought, vanilla discrete-token RLVR, and RL-compatible soft-token branching baselines. These results suggest that lightweight local branching offers an efficient, trainable, and discrete form of language-model test-time scaling.

Unified multi-modal large language models (MLLMs) have achieved strong text-to-image generation quality, but still struggle with structure-aware prompt following, where object counts, spatial relations, attribute bindings, and coarse layouts must be preserved. We attribute this limitation in part to the entanglement of structural planning and appearance rendering within a single conditioning stream. To address this issue, we propose Implicit Visual Chain-of-Thought (IV-CoT), a latent visual reasoning framework for query-conditioned image generation. IV-CoT decomposes the visual conditioning queries into a structural-to-semantic cascade, where structural queries first form a latent visual plan and semantic queries then render appearance conditioned on this plan. To guide the structural queries, we introduce training-only sketch supervision, which encourages them to capture structure from sketches without requiring sketch extraction or intermediate decoding at inference time. IV-CoT performs implicit CoT reasoning in a single forward pass and achieves superior results on GenEval and T2I-CompBench. Visualizations and analyses demonstrate that the learned structural and semantic queries play complementary roles in structure-aware generation.

Pointing-based visual grounding requires models to precisely locate target objects by deciphering complex spatial relationships between the visual scene and pointing gestures. Traditional methods typically encode input images into static feature representations and perform reasoning primarily within the linguistic domain, often overlooking the rich perceptual cues and explicit spatial geometry inherent in images. In this study, we aim to mitigate the cognitive vulnerability of models in interpreting gestural spatial relations by proposing PointVG-R, a reasoning-guided Multi-modal Large Language Model (MLLM). PointVG-R introduces geometric-aware reasoning for pointing-based grounding, enabling the model to think with images through the strategic integration of Reinforcement Learning (RL) and cold-start data. Specifically, we design a novel geometric reasoning pipeline that simulates the iterative cognitive process humans employ when interpreting pointing gestures. Furthermore, we construct EgoPoint-CoT, a high-quality visual Chain-of-Thought (CoT) dataset featuring detailed reasoning trajectories to guide the model via Supervised Fine-Tuning (SFT) and RL. To address the varying quality of learning signals encountered during training, we further propose an Adaptive Importance Weighting strategy based on Group Variance, which dynamically adjusts reward signals to optimize the learning process. Experimental results demonstrate that PointVG-R achieves SOTA performance, outperforming the baseline by $\textbf{15.86}$ points in mIoU. Extensive ablation studies further validate the efficacy of our proposed modules. Code: https://github.com/lingli1724/PointVG-R.

Understanding the causal structure of a language model's thought process is a problem of significant importance for both transparency and safety. In this work, we take a local approach toward this goal by analyzing the causal relationships among individual components, termed units, of a given, specific chain-of-thought trace. We construct a structural causal model on these units and relate each unit to the log probability of generating (subsequent) output units. Our algorithm, termed AttriCoT, is a black-box method that performs attribution by estimating importance parameters in the structural causal model using $O(U)$ forward passes through the model, where $U$ is the number of units. Evaluation of perturbation curves across 5 datasets and 4 reasoning models shows that AttriCoT produces attributions that are more faithful to the model's behavior than alternative methods. The attribution results also reveal notable differences in thought structure between models and domains.

Small-scale Large Language Models (LLMs) natively default to literal semantic interpretations, making few-shot irony detection a persistent challenge in noisy, user-generated text. In this study, we show that, despite this limitation, inference from compact LLMs can still be effectively harnessed for this task. We introduce the Robust Dual-Signal (RDS) Fusion framework, a hybrid neuro-symbolic architecture that utilizes a compressed Chain-of-Thought (CoT) of an LLM, alongside a static, pretrained RoBERTa and a symbolic prior module in two downstream fusions. RDS Fusion demonstrates better performance than an unrestricted reasoning ablation, while requiring substantially lower inference time. We also find that in our experiments, unrestricted reasoning does not yield better results than restricted reasoning. Evaluated on a strictly held-out TweetEval test set ($N=734$), RDS Fusion achieves $78.1\%$ accuracy and a Macro F1 of $0.777$, which is comparable to a finetuned BERTweet-base. On the heavily imbalanced iSarcasm dataset, the frozen CoT pipeline suppresses $22.5\%$ of baseline false positives, yielding a Macro F1 of $0.6726$ and Ironic F1 of $0.4821$, outperforming multiple heavily supervised SemEval transformer ensembles. Paired McNemar's tests show that, while adding the symbolic prior to the neural baseline yields an insignificant gain, and the RDS Fusion is statistically insignificant compared to the combined RoBERTa and symbolic prior ablation; the concurrent fusion achieves a statistically significant improvement over the standalone baseline ($p=0.005$).

Multimodal large language models (MLLMs) excel at visual reasoning but rely on text-based chain-of-thought (CoT), lacking interpretable visual intermediates. Existing methods use opaque tokens or external tools, missing key properties. We propose Gen-VCoT, a framework using expert vision models to generate RGB images as reasoning intermediates. It has three stages: visual grounding (SAM segmentation), geometric reasoning (Marigold depth maps), and semantic reasoning (Qwen2-VL integration). An adaptive router selects reasoning depth. Evaluations show Gen-VCoT improves spatial (25% better) and depth (50% better) questions, but may hurt simple factual queries. Text CoT outperforms visual intermediates on CLEVR (91.2% vs 62.5%), showing task-dependent optimal representations. Gen-VCoT establishes a new paradigm for interpretable multimodal reasoning.

Embodied reasoning requires models to perceive task-relevant objects and spaces in physical environments and maintain consistent visual grounding throughout multi-step reasoning. However, current vision-language models rely on text-only or coordinate-augmented chain-of-thought, where entity references remain implicit and ambiguous. This may cause the reasoning process to decouple from visual evidence, entity references to drift across steps, and a causal disconnection between the reasoning trajectory and the final answer, with these problems further amplified in multi-view scenarios due to cross-view appearance changes. To address these issues, we propose Pinned Chain-of-Thought (PinCoT), a structured reasoning paradigm that pins every reasoning step to visual evidence. PinCoT introduces the concept of reasoning anchor, which binds each task-relevant entity to a structured visual anchor with entity name, unique identity, view index, and spatial grounding, enabling consistent entity tracking across reasoning steps and views. We build a fully automated data generation pipeline to construct PIN-170K, a high-quality PinCoT-formatted reasoning dataset. We then train RoboPIN through three-stage post-training that progressively injects embodied knowledge, structured reasoning ability, and process-supervised alignment, with rewards that directly constrain both anchor localization and identity consistency during reasoning. On 14 benchmarks covering embodied spatial reasoning, multi-view reasoning, and pointing, RoboPIN with only 4B parameters consistently outperforms 7B level open-source embodied models, achieving a 12% average improvement over the strongest 7B baseline, Mimo-Embodied. Further analysis shows that PinCoT improves grounding accuracy and cross-step identity consistency, validating the effectiveness of process supervision.

Trusted monitoring is a cornerstone of AI control. However, as frontier models grow more capable, the increasing capabilities gap between trusted and untrusted models may render trusted models unreliable monitors. We introduce \emph{bootstrapped monitoring}, a protocol that addresses this by inserting a stronger, intermediate untrusted model with transparent chain-of-thought reasoning into the oversight chain. The untrusted monitor ($U_m$) evaluates the agent's actions, while a weaker trusted model ($T$) oversees $U_m$'s reasoning to detect collusion. We evaluate bootstrapped monitoring on multi-turn software engineering tasks (BashArena) across multiple agents and monitors. Bootstrapped monitoring substantially improves catch rates over trusted-only monitoring, even when the untrusted monitor actively colludes with the agent, provided we have access to its raw chain-of-thought. Our results suggest that bootstrapped monitoring can extend the useful lifetime of trusted models in control as AI capabilities advance.

Generative recommendation models in the OneRec family have been widely deployed in many real-world services, such as short-video, live-streaming, advertising, and e-commerce. However, these generative models can only benefit from the scaling advantage, while their reasoning ability is hard to activate, since we cannot construct meaningful Chain-of-Thought (CoT) sequences consisting of itemic tokens only. Inspired by the success of the reasoning-style ``think before answer'' paradigm in the LLM field, we conduct preliminary studies (i.e., OneRec-Think, OpenOneRec) to explore reasoning capability in generative recommendation. Nevertheless, we notice an unexpected phenomenon: the thinking mode does not show advantages over the non-thinking mode. Drawing insights from recent findings on CoT robustness in multi-modal language models, we argue that effective reasoning in recommendation rests on two factors: perception, the ability to ground itemic tokens in their underlying language semantics, and cognition, the ability to reorganize a user's behavior sequence into coherent latent interest points. We therefore propose OneReason, which includes: (1) strong itemic token perception in pre-training, (2) a three-level cognition-enhanced CoT format for recommendation tasks in SFT, and (3) a specialize-then-unify training recipe in RL to enhance the thinking ability.

Implicit chain-of-thought (iCoT) methods aim to internalize reasoning in large language models, but often underperform explicit CoT prompting. We empirically find that hidden-state reasoning trajectories exhibit low-rank structure. Motivated by this observation, we propose a low-rank distillation framework that transfers reasoning by aligning teacher and student trajectories in a shared low-rank tensor subspace using first- and second-order statistics. The resulting formulation captures the global structure of reasoning while supporting a compact latent reasoning process. We evaluate the method across multiple model families, including LLaMA and Qwen, at different scales on mathematical reasoning benchmarks. Our approach consistently improves performance, especially on challenging multi-step tasks, approaching explicit CoT accuracy and outperforming prior iCoT distillation methods.

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.

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.

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.

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.

Recent advances in Large Reasoning Models have significantly improved chain-of-thought (CoT) capabilities via reinforcement learning (RL). However, generated reasoning chains frequently suffer from structural redundancy (i.e., \emph{overthinking}), incurring high computational overhead without improving answer correctness. Existing mitigation strategies typically rely on token-uniform length penalties, which provide coarse, segment-agnostic pressure toward shorter outputs and can inadvertently suppress useful reasoning alongside redundancy. To address this, we demonstrate that inefficiency concentrates in high-probability segments with low marginal utility. We derive a theoretical characterization of segment suboptimality under the correctness-length trade-off objective and propose \textsc{SLAT} (Segment-Level Adaptive Trimming), an RL framework that selectively suppresses redundant segments based on this criterion. Empirical results on standard benchmarks indicate that \textsc{SLAT} establishes a superior accuracy-efficiency Pareto frontier, reducing reasoning length by $50\%$ relative to uncompressed baselines while maintaining competitive accuracy. Overall, our results suggest that theoretically grounded, segment-aware trimming is a promising direction for efficient CoT reasoning in large language models.

Chain-of-thought prompting and looped Transformers both give a fixed model more test-time computation, but they differ in what they remember. Chain-of-thought stores intermediate state in generated tokens that remain in the context, whereas a looped Transformer carries state through recurrent hidden activations. We argue that this persistent mutable memory is a central resource for test-time reasoning. We compare three memory regimes, the compressed latent loop, the full sequence-state loop, and the chain-of-thought scratchpad. Our main result shows that a compressed loop is limited by the size of its recurrent state. Running the loop longer adds computation but does not by itself create a growing scratchpad, so a loop with a small recurrent state remains a small-space reasoner even when run for many steps. Under a standard complexity assumption, such loops cannot decide problems that are P-complete under logspace reductions, whereas polynomial-length chain-of-thought can. The separation is specific to compressed loops, as full sequence-state loops carry state at every input position and live in a memory-rich regime closer to explicit scratchpads. Controlled pointer-chasing and associative-recall sweeps illustrate this memory-budget view, with performance sensitive to whether the persistent-state budget matches the task's working-memory demand.

Large reasoning models (LRMs) often generate extensive chain-of-thought (CoT) traces before producing a final answer. As explicit textual artifacts, these traces can be passed to other models to solve the same task, enabling cross-model reasoning transfer. Yet successful transfer alone does not reveal how the provided CoT contributes to another model's answer. We study this question with a controlled provider--receiver framework, where a provider generates a reasoning trace and a receiver solves the same problem from increasingly longer trace prefixes. We compare force-answer, where the receiver answers directly from the prefix, with free-generation, where it may continue reasoning before answering. Across models and benchmarks, full traces often transfer successfully, but prefix trajectories reveal distinct mechanisms. In force-answer mode, AIME transfer is largely driven by explicit answer availability. MMLU-Pro instead reflects a larger role for receiver competence, while ZebraLogic depends on partial structured-answer information rather than complete-answer leakage alone. In free-generation mode, partial CoTs improve performance across benchmarks, indicating that prefixes can guide continued reasoning. Finally, answer agreement among receivers provides a gold-free signal for stopping provider reasoning early. Overall, cross-model CoT transfer is not a single phenomenon: it can reflect answer extraction, reasoning scaffolding, or receiver-dependent competence.

Chain-of-Thought (CoT) prompting substantially improves the sample efficiency of transformers, reducing the complexity of tasks like parity learning from exponential to polynomial in the input length. However, generating explicit reasoning steps at inference is computationally expensive. Implicit Chain-of-Thought (ICoT) has emerged as a promising empirical remedy that trains models to internalize intermediate steps within their hidden states, but its theoretical foundations remain poorly understood. We give the first theoretical analysis of ICoT, proving that an $L$-layer transformer trained under our proposed Log-ICoT curriculum learns $k$-parity with $\mathsf{poly}(n)$ samples and $L = \log_2 k$ training stages. This matches the sample efficiency of explicit CoT while eliminating its inference overhead, and extends prior one-layer parity guarantees to multi-layer architectures. Compared to standard ICoT, which removes thinking tokens one at a time, Log-ICoT removes them in geometric chunks, reducing the number of stages from linear in $k$ to logarithmic. Experiments on multi-layer transformers confirm the theory and visualize how reasoning is progressively absorbed into deeper layers.

Implicit Chain-of-Thought (CoT) reduces the inference cost of large language models by internalizing the explicit rationales. However, existing approaches typically lack alignment with explicit rationales and adaptivity to example complexity. In this work, we propose CIRF (\textit{\underline{C}hain-of-thoughts \underline{I}nto \underline{R}eusable \underline{F}unctional units}), an implicit CoT framework that performs reasoning as a dynamic sequence of discrete functional tokens. CIRF assigns a functional token to each semantically coherent reasoning unit in explicit CoT traces. The model is then fine-tuned to autoregressively generate functional tokens and their optional results, followed by the final answer. This design aligns latent reasoning with a sequence of functional units, facilitating parallel training, explicit rationale alignment, and adaptive reasoning. Extensive experiments on mathematical, symbolic, and commonsense reasoning benchmarks show that CIRF provides a favorable accuracy-latency trade-off compared with state-of-the-art implicit CoT methods. Further analyses demonstrate that CIRF constructs distinct, interpretable functional tokens, leading to consistent performance improvements.

Recent advances in large language models (LLMs) have shown that Chain-of-Thought (CoT) reasoning can substantially improve performance on complex reasoning tasks. At the same time, In-Context Learning (ICL) has become an important mechanism for adapting LLMs to new tasks without updating model parameters, using only examples provided in the prompt. However, standard ICL often struggles on tasks that require multi-step reasoning, because the demonstrations usually contain only input-output pairs and lack explicit intermediate reasoning steps. This paper introduces an Automatic Chain-of-Thought (Auto-CoT) framework to improve ICL by automatically constructing reasoning-enhanced demonstrations. Auto-CoT generates reasoning chains for input-output examples, augments the prompt context with structured intermediate explanations, and removes irrelevant or low-quality demonstrations through a systematic selection process. By incorporating high-quality reasoning examples into the ICL prompt, Auto-CoT guides the model toward more reliable reasoning and improves prediction accuracy. Experiments across multiple reasoning tasks demonstrate that the proposed framework improves ICL performance by providing explicit intermediate reasoning guidance.

Multimodal large language models are increasingly expected to perform thinking with images, yet existing visual latent reasoning methods still rely on explicit textual chain-of-thought interleaved with visual latent tokens. This interleaved design limits efficiency and keeps reasoning fragmented across separate text and vision channels. We propose UniVLR, a unified visual latent reasoning framework that treats textual reasoning and auxiliary visual evidence as a shared visual workspace. Instead of preserving text CoT as an independent inference-time path, UniVLR renders reasoning traces together with auxiliary images and learns to compress this unified representation into compact visual latent tokens. At inference time, the model reasons only through visual latents and directly decodes the final answer, avoiding both external tool calls and verbose text reasoning. Experiments on real-world perception and visual reasoning tasks show that UniVLR outperforms prior visual latent reasoning methods while using substantially fewer generated reasoning tokens, suggesting a more unified and efficient paradigm for visual thinking in MLLMs.

Chain-of-thought reasoning is often treated as a monotone way to improve language-model accuracy by letting a model think longer. We identify a countervailing effect, the coupling tax: when reasoning traces and final answers share one output-token budget, long traces can crowd out the answer they are meant to support. Across GSM8K, MATH-500, and five BIG-Bench Hard tasks with Qwen3 models at three scales, non-thinking mode matches or outperforms thinking mode on GSM8K and MATH-500 at every budget up to 2048 tokens, while harder tasks shift the crossover to larger budgets. We derive a truncation-waste decomposition, $\mathrm{Acc}_{\mathrm{think}}(b)=α_c F_L(b)+α_t(1-F_L(b))$, that predicts this crossover from chain-length and accuracy statistics and explains inverse scaling within the Qwen family. A DeepSeek-R1-Distill-Llama-8B replication shows the same pattern under a different thinking interface. As a mitigation, split-budget generation decouples reasoning and answer budgets; on full MATH-500, IRIS reaches 74.0% accuracy, a strengthened extraction variant reaches 78.8%, and a fixed non-oracle SC+IRIS gate reaches 83.6%. The results show that test-time reasoning should be evaluated as a budget-allocation problem, not only as a question of whether longer traces are available.

While Large Language Models (LLMs) excel in certain reasoning tasks, they struggle in multi-agent games where the final outcome depends on the joint strategies of all agents. In multi-agent games, the non-stationarity of other agents brings significant challenges on the evaluation of the reasoning process and the credit assignment over multiple reasoning steps. Existing single-agent reinforcement learning (RL) approaches and their multi-agent extensions fail to address these challenges as they do not incorporate other agents in the reasoning process. In this work, we propose Strat-Reasoner, a novel RL-based framework that improves LLMs' strategic reasoning ability in multi-agent games. We introduce a novel recursive reasoning paradigm where an agent's reasoning also integrates other agents' reasoning processes. To provide effective reward signals for the intermediate reasoning sequences, we employ a centralized Chain-of-Thought (CoT) comparison module to evaluate the reasoning quality. Finally, we compute an accurate hybrid advantage and develop a group-relative RL approach to optimize the LLM policy. Experimental results show that Strat-Reasoner substantially improves strategic abilities of underlying LLMs, achieving 22.1% average performance improvements across various multi-agent games. Code is publicly available at https://github.com/ydhe1012/Strat-Reasoner.

Time series (TS) reasoning models (TSRMs) have shown promising capabilities in general domains, yet they consistently fail in the financial domain, which exhibits unique characteristics. We propose a general 2 x 2 capability taxonomy for TSRMs by crossing 1) single-entity vs. multi-entity analysis with 2) assessment of the current state vs. prediction of future behavior. We instantiate this taxonomy in the financial domain-where the distinction between deterministic assessment and stochastic prediction is particularly critical-as ten financial reasoning tasks, forming the FinTSR-Bench benchmark based on S&P stocks. To this end, we propose FinSTaR (Financial Time Series Thinking and Reasoning), trained on FinTSR-Bench with distinct chain-of-thought (CoT) strategies tailored to each category. For assessment, which is deterministic (i.e., computable from observable data), we employ Compute-in-CoT, a programmatic CoT that enables models to derive answers directly from raw prices. For prediction, which is inherently stochastic (i.e., subject to unobservable factors), we adopt Scenario-Aware CoT, which generates diverse scenarios before making a judgment, mirroring how financial analysts reason under uncertainty. The proposed method achieves 78.9% average accuracy on FinTSR-Bench, substantially outperforming LLM and TSRM baselines. Furthermore, we show that the four capability categories are complementary and mutually reinforcing through joint training, and that Scenario-Aware CoT consistently improves prediction accuracy over standard CoT. Code is available at https://github.com/seunghan96/FinSTaR.

While long, explicit chains-of-thought (CoT) have proven effective on complex reasoning tasks, they are costly to generate during inference. Non-verbal reasoning methods have emerged with shorter generation lengths by leveraging continuous representations, yet their performance lags behind verbalized CoT. We propose $\textbf{Abstract Chain-of-Thought}$, a discrete latent reasoning post-training mechanism in which the language model produces a short sequence of tokens from a reserved vocabulary in lieu of a natural language CoT, before generating a response. To make previously unseen ''abstract'' tokens useful, we introduce a policy iteration-style warm-up loop that alternates between (i.) bottlenecking from a verbal CoT via masking and performing supervised fine-tuning, and (ii.) self-distillation by training the model to generate abstract tokens from the prompt alone via constrained decoding with the codebook. After warm-up, we optimize the generation of abstract sequences with warm-started reinforcement learning under constrained decoding. Abstract-CoT achieves up to $11.6\times$ fewer reasoning tokens while demonstrating comparable performance across mathematical reasoning, instruction-following, and multi-hop reasoning, and generalizes across language model families. We also find an emergent power law distribution over the abstract vocabulary, akin to those seen in natural language, that evolves across the training phases. Our findings highlight the potential for post-training latent reasoning mechanisms that enable efficient inference through a learned abstract reasoning language.

State-of-the-art reasoning models utilize long chain-of-thought (CoT) to solve increasingly complex problems using more test-time computation. In this work, we explore a long CoT setting where the model makes up to K successive attempts at solving a problem, in which each attempt is allowed to build on earlier ones after the model receives a hard verifier feedback. This motivates RL methods that can harness per-attempt rewards by carefully weighting individual attempts. We study optimizing the Verification@K reward (the model succeeds by the K-th attempt) and show that naively weighing the attempts by their pass/fail results in biased gradients. We introduce Calibrated Attempt-Level (CAL) GRPO by devising a weighing strategy to obtain unbiased gradients while maintaining small variance. Our theory reveals how incorporating per-attempt rewards influence the training and the eventual Verification@K performance. Experiments, baselines, and ablations on synthetic and real data corroborate our theory and the benefits of CAL-GRPO over vanilla GRPO as well as naive weighting.

Large language models (LLMs) can achieve strong reasoning performance through chain-of-thought (CoT) reasoning, yet they often generate unnecessarily long reasoning paths that incur high inference cost. Self-consistency-based approaches push accuracy higher still, but they require sampling and aggregating multiple reasoning trajectories, leading to substantial computational overhead. In this paper, we introduce a confidence-aware selective sampling framework that, at inference time, analyzes a single reasoning trajectory to adaptively determine whether to rely on that trajectory alone or trigger multi-path sampling. The framework uses trajectory-level numeric features and sentence-level linguistic features extracted from reasoning states to guide selective multi-path reasoning. We train it on MedQA and evaluate it in-domain on MedQA and under calibration-only transfer on MathQA, MedMCQA, and MMLU, without further fine-tuning. Experimental results show that the proposed framework maintains comparable performance to full and efficient multi-path reasoning baselines, with accuracy changes of $-0.41 \pm 0.58$ and $-0.31 \pm 0.58$ percentage points, respectively, while reducing token usage by $71.7 \pm 5.0$ and $36.6 \pm 9.1$. These findings demonstrate that reasoning trajectories contain rich signals for uncertainty estimation, enabling a simple, transferable mechanism to balance accuracy and efficiency in LLM reasoning.

Chain-of-Thought (CoT) reasoning has significantly improved LLMs' mathematical problem-solving capabilities, but distilling such capabilities into smaller models remains challenging due to the capacity mismatch between verbose teachers and compact students. Directly copying teachers' lengthy reasoning chains causes capacity overload, resulting in truncated outputs or repetitive failure. Existing remedies each sacrifice a critical property of CoT: implicit reasoning methods (e.g., compressing reasoning into hidden states) trade away interpretability and verifiability, while heuristic compression strategies (e.g., random step pruning) destroy logical integrity. To address this, we propose BRIDGE, a curriculum framework that first establishes structural understanding via masked reconstruction, then uses GRPO-based reinforcement learning to guide students in self-discovering the optimal balance between accuracy and brevity, and finally internalizes complex reasoning through teacher-guided rewriting on failure cases. On GSM8K, BRIDGE enables Qwen2.5-3B to achieve 11.29% accuracy improvement and 27.4% token reduction over the original model, outperforming instruction-tuned variants and distillation baselines. Zero-shot transfer experiments on SVAMP and MATH-500 further confirm the generalization of internalized reasoning. Our code and model checkpoints are publicly available at https://github.com/Applied-Machine-Learning-Lab/SDM2026_BRIDGE and https://huggingface.co/bowen0815/BRIDGE.