Efficient Language Model Reasoning

Reasoning Large Language Models can improve problem-solving performance through deliberative inference, but invoking slow reasoning for every input is computationally expensive and often unnecessary. We propose IDPR, a framework for response-conditioned inhibitory deliberation. IDPR first generates a concise intuitive answer and then uses an inhibition controller to decide whether that specific response should be released or suppressed in favor of slow reasoning. Unlike input-only routers, the inhibition controller conditions on the fast answer and fast-side evidence, including confidence, logit margin, parseability, and generation cost. We train the controller from paired fast-slow outcomes and select the inhibition threshold on a held-out validation set under an accuracy-first slow-call budget. On a held-out 5,000-example mathematical reasoning test set, IDPR invokes slow reasoning on only 8.20% of examples and improves accuracy from 47.90% to 48.92%. Under the same slow-call budget, random routing decreases accuracy to 46.76%, while the strongest confidence-based baseline reaches 48.22%. IDPR also achieves the highest corrective precision, showing that response-conditioned inhibition better identifies fast answers that benefit from slow reasoning.

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.

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.

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.

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.

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.

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.

Large language models often improve on difficult tasks by spending inference-time compute on a reasoning trace before producing the final answer. That extra computation can be useful, but it also raises latency, token cost, and deployment complexity. We introduce \textbf{ThinkSwitch}, a low-compute procedure for co-training paired instruct and thinking checkpoints. Starting from compatible Qwen3-4B instruct and thinking models, each iteration asks the thinking checkpoint to generate answers, removes the reasoning trace, distills the answer-only pairs into the instruct checkpoint with QLoRA, and reconstructs a thinking checkpoint with spherical weight interpolation. The only human-supplied inputs are task prompts; the labels are generated by the model itself. On a 30-question AIME 2026 evaluation, ThinkSwitch improves the instruct checkpoint from 10/30 to 20/30 and the thinking checkpoint from 14/30 to 22/30. On a 30-question PubMedQA subset, it improves the instruct checkpoint from 13/30 to 18/30 and the thinking checkpoint from 18/30 to 25/30. The complete experiment uses 15 training prompts per domain and costs $2.86 on a single cloud RTX 3070. The results are small-scale, but they indicate that targeted distillation loops can move part of the benefit of explicit reasoning into weights while preserving a separate thinking mode.

Post-training quantization (PTQ) is widely used to deploy large language models efficiently, but its effect on reasoning models is not well understood. Across math, coding, and science QA, we find that aggressive PTQ reduces accuracy while increasing chain-of-thought (CoT) length. Surprisingly, we show that in up to 52% of the quantized models' failures, models reach the right answer in intermediate reasoning steps but do not output it as a final answer. To understand why quantization leads to this increase in overthinking errors, we measure the token-level KL divergence between quantized and full-precision output distributions. Positions with high KL divergence correlate strongly with high next-token entropy, and at these positions quantized models disproportionately sample overthinking markers such as "wait", "but", and "alternatively". We show that simply introducing a training-free logit penalty on a curated set of overthinking markers can reduce CoT length by 12--23% while preserving or improving accuracy across 5 models (1.5B-32B parameters), 3 quantization methods, and 5 benchmarks, yielding a favorable Pareto frontier of accuracy against reasoning cost compared to penalizing other token sets. Overthinking errors produced by quantized models are particularly reduced by up to 58%.

To improve the reasoning capabilities of large language models, test-time compute is typically scaled by generating intermediate tokens before the final answer. However, this couples reasoning to autoregressive generation and thereby conflates internal computation with external communication. In contrast, human cognition can use working memory to hold and manipulate information internally without the need to externalize intermediate thoughts. Drawing on this principle, we introduce Reasoning in Memory (RiM), a latent reasoning method that replaces the autoregressive generation of reasoning steps with memory blocks. These memory blocks are fixed sequences of special tokens that unlock the working-memory capacity of large language models. Since they are fixed rather than generated, they can be processed in a single forward pass, enabling compute-efficient latent reasoning. To operationalize these memory blocks, we employ a two-stage curriculum. First, we ground them by predicting explicit reasoning steps after each memory block. Second, we discard this step-level supervision and iteratively refine the final answer after each memory block. Our experiments on reasoning benchmarks show that, across language models of different families and sizes, RiM matches or exceeds existing latent reasoning methods while avoiding the autoregressive generation of thoughts. These results demonstrate that large language models can be trained to use working memory as an effective mechanism for latent reasoning.

Frontier reasoning models are produced by post-training base language models with reinforcement learning. Recent work has challenged this by showing that sampling from a sharpened version of the base model's distribution, a so-called power distribution, elicits comparable reasoning without additional training, curated datasets, or verifiers. However, making this method practical requires efficiently sampling from the power distribution. A sampler needs to "mix" to the power distribution, which necessitates moving between modes of the target distribution; intuitively, e.g., trying different reasoning strategies. The samplers proposed in prior works repeatedly select a "cut" position in the current reasoning trace uniformly at random and resample the suffix from that position onward. However, reasoning traces typically contain a few consequential decisions (e.g., the choice of proof strategy or algorithm), and we observe that a uniformly chosen cut tends to rewrite local details rather than revisit decision points. We introduce an algorithm (Entropy-Cut Metropolis-Hastings) that uses the base model's next-token entropy as a proxy to identify key decision points and resample from those positions. We empirically verify that entropy jumps are a useful proxy for decision points and, in a stylized model of reasoning, prove that our method's mixing time scales with the number of decisions in a trace rather than with the number of tokens, which can be much larger. Across MATH500, HumanEval, GPQA Diamond, and AIME26, our method consistently improves over baselines and RL-trained models, including best-of-N at the same token budget.

When a large language model under reinforcement learning commits a wrong reasoning step early in a trajectory, standard algorithms force it to keep generating until the maximum horizon, spending compute on tokens that never receive positive reward and polluting advantage estimates with post-failure noise. We propose ESPO (Early-Stopping Proximal Policy Optimization), which detects trajectory failure on-the-fly and terminates rollouts early. At each generation step, ESPO computes a surrogate regret using only the logits already computed during sampling, and terminates when the smoothed cumulative regret significantly exceeds its estimated values. Truncated trajectories are treated as absorbing failure states with a terminal reward, concentrating negative temporal-difference (TD) errors near the detected failure step without any additional reward model or human annotation. On DeepSeek-R1-Distill-Qwen-7B trained for mathematical reasoning, ESPO surpasses PPO on AIME2024 (46.28% vs. 45.25%), AMC2023 (85.83% vs. 82.94%), and MATH-500 (87.42% vs. 85.43%), while saving more than 20% rollout tokens cumulatively.

Grounded claim factuality checking is important for large language model (LLM) applications such as retrieval-augmented generation, as it helps users assess the correctness of generated outputs. Existing metrics using entailment classifiers require dataset-specific threshold tuning, while LLM-based approaches often use direct prompting, which underutilises the reasoning capabilities of LLMs. We address this by formulating grounded claim factuality checking as a true/false reading comprehension task and prompting LLMs with explicit test-taking strategies for efficient reasoning. Our method reduces token usage by over 80% compared to unguided open-ended reasoning, and achieves competitive performance to more expensive alternatives across two factuality benchmarks, setting a new state of the art on one. To further reduce inference cost, we train small language models (SLMs) to replace LLMs in the checking pipeline. Using supervised fine-tuning (SFT) and a self-revision mechanism, the SLMs learn to improve their factuality judgements. Experimental results show that the resulting SLMs perform on par with strong baselines, combining low inference costs with generating supporting rationales to support interpretability. Code and datasets will be released upon acceptance.

Language models can use verifiable rewards to improve at a wide variety of reasoning tasks. However, both parametric (e.g. RLVR) and non-parametric (e.g. prompt optimization) approaches to doing so typically require hundreds of training samples and thousands of model rollouts, making them expensive in the best case and intractable in the worst. To address this challenge, we introduce Contrastive Reflection (CORE), a non-parametric learning algorithm that compares past reasoning traces to generate insights: short natural-language descriptions of reasoning strategies and constraints that capture differences between successful and unsuccessful problem attempts. Across four reasoning tasks, we demonstrate that CORE enables more rapid improvement than both parametric (GRPO) and non-parametric (GEPA, episodic RAG, and MemRL) methods, while using fewer rollouts. Under fixed rollout budgets with as few as five training samples, CORE achieves the strongest performance in most task-data regimes. Finally, we highlight how CORE is substantially more context-efficient than non-parametric baselines, requiring fewer prompt tokens while storing learned knowledge as compact, interpretable natural-language insights. Our results therefore suggest that distilling contrasts between successful and unsuccessful reasoning traces into abstract and useful insights can provide a more efficient and interpretable route to model self-improvement than weight updates, prompt optimization, or direct reuse of stored reasoning traces.

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.

Inference-time sampling can elicit strong reasoning abilities from language models without additional training. Existing power-sampling methods do so by sharpening the distribution over full generated outputs, favoring completions that are individually likely under the model. We argue that this is the wrong object to target for reasoning: a completion entangles a reasoning trace with a final answer, whereas what matters is whether an answer is supported by many plausible reasoning paths. We therefore shift the target from the full-output distribution to the sharpened answer marginal, making self-consistency an inference-time objective rather than a post-hoc voting criterion. Surprisingly, this marginal target admits an efficient approximation: we propose a simple, purely autoregressive parallel sampling algorithm that approximately samples from the sharpened answer marginal, eliciting stronger performance than standard power sampling on mathematics and coding benchmarks while being orders of magnitude faster.

Sampling multiple responses improves language model reasoning, but uniform compute allocation is inefficient because easy questions are over-sampled while hard questions remain under-explored. We propose \textbf{Uncertainty-Aware Budget Allocation (UAB)}, a concave integer optimization framework that reallocates a fixed sampling budget using uncertainty estimated from the initial samples themselves. In Phase-1, every question receives a small fixed number of generations. Their answer disagreement, measured by vote entropy, provides a difficulty signal while these generations contribute to the final vote. In Phase-2, the remaining budget is allocated by a marginal-greedy algorithm that optimally solves a concave coverage-maximization surrogate, concentrating samples on questions whose initial answers disagree. Across five open-weight models (1.5B--27B parameters) and five reasoning benchmarks of varying difficulty, UAB improves average accuracy by $+2.3\%$ over uniform allocation, and achieves gains of up to $+5.5\%$ on individual benchmarks, with the largest gains in low-resource settings. Moreover, UAB meets the target budget exactly and requires no auxiliary model or additional LLM calls. Code is publicly available at https://github.com/manhitv/UAB.

Explicit chain-of-thought (CoT) reasoning substantially improves the reasoning ability of large language models (LLMs), but incurs high inference cost due to lengthy autoregressive traces. Existing latent reasoning methods offer a promising alternative, yet they often treat reasoning as uniformly compressible, causing precision-critical intermediate steps to be overly compressed and thereby degrading reasoning accuracy. In this work, we propose Selective Latent Thinking (SLT), a framework that selectively compresses redundant reasoning spans into latent representations while preserving precision-critical spans as explicit CoT within the same reasoning trajectory. Specifically, SLT first uses a lightweight decoder to anticipate a short upcoming reasoning span, and then applies confidence-based gating to determine the longest span that can be reliably compressed. The accepted span is encoded into a compact latent representation to improve reasoning efficiency, while uncertain or precision-critical reasoning remains in explicit CoT form to preserve accuracy. To learn this selective compression policy, SLT adopts a three-stage training strategy that combines span-level latent compression, reliability-aware future reasoning prediction, and trajectory-level reinforcement learning to optimize the trade-off between answer correctness and reasoning cost. Extensive experiments across four mathematical reasoning benchmarks demonstrate that SLT achieves 22.7% higher accuracy than latent reasoning baselines at comparable compression ratios, while reducing reasoning chain length by 58.4% with only 2.8% accuracy degradation compared to explicit CoT,Our code can be found in https://github.com/hunshi34/SLT.

Test-time scaling improves language model reasoning by spending additional compute to explore multiple solution trajectories. The key challenge is to maximize accuracy while minimizing the total number of generated tokens during reasoning. Recent PRM-guided methods score intermediate prefixes to steer this search, but most are frontier-only: they keep only the current active prefixes and irreversibly prune or resample away the rest using noisy PRM scores. This can cause premature commitment, diversity collapse, and the loss of prefixes that still admit correct continuations. We introduce stochastic backtracking over a persistent pool of historical prefixes, allowing test-time compute to revisit previously generated states instead of only expanding the current frontier. To make this efficient, we propose two complementary mechanisms. Subpool Selection strengthens greedy PRM-guided search by applying Top-N selection within random subpools, giving historical prefixes a chance to bypass over-scored frontier candidates. Power Backtrack Sequential Monte Carlo extends SMC-style resampling to the persistent pool using powered PRM scores and mixture-corrected weights. Across mathematical reasoning benchmarks and model scales, our methods consistently achieve higher accuracy per token count, and the same level of accuracy using only a fraction of the token count in comparison to strong PRM-guided baselines, demonstrating that persistent-pool stochastic backtracking provides a simple and effective way to improve the accuracy-token trade-off in test-time scaling.

Many applications of large language models (LLMs) require deductive reasoning, yet models frequently produce incorrect or redundant inference steps. We frame natural language inference as a search problem where the final answer is the valid proof itself, requiring a reasoning procedure in which intermediate inferences are correct. Specifically, we investigate whether LLMs can learn to generate correct and efficient proofs with guidance from A* search -- an algorithm that guarantees an optimally efficient path to a goal. We explore two training techniques: supervised fine-tuning on execution traces from A* and reinforcement learning with A*-informed process reward models. Empirically, we find that Llama-3.2 models in the 1B--3B range benefit substantially from A* post training, going from near-zero accuracy to outperforming DeepSeek-V3.2 -- a much larger model. Our analysis uncovers a trade-off: while simple correctness rewards maximize accuracy, A*-informed signals strike a balance between accuracy and efficiency. Furthermore, we find that on larger search spaces, models trained with imperfect heuristics exhibit superior accuracy. Our results demonstrate a promising direction towards reasoning guided by principles derived from classical search algorithms.

Multi-step reasoning remains a central challenge for large language models: single-pass generation is efficient but lacks accuracy; tree-search methods explore multiple paths but are computation-heavy. We address this gap by distilling reasoning progress into a hyperbolic geometric signal that guides step-by-step generation. Our approach is motivated by a structural observation: in combinatorial reasoning trees, solution-bearing states are few while dead ends are exponentially numerous. The hyperbolic space matches this asymmetry, with compact volume near the origin and exponentially expanding capacity toward the boundary, so that distance-to-origin naturally encodes solution proximity while angular separation distinguishes branches requiring different next operations. We train a lightweight head to project LLM hidden states into this space, then fine-tune a low-rank adapter interactively on its own reasoning attempts to act on the injected signal. Across multiple benchmarks, the geometric signal yields consistent gains, with larger improvements on deeper reasoning chains. Our code is publicly available at https://github.com/yuyuliu11037/HyperGuide.

The emergence of Large Reasoning Language Models (LRMs) has paved the way for tackling complex reasoning tasks through test-time scaling by generating long-form Chain-of-Thought (CoT) trajectories during inference. Meanwhile, these trajectories often contain explicit reflection markers such as wait'', but'', and ``alternatively'', signaling hesitation, revision, and the consideration of alternative explorations, respectively. Recent studies on test-time control leverage such markers as lightweight handles for steering reasoning, typically treating them as a single coarse-grained category rather than distinguishing their distinct functional roles. In this paper, we conduct type-wise suppression and fixed-prefix intervention, revealing that reflection markers differ not only in their functional roles but also in when they exert the greatest influence. Specifically, different marker classes affect accuracy and generation length in distinct ways, and marker choices are most consequential before the model settles into a stable reasoning trajectory. Motivated by these findings, we introduce PathCal, a novel training-free decoding controller that calibrates reasoning paths by distinguishing marker types and intervening only at locally uncertain states. At each decoding step, PathCal utilizes the distribution over reflection-markers to estimate local competition between maintaining the current reasoning trajectory and initiating a competing branch, and softly rebalances marker logits when competing-branch evidence becomes excessive. Experiments across six reasoning benchmarks demonstrate that PathCal achieves a better efficiency--performance trade-off, improving or preserving accuracy while reducing generation length, without relying on external verifiers or additional sampling.

Reinforcement learning post-training has improved the reasoning ability of large language models, but often produces unnecessarily long, repetitive, or semantically opaque reasoning traces. Existing efficient reasoning methods mainly regulate response length through explicit budgets or length-aware rewards, leaving intermediate reasoning content weakly supervised. We propose CLORE, a content-level optimization framework that improves reasoning efficiency by editing correct on-policy rollouts. CLORE uses an external augmentation model to delete repetitive segments, illegible or task-irrelevant content, and superfluous reasoning after the solution is established, while preserving the final answer. The resulting augmented--original pairs are optimized with an auxiliary reference-free DPO objective alongside standard policy-gradient training. By restricting augmentation to correct trajectories and performing local deletion, CLORE keeps edited rollouts close to the policy distribution and mitigates off-policy mismatch. Experiments on DeepSeek-R1-Distill-Qwen-7B and Qwen2.5-Math-7B across five mathematical reasoning benchmarks show that CLORE improves the accuracy--efficiency trade-off and remains compatible with GRPO, DAPO, Training Efficient, and ThinkPrune. Content-level analyses further show that CLORE reduces repetitive reasoning, illegible content, and post-answer exploration, supporting content-level supervision as a complementary direction to length-level control.

Chain-of-thought (CoT) reasoning has become the default strategy for enhancing LLM capabilities, yet its application raises a fundamental question: when is explicit reasoning actually beneficial? Empirical evidence reveals a striking paradox: CoT often provides marginal or even negative gains on factual and open-ended tasks while multiplying token consumption. In this work, we show that LLM reasoning is not a static property of tasks or models, but a \emph{dynamic decoding state} that emerges during generation. Through systematic analysis, we find early-stage entropy dynamics provide a reliable signal of this state: tasks benefiting from CoT exhibit consistent entropy reduction, while others display unstable or increasing patterns. This behavior can be interpreted as a phase-transition-like shift from a high-entropy exploratory regime to a low-entropy structured reasoning regime. Based on these insights, we propose \textbf{EDRM} (Entropy Dynamics-based Reasoning Manifold), a lightweight and training-free routing framework that leverages early decoding entropy to adaptively select inference strategies. EDRM embeds entropy trajectories into a compact and interpretable manifold representation, enabling both zero-shot deployment and fine-grained instance-level adaptation. Across 15 benchmarks and 4 LLMs of varying scales and architectures, EDRM consistently outperforms static baselines. At the dataset level, EDRM achieves \textbf{41--55%} token reduction while improving accuracy with as few as 50 calibration samples. At the instance level, it further improves accuracy by up to \textbf{4.7%} while maintaining \textbf{27--45%} token savings. These results suggest that reasoning should be invoked selectively rather than by default, and demonstrate the effectiveness of entropy-driven decoding control for efficient and adaptive LLM inference.

Large Reasoning Models (LRMs) achieve strong performance by generating long chains of thought (CoT), but often overthink, continuing to reason after a solution has already stabilized and thereby wasting tokens and increasing latency. Existing inference-time early-exit methods rely primarily on answer-level signals, such as confidence or trial-answer consistency, to decide when to stop. However, these signals mainly reflect answer readiness rather than reasoning convergence: they may trigger before the model has finished exploring or self-correcting, causing premature exits that can degrade final-answer accuracy and leave the retained reasoning chain semantically incomplete. We identify reasoning-level semantic redundancy as a complementary signal for semantic-preserving early exit: when successive steps no longer add novel progress and instead revisit established conclusions, the reasoning trajectory has likely converged. Building on this insight, we propose PUMA, a plug-and-play framework that combines a lightweight Redundancy Detector with answer-level verification. The detector flags semantically redundant candidate exits, while verification confirms whether stopping is safe, allowing PUMA to remove redundant continuation while preserving both answer accuracy and a coherent reasoning prefix. Across five LRMs and five challenging reasoning benchmarks, PUMA achieves 26.2% average token reduction while preserving accuracy and retained CoT quality. Additional experiments on code generation, zero-shot vision-language reasoning, and learned stopping-policy internalization further demonstrate that reasoning-level redundancy is a robust, transferable, and learnable signal for efficient reasoning. Our code is available at https://github.com/giovanni-vaccarino/PUMA.

Large reasoning models (LRMs) substantially outperform their base LLM counterparts on challenging reasoning benchmarks, yet it remains poorly understood where base models go wrong during token-by-token generation and how to narrow this gap efficiently. We study the base-reasoning gap through quantifying token-level distributional disagreement between a base model and a stronger reasoning model using likelihood-based divergences. Across benchmarks, we find that the reasoning advantage is highly sparse and concentrates on a small set of early, planning-related decision tokens. For instance, on Qwen3-0.6B, only ~8% of generated tokens account for the salient disagreement, and these tokens concentrate early in the response, are strongly enriched in planning-related decisions (17x), and coincide with high base-model uncertainty -- suggesting that base models fail mainly at early planning points that steer the subsequent reasoning trajectory. Building on these findings, we propose disagreement-guided token intervention, a simple inference-time delegation scheme that performs a one-token takeover by the reasoning model only at high-disagreement positions and immediately switches back to the base model. With a small intervention budget, this sparse delegation substantially recovers and can even surpass the performance of a same-size reasoning model on challenging reasoning tasks. Code is available at https://github.com/AlphaLab-USTC/RRTokenIntervention.

Parallel reasoning, where a generator samples many candidate solutions and an aggregator selects the best, is one of the most effective forms of test-time scaling in large language models, and pairwise self-verification has become its strongest aggregation primitive. Yet pairwise verification carries a heavy cost: each judgment reads two complete solutions in full, and existing methods perform tens of such judgments per problem regardless of whether the comparison is informative. We introduce CAPS (Cascaded Adaptive Pairwise Selection), an inference-only framework that allocates verifier compute non-uniformly along two orthogonal axes: an evidence axis that adapts how much of each candidate the judge sees, and a distribution axis that adapts how comparisons are spread across the pool. CAPS instantiates these into a four-stage cascade with an optional rescue subroutine, and admits a closed-form verifier-token cost in which the per-candidate marginal cost is roughly halved relative to uniform full-evidence schedules. On four self-verifying models (Qwen3-14B, GPT-OSS-20B, Qwen3-4B-Instruct/Thinking) and five reasoning benchmarks spanning code (LiveCodeBench-v5/v6, CodeContests) and math (AIME 2025, HMMT 2025), CAPS outperforms the leading pairwise verifier on 14 of 20 suites while using 25.4% of its verifier-token budget on code, and outperforms pointwise self-verification on all 20. The trade-off suites admit an interpretable diagnostic in terms of the verifier's accuracy at partial versus full evidence, providing a concrete pre-deployment check for cascade suitability.

Distilling reasoning traces from strong large language models into smaller ones is a promising route to improve intelligence in resource-constrained settings. Existing approaches face a fundamental trade-off: offline distillation from teacher-generated traces provides high-quality, sample-efficient supervision but suffers from distributional drift: during training, the student model conditions on teacher-generated prefixes, whereas during inference the student autoregresses on self-generated prefixes, leading to compounding errors over long reasoning trajectories. Meanwhile, on-policy or self-distillation methods better match the student's inference-time distribution, but require costly online sampling and often produce low-quality traces in early training. We propose a principled offline reasoning distillation framework that preserves the efficiency and supervision quality of offline teacher-generated data while correcting teacher-student distribution drift. It adaptively emphasizes teacher supervision that is better aligned with the student's on-policy distribution. Evaluations on mathematical reasoning benchmarks of GSM8K, MATH, MATH500, and harder held-out competition-style tasks, including AMC, AIME, and OlympiadBench, show that our method improves reasoning accuracy over prior offline distillation algorithms and yields more stable reasoning traces while preserving instruction-following capabilities. Our work shows that lightweight, distribution-correction-aware training can substantially strengthen offline reasoning distillation without online rollouts.

In current Large Language Models we can trust the production of smoothly flowing prose on the basis of the principles of machine learning. However, there is no comparably principled basis to justify trust in the content of the text produced. It appears to be conventional wisdom that addressing this issue by adding more principled reasoning is not computationally affordable. Here we propose a principled method of reasoning that is efficient enough to be practical for large language models. Further, the method allows the retention of much of the currently used software and hardware base. Our method for improving the functioning of large language models consists of a first stage of preprocessing that recodes the data to a Unary Relational Integracode that is more explicit about the relationships among the objects described in the text, followed as a second stage by a standard but possibly streamlined machine learning process that then also learns to predict these relationships. The method may be viewed as realizing a world model and applying beyond natural language, to vision and actions, for example, where the multiple properties of an object referred to in an input are brought together explicitly, rather than remaining distributed in the various references to it in the input. We articulate its advantages in terms of Robust Logic, a system for performing principled chaining on learned, and hence uncertain, information. We show that this recoding has the surprising and fortuitous property that, while succinct, it makes the task of learning a core subset of relational rules that hold in the world described in the training data polynomial time learnable in a defined sense, the polynomial depending on the complexity of the rule. This gives support for sound reasoning within each single call of the learned classifier as well as between multiple calls.

Long chain-of-thought (Long CoT) reasoning improves performance on multi-step problems, but it also induces overthinking. This inefficiency is especially problematic in low-data fine-tuning regimes, where real applications adapt reasoning models with limited supervision and cannot rely on large-scale teacher distillation or heavy test-time control. To address this, we propose STOP (Structured On-policy Pruning), an on-policy algorithm for analyzing and pruning long-form reasoning traces. STOP constructs self-distilled traces from the model. Then it maps each trace into a structured reasoning interface through node segmentation, taxonomy annotation, and reasoning-tree construction. On top of this interface, we introduce ECN (Earliest Correct Node), which retains the shortest prefix ending at the earliest node. Experiments on DeepSeek-R1-Distill-Qwen-7B and DeepSeek-R1-Distill-LLaMA-3-8B across GSM8K, Math 500, and AIME 2024 show that STOP reduces generated tokens by 19.4% to 42.4% while largely preserving accuracy in low-data fine-tuning. Beyond efficiency, our analyses show that STOP induces much smaller distributional shift than teacher-guided pruning, improves the structural efficiency of generated reasoning, and reallocates reasoning effort away from redundant verification and backtracking toward more productive exploration.