Efficient Language Model Reasoning

Large reasoning models can produce correct yet unnecessarily long reasoning traces. Existing methods improve reasoning efficiency with trajectory-level objectives or local token- and step-level signals, but rarely model inter-step semantic dependencies. This limits their ability to distinguish redundant steps from those that support later deductions, making it harder to shorten reasoning without sacrificing accuracy. We introduce RECAP (REdundancy-aware Credit Assignment via Propagation), which addresses this limitation by assigning credit where it is due based on both a step's downstream role in the reasoning structure and its contribution to solving the problem correctly. We define structural responsibility to capture the step's downstream role by measuring how strongly later reasoning depends on it, using credit propagated backward from the final-answer node through an outcome-independent, LLM-annotated semantic dependency graph. However, a step can have high structural responsibility yet steer the reasoning away from the correct solution. RECAP therefore introduces step efficacy to measure answer-directed progress through changes in gold-answer log-likelihood as each step is added. Together, these signals reshape rollout-level GRPO advantages into step-specific updates. RECAP requires neither a separately trained process reward model nor preconstructed concise trajectories. Across two 7B models and four mathematical reasoning benchmarks, RECAP improves the accuracy-efficiency trade-off. On Qwen2.5-Math-7B, it improves pass@1 by 2.0-3.7 percentage points while reducing reasoning tokens by 8%-31% relative to GRPO across all four benchmarks. Analysis suggests these savings reflect fewer reasoning operations and less dead-end reasoning, rather than more compact expression.

The rapid capability gains of frontier language models are widely attributed to improved reasoning abilities, yet this cannot be verified as raw CoT traces in closed-source systems are hidden. By registering a simple custom tool through a standard API feature, we induce frontier models to externalize intermediate reasoning. Because these traces may reflect post-hoc rationalization rather than genuine reasoning, we first evaluate against native CoT on open-source models and extend to closed-source frontier models including GPT-6 Astra. We find that the extracted reasoning matches native reasoning performance and substantially outperforms no-reasoning baselines, across competition mathematics, science, and code generation. We then characterize how frontier models structure their intermediate reasoning. Across token efficiency, reasoning-step types, and induced reasoning trees, we identify systematic differences in how models externalize, compress, and organize reasoning. We find that Astra exhibits token-efficient directed reasoning, selecting a correct trajectory earlier, while resolving elementary steps internally and externalizing only crucial reasoning. These findings provide a behavioral lens on frontier-model reasoning beyond benchmark scores.

Reasoning-oriented reinforcement learning enables large language models to solve mathematical, coding, and other multi-step tasks, but shifts a substantial portion of the training cost to rollout, where trajectories are generated for policy updates. Efficient rollout mechanisms are therefore essential to reduce this cost while maintaining the freshness, consistency, and statistical validity of training data. This survey provides a systematic taxonomy of recent research on rollout efficiency for reasoning-oriented reinforcement learning, classifying existing approaches from both mechanism and bottleneck perspectives. Based on this taxonomy, we analyze how different technique families address distinct sources of rollout inefficiency, examine opportunities and potential conflicts for combining them, identify gaps in the evaluation and reporting of efficiency gains, and discuss open challenges and future research directions.

Large Reasoning Models (LRMs) often overthink easy problems and underthink hard ones, leading to inefficient computation allocation. Existing methods regulate generated computation or select between direct answering and explicit reasoning, but do not jointly control whether}to reason and how much computation to allocate within reasoning. We call the resulting difficulty-dependent loss in accuracy under computation reduction the efficiency tax. We propose When2Think, an RLVR-based post-training framework for instance-adaptive computation allocation. Its core mechanism, Instance-level Difficulty-Aware Control (IDAC), uses cached reference statistics of success and token cost to modulate a correctness-gated efficiency bonus based on generated token count. Importance sampling supports exploration of Think and NoThink, while Batch-Wise Standardization constructs standardized advantages for critic-free optimization. The framework requires neither a learned reward model nor a learned critic, and offline reference caching avoids online reference-model queries during policy updates. On AIME24, When2Think improves Pass@3 by 10.0 percentage points while reducing token usage by 27.9% relative to the backbone.

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.

Large language models (LLMs) demonstrate impressive capabilities, but their deployment presents significant efficiency challenges. Autoregressive decoding imposes substantial inference latency and under-utilizes hardware accelerators in low batch size regimes. Discrete diffusion models can generate in parallel but struggle to match autoregressive quality without many diffusion denoising steps. Long-context reasoning creates memory bottlenecks that strain even state-of-the-art accelerators. My thesis is that language models can direct their own inference execution strategy by annotating semantic dependence -- which tokens depend on which others -- in their generation. I call such models self-orchestrating language models. For each system, I design a runtime that acts on these annotations to parallelize autoregressive decoding, evict intermediate context, or derive denoising orders, achieving Pareto-optimal quality-efficiency trade-offs. I demonstrate this approach through three self-orchestrating systems. First, PASTA uses semantic dependence to parallelize autoregressive decoding, training the model to annotate which output chunks can generate independently. Second, TIP uses semantic dependence to evict intermediate reasoning steps from the KV cache, reducing memory consumption while preserving accuracy. Third, Planned Diffusion uses semantic dependence to derive a denoising order for discrete diffusion, autoregressively generating a plan that specifies which chunks to denoise in parallel.

A core goal of efficient reasoning is to improve the accuracy-efficiency frontier. However, jointly improving reasoning accuracy and inference efficiency can be challenging, as the two objectives can favor different reasoning behaviors. Independently post-trained models already offer distinct strengths in accuracy and efficiency. We introduce Lightning Weave, a post-training framework that extracts and composes these independently learned capabilities in a single student through on-policy distillation. Each acquired capability is represented by the policy shift from the model before post-training to the resulting specialist. Lightning Weave combines aligned log-ratio shifts at shared student token states and uses Tilted-Target DOPD to convert the cached signals into a stable learning target. Each anchor pair scores the cached trajectories once, enabling subsequent student training without serving multiple live anchor models concurrently. Across diverse student models and benchmarks in mathematics and code, Lightning Weave substantially improves upon the base students and achieves a state-of-the-art accuracy-efficiency frontier. On Qwen3.5-4B, it raises HMMT 2025 accuracy from 59.2% to 64.0% with 10.7% fewer response tokens, and LiveCodeBench v5 accuracy from 41.7% to 54.2% with 9.6% fewer response tokens. Adjusting the relative strengths of the anchor signals yields a strong empirical accuracy-efficiency Pareto frontier. These results establish Lightning Weave as a new practical route to efficient reasoning through capability composition. Code is released at https://github.com/jet-ai-projects/Lightning-Weave.

Speech large language models (SpeechLLMs) offer reduced latency and retain paralinguistic nuances that are typically lost in cascaded automatic speech recognition (ASR) and text-based LM architectures. However, they continue to lag behind text-only LLMs on complex reasoning tasks, while real-time spoken interaction imposes strict latency constraints. Although prior works employ Chain-of-Thought (CoT) and concurrent reasoning to enhance reasoning capabilities without inducing prohibitive delays, an inherent accuracy-latency trade-off persists. In this paper, we investigate whether a streaming SpeechLLM can dynamically revise its reasoning traces on the fly. We introduce RetroThinker, a multi-stage post-training framework that equips the Moshi model to self-verify and forward-correct CoT steps during inference. RetroThinker combines supervised fine-tuning (SFT) on curated retrospective thinking data with length-based direct preference optimization (DPO) to optimize retrospective during early reasoning (i.e., reasoning concurrently while the user speaks). Evaluated on the GSM8K benchmark, RetroThinker significantly improves the accuracy-latency trade-off over non-retrospective baselines, achieving an 11% absolute accuracy gain at a comparable latency.

Chain-of-Thought (CoT) improves the reasoning ability of Large Language Models (LLMs) but incurs substantial computation and context costs. Existing methods either lose intermediate information through hard pruning or lack a principled criterion for continuous compression. We present A*-Thought-V2, a geometric dynamics of LLM guided framework that models CoT as a hidden-state trajectory and replaces hard deletion with an explicit-implicit interleaved latent architecture. After projecting question, step, and solution representations into a 3D PCA space, it measures alignment between each local transition and global question-to-solution direction. Aligned steps remain explicit text, whereas deviating steps are compressed into continuous latent tokens. Directional angles capture both local semantics and reasoning dynamics: small angles indicate direct execution and answer formation, while large angles more frequently involve checking, correction, and branch exploration; their temporal variation reveals exploration, convergence, and refinement stages. To train this architecture, we introduce stepwise embedding forcing, which pools each redundant step into a single latent embedding, and label forcing, which supervises that latent token with a soft multi-modal vocabulary distribution instead of a hard one-hot label. Experiments on Qwen3.5-9B and Qwen3.6-27B across six in-domain and out-of-domain benchmarks show that A*-Thought-V2 improves average accuracy by up to 2.6% while reducing response length by up to half, increasing Accuracy per Computation Unit by 2.29$\times$, and reducing preprocessing and training time by 94.6% and up to 80.3%, respectively. Representation analyses suggest that latent states form a compact region distinct from textual states, while higher entropy at latent-token positions reflects broader soft targets that encourage richer step-level feature learning.

Chain-of-thought (CoT) reasoning improves large reasoning models (LRMs) on complex tasks but often produces long, redundant traces. Recent training-free early-exit methods shorten these traces by choosing an intermediate point to stop reasoning. We study one such strategy that injects an end-of-think token (EoT, </think>) at this point to trigger the reasoning-to-answering transition, and find that the injected EoT does not always induce a clean answering phase. Answering-phase generation can continue before the model regenerates another EoT, with the span preceding this regenerated EoT scaling with the reasoning tokens saved by early exit and exhibiting continued reasoning behavior. We call this spurious CoT termination, where reasoning-like generation continues into the answering phase. We hypothesize that insufficient attention to the injected EoT contributes to spurious CoT termination and probe this hypothesis with Exit-token Attention Biasing (EAB). Across four LRMs, five benchmarks, and two early-exit methods, increasing attention to the injected EoT reduces spurious CoT termination and answering-phase length. These results reveal a limitation of controlling LRMs by externally matching their explicit think-block format. Inserting the EoT token conforms to this format but does not by itself guarantee the intended reasoning-to-answering transition. Our code is available at https://github.com/Seunghee-Koh/Spurious-CoT-Termination.

Large language models achieve superior performance on tasks that require extended reasoning, but long chains of thought make the KV cache a severe memory bottleneck. Existing KV cache compression methods share one paradigm: score each cached token by some estimate of how much it will matter later, and keep the top-scoring ones. We show that the selection signal contributes almost nothing. Random Attention keeps the prompt and evicts uniformly at random within each attention head, computing no score at all; across four models and six reasoning tasks, it matches the strongest baseline in task performance while delivering 32-43% higher throughput than that method when deployed with vLLM. Controlled experiments explain this by showing that 1) the prompt is the fragile part of the cache, and most of the gap between selectors is just whether their selection signal happened to keep it; 2) the reasoning trace protects itself against eviction with redundancy at two levels, in the text (the model restates what it still needs as it works) and across attention heads (each keeps its own copy of the trace), so once the prompt is safe, a random draw retains enough copies of what the model still needs, and no score is required to pick them. Our code is publicly available at https://github.com/SalesforceAIResearch/Random-Attention.

Chain-of-thought reasoning unfolds in discrete token space: each step is committed as text, errors propagate, and eliciting good traces presupposes traces to imitate. Reasoning instead in a model's continuous representation space - where intermediate states are vectors rather than words - sidesteps these constraints, but leaves open how those latent states should be computed. We approach this along two axes. First, we keep a large language model (LLM) frozen and use it for what it is already good at - modeling and decoding sequences - while a small auxiliary network supplies continuous latent thoughts as input. Second, we produce those latents by recurrence: a tiny recurrent reasoner refines them over many steps, decoupling the depth of computation from the size of the model, so that the latents are a product of iterative processing rather than a single forward pass. We instantiate this as Latent Recurrent Thoughts (LRT): a task-dedicated proposer supplies base latents, a recurrent reasoner refines them through bounded residual corrections, and the frozen LLM decodes the answer. On symbolic reasoning with answer supervision but no reasoning traces (Countdown-4, Sudoku) and on natural-language reasoning (HumanEval, MBPP, StrategyQA), LRT substantially outperforms prior frozen-decoder continuous-space reasoning methods under an identical decoder, prompt, data, and training budget, and outperforms non-thinking-mode chain-of-thought prompting on the same backbone at a small fraction of its inference compute.

Large language models decode by projecting hidden states through a large vocabulary head at every step. This operation is computationally costly and forces all reasoning to be expressed in discrete tokens. We introduce Soft Latent Thinking, a method that replaces the LM head during reasoning with a lightweight projector, enabling autoregressive rollout in embedding space where reasoning steps remain continuous rather than tokenized. Experiments on DeepSeek-Qwen-1.5B and LLaMA-3.2-3B show that Soft Latent Thinking consistently improves pass@k across all k while reducing per-step compute during chain-of-thought. Our method achieves the highest pass@32 among all soft-thinking approaches, demonstrating that effective reasoning can be carried out in continuous space without discrete token generation.

Chain-of-thought (CoT) reasoning improves multi-step problem solving, but long reasoning traces inflate inference cost. Token-level CoT compression reduces this cost by pruning full reasoning chains into shorter traces for model adaptation, making token selection the central challenge. Existing methods often rely on external scorers or heuristic signals only indirectly tied to the model's internal answer computation. We instead adopt a model-internal perspective: as the model forms an answer, each reasoning token induces a ripple in the residual stream whose effect on the answer reflects the token's contribution to the underlying computation. Building on this view, we propose \textsc{MIST} (Model-Internal Saliency for Token-level CoT compression), which defines token importance along two complementary axes: \emph{necessity}, the drop in answer likelihood when a token's internal contribution is removed, and \emph{sufficiency}, the gain in answer likelihood when that contribution alone is provided. Combining the two yields a unified importance score for pruning. Across four reasoning benchmarks and four models, \textsc{MIST} consistently outperforms baseline methods, suggesting that model-internal saliency provides an effective proxy for reasoning-token importance.

Large language models can often generate plausible mathematical reasoning traces, but reliably identifying the correct solution among multiple candidates remains a key challenge. Existing test-time reasoning pipelines typically rely on text-based verifiers that re-read each generated solution, making verification an expensive component of inference. Prior work has shown, however, that LLMs often encode correctness-related signals in their internal representations, including awareness of when their own answers are likely to be wrong. Building on this observation, we introduce HSRM, a lightweight hidden-state reward model that verifies candidate solutions by directly reading the generator's internal representations rather than re-processing its text. HSRM extracts hidden states from a frozen generator at reasoning-step boundaries and uses a small Transformer encoder to rank candidates. It is trained from self-generated trajectories with outcome labels, requiring neither human-written process supervision nor a large pretrained verifier. Across four mathematical reasoning benchmarks, HSRM matches or outperforms a 55M-parameter text-only energy verifier in 15 of 16 generator--dataset settings while using only about 2M parameters, providing an efficient alternative to text-only verification by reusing representations already computed during generation.

Large reasoning models achieve strong performance on complex tasks by generating extended chain-of-thought (CoT) traces via reinforcement learning with verifiable rewards (RLVR). While current RLVR methods have achieved strong results with correctness-based reward signals, they provide limited guidance on the quality of the reasoning process itself, leaving the internal reasoning structure largely unoptimized. Through empirical analysis across multiple model families, we identify a consistent pattern: correct reasoning trac es exhibit more frequent and larger token-level entropy drops within the thinking phase than incorrect ones. We propose ERR+, a two-phase RLVR framework grounded in this observation. The first phase trains with the Entropy Relief Reward (ERR), a bonus proportional to cumulative token-level entropy drops in the thinking phase, log-normalized by response length. Unlike prior methods that suppress entropy, ERR rewards the resolution of uncertainty while leaving exploratory high-entropy states unconstrained. The second phase introduces the Robust Relative Efficiency Reward, which scores each response's length against co-generated peers via a $\tanh$-transformed within-group $z$-score. We provide a formal analysis showing that joint optimization of the two objectives induces gradient conflict in early training, motivating the sequential design . Experiments on five datasets demonstrate consistent improvements in both accuracy and response conciseness across model backbones. Our code is available at https://github.com/XrkArul/err_response

We introduce BDH-CQ, a reasoning model that combines in-context learning with recurrent latent reasoning. Inputs presented at inference time continuously update the model's recurrent memory; the model then solves a query through iterative computation in a high-dimensional latent space, without verbalizing its intermediate reasoning. We evaluate the model on the public ARC-AGI-1 evaluation set and use controlled ARC-like interventions to study what it learns from demonstrations, how consistently it applies an inferred transformation, and which concepts remain difficult. A 150M-parameter configuration reaches 29.5% pass@2 at a computed inference cost of $0.0007 per task. This operating point breaks through the previously reported ARC-AGI-1 cost-accuracy Pareto frontier, establishing a new state of the art in benchmark cost efficiency.

Test-time compute scaling is a primary driver of performance in large reasoning models (LRMs), but extreme inefficiency bounds current approaches, shifting the critical question from \emph{how much} compute to spend, to \emph{where} to allocate it. We formalize test-time reasoning as a constrained compute allocation problem over partial trajectories. Under a fixed hardware budget, existing paradigms fail to actively allocate the compute to the most promising partial progress: traditional parallel sampling treats traces independently and induces severe memory bottlenecks, while subtractive pruning starves hardware and fails to actively and sufficiently shift the output distribution. To overcome this dichotomy, we introduce Gambit, an inference algorithm that executes \emph{thought-level beam search}. By periodically pruning unpromising trajectories and immediately branching from high-quality prefixes, Gambit dynamically concentrates compute onto the most promising reasoning traces via a light-weight scorer probing hidden states while maintaining continuous high hardware utilization. Extensive evaluations across multiple models and benchmarks demonstrate that Gambit strictly dominates existing baselines. Under identical hardware constraints, our method yields up to a +6.7% absolute accuracy gain on HMMT-24 and +3.3% on AIME-25 over pruning baselines, delivers $>2\times$ higher throughput on trace completion, and reduces total token consumption by up to 68.5% relative to standard parallel sampling.

Reasoning modes of language models outperform their non-reasoning counterparts on multi-step agentic tasks, but pay a 3-6x premium in output tokens on every episode -- much of it spent re-deriving procedures that are shared across episodes of the same domain. We show this recurring cost can be amortized: a coding agent analyses a small corpus of existing trajectories from a training split and compiles a compact natural-language skill that is injected into the non-reasoning model's system prompt. Across four agentic benchmarks (ALFWorld, tau$^2$-bench telecom and retail, and SpreadsheetBench-Verified), skills recover 55%-100%+ of the reasoning gap for GPT-5.4-mini on held-out tasks -- exceeding the reasoning mode outright on two of four -- while emitting 2.7-6x fewer output tokens and zero reasoning tokens. Notably, reasoning traces are not a prerequisite: skills distilled from non-reasoning trajectories alone remain competitive with skills distilled from paired reasoning/non-reasoning corpora, with domain-dependent differences between the two sources. We interpret these results through a search lens: test-time reasoning is deep search inside a single episode, re-paid at every deployment, while corpus distillation is wide search across episodes, paid once. The two recover overlapping procedural knowledge, and width over cheap trajectories is often the better buy -- with the residual gap on some domains (telecom, SpreadsheetBench) delineating where genuinely per-instance deep search remains necessary.

Large Reasoning Models (LRMs) excel on complex tasks through long chain-of-thought (CoT) reasoning, but their lengthy intermediate steps cause severe overthinking that inflates inference cost. KV-cache compression is a common solution, yet existing reasoning-oriented methods apply a uniform policy across the trajectory and judge compression only by what it removes from the cache. Two observations point the other way. First, a reasoning state's tolerance to context loss varies along the trajectory, and process reward tracks it: deleting tokens at high-reward steps preserves accuracy far better than deleting the same budget at random. Second, compression is not free on the generation side, since a smaller cache leads the model to generate more tokens, partly canceling the saving. Together these motivate coordinating both sides under a single process reward. We propose ReCo (Reward-Coordinated Compression), a step-wise framework in which a lightweight process-reward estimator scores each completed step and drives three components: (1) reward-adaptive KV-cache compression that shrinks the retained cache harder at high-reward steps and less at low-reward ones, (2) a reward-banded penalty on reflection tokens that curbs redundant generation, and (3) confidence-based early stopping that triggers when the reasoning is reliable. Across three reasoning models and six benchmarks, ReCo reduces generated tokens by 37%-65% and end-to-end latency by 2.08x-2.35x over Full CoT, all while largely preserving accuracy.

Test-time scaling improves LLM reasoning by generating and aggregating multiple candidate answers, yet many pipelines use fixed per-query budgets that spend the same compute on easy and difficult prompts. These fixed budgets are also difficult to inspect because they do not explain why a given prompt receives a particular number of samples. We propose adaptive} test-time scaling with a lightweight fuzzy controller that maps interpretable signals, including estimated prompt complexity and model confidence, to a per-query sampling budget. The controller assigns fewer samples to easier or more confident prompts and more samples to harder or less certain prompts, making inference-time compute inspectable rather than fixed or opaque. We evaluate under a fair-alignment protocol with matched decoding settings and controlled answer selection, and compare against best-of-$N$, compute-aware scaling, and self-certainty-based baselines on question-answering and mathematical reasoning tasks. Across models and datasets, adaptive fuzzy control improves over several standard baselines and remains close to a selector-matched full-budget control while reducing the average number of samples. These findings suggest that interpretable adaptive sampling is a practical direction for more efficient test-time reasoning in large language models.

Large language models often reason at length before answering, increasing cost and latency. Prompts and trained settings can shorten this reasoning, but a shorter trace may only show that the model stopped sooner. Here, we evaluate paired runs of the same question at matched reasoning horizons across 198 GPQA Diamond and 500 MMLU-Pro questions. We test a numeric/concision prompt that announces a token limit for Qwen3-14B and the trained effort settings of gpt-oss-20b and -120b. The Qwen prompt shortens reasoning traces by 12-17%, while accuracy changes at matched token limits are small and mixed. A concise/early-answer instruction raises MMLU-Pro accuracy by 3.8 percentage points at 512 tokens, including +2.7 points when both runs are unfinished. Its gain at 2,048 tokens is uncertain. For gpt-oss, candidate-logit answers from completed low- and medium-effort reasoning are 14.5-26.3 points more accurate than matched-horizon high-effort answers. Most of the 512-token advantage comes from lower effort finishing earlier, while differences among unfinished runs are smaller and mixed. Wrong early answers often concentrate probability on the chosen option, so earlier stopping does not uniformly improve probability quality. In these tests, a tight deadline can favor lower effort or a concise instruction, whereas allowing high effort to finish can recover higher final accuracy. Evaluations should report correct completion before a deadline, the answer obtained when a run is stopped, differences among unfinished runs, and probability assigned to the correct answer separately.

Large language models often improve task performance by generating long reasoning traces, but the resulting computation is frequently wasted on redundant verification and revision. Existing probe-based early-exit approaches mainly inspect explicit self-doubt expressions, leaving many earlier termination opportunities undetected. Expanding inspection to ordinary reasoning boundaries improves coverage, but also exposes highly diverse intermediate states whose predictive information may reside in different hidden layers. We present Boundary-Expanded and Layer-Adaptive Dynamic Exit for Efficient LLM Reasoning (BLADE), a lightweight framework that dynamically terminates reasoning by estimating whether the generated prefix is sufficient for correct answering. BLADE constructs multi-granular checkpoints from sentence, self-doubt, and paragraph boundaries, and derives robust training labels through repeated answer completions. It further learns a compact subset of informative probe layers instead of relying on fixed choices or expensive representations from all layers. At inference time, calibrated predictions are combined with checkpoint-specific confirmation rules to balance responsiveness and premature-exit risk. Experiments on five benchmarks and two Qwen3 reasoning models show that BLADE preserves near-baseline accuracy while reducing generated tokens by 24.8% on Qwen3-8B and 15.8% on Qwen3-4B. Ablation studies further confirm the benefits of diverse checkpoints and automatic layer selection, demonstrating an effective approach to more efficient LLM reasoning.

Recent large reasoning models often develop long chain-of-thought responses during reinforcement learning (RL), resulting in high inference latency and deployment cost. Existing methods for response length control typically rely on explicit length penalties or additional control modules, which require careful tuning and may compromise reasoning quality. We propose Quadrant-weighted Sampling for Length-aware Policy Optimization (QLPO), a simple resampling-based variant of GRPO that introduces implicit length control without modifying the reward function. QLPO first over-generates candidate responses and then resamples the training group by preserving the empirical correct/incorrect ratio while favoring short correct responses and long incorrect responses. This reshapes the training distribution and implicitly encourages shorter model outputs. Across models ranging from 1.5B to 32B parameters, including both base models and strong reasoning models, QLPO consistently improves the accuracy-length trade-off. It reduces response length by 30% to 70% while preserving reasoning performance. These results suggest that structured resampling provides an effective and robust approach to efficient reasoning.

Large language models (LLMs) provide strong reasoning capabilities but are expensive to serve at scale, whereas small language models (SLMs) are cheaper but less reliable on difficult problems. We introduce PyroDash, a cost-aware framework for token-level SLM-LLM collaborative inference. During generation, the SLM decides whether to request assistance by emitting a control token. A Collaborate Engine then sends the query and partial reasoning trace to a frozen LLM for completion through a single handoff. The policy is internalized in the SLM, requiring neither a separate router, LLM retraining, nor access to LLM logits. PyroDash trains the SLM in three stages: control-token embedding learning, offloading-oriented supervised fine-tuning, and cost-aware alignment with Group Relative Policy Optimization. Its reward balances answer accuracy against inference cost normalized by LLM-only inference. Across five mathematical reasoning benchmarks, PyroDash supports different accuracy-cost operating points. With $λ=0.05$, it achieves 64.04 percent average accuracy, 6.36 percentage points above the LLM-only baseline, while reducing cost by 20.4 percent. With $λ=0.6$, it achieves 54.55 percent accuracy with a 1.90 percent LLM token ratio and 0.012 LLM calls per example, reducing total cost from USD 49.36 to USD 1.78. These results show that learned token-level handoffs can reduce LLM use while preserving strong reasoning performance.

Large Reasoning Models (LRMs) often suffer from overthinking due to redundant verification steps. Existing approaches for mitigating overthinking, such as fast-slow thinking switching and reasoning trajectory compression, fail to make a fine-grained distinction between beneficial and redundant steps within the LRM's reasoning process, and may thus impair reasoning capability in their pursuit of efficiency. To simultaneously improve reasoning efficiency and capability, we propose EvoThink, a framework that reduces redundant verification and encourages the exploration of new reasoning paths. EvoThink comprises two key components: Self-Pruning Training (SPT), an unsupervised method that iteratively prunes redundant reasoning steps and self-trains on the concise trajectories; and Aha-Moment Preference Optimization (AMPO), which, inspired by genetic algorithms, identifies valuable failed reasoning attempts, synthesizes from-wrong-to-right aha-moment data, and optimizes the model to internalize this reasoning pattern. Extensive evaluations across mathematical reasoning and code generation benchmarks demonstrate that EvoThink not only substantially reduces inference-time token usage but also improves the reasoning capability of LRMs.

Spoken language models (SLMs) enable natural human-computer interaction, but their reasoning ability still lags behind that of text-based large language models, especially on spoken mathematical question answering tasks. One important reason is that SLMs reason over purely verbalized mathematical expressions, which are harder to interpret than symbolic text. However, directly transferring text-based reasoning to SLMs is nontrivial due to architectural constraints and the additional computational requirements. To address this challenge, we propose Efficient Chain-of-Modality Reasoning (ECoM Reasoning), the first framework to introduce compressed reasoning into SLMs. By compressing the textual component so that it jointly serves as speech guidance and reasoning representation, ECoM Reasoning improves reasoning accuracy while using a smaller token budget than the standard Chain-of-Modality (CoM) architecture, which generates intermediate text before speech. To train this capability, we further propose Progressive Compression, a curriculum-based strategy that gradually trains the model from full-form reasoning to compressed reasoning. Experiments on spoken mathematical question answering benchmarks show that ECoM Reasoning improves accuracy by 21% over standard CoM without explicit reasoning, and by 3% over CoM with full reasoning traces while using only 40% of the text tokens, demonstrating that it enhances SLM reasoning while remaining inference-efficient.

Reinforcement learning with verifiable rewards (RLVR) has been established as a viable paradigm for the post-training of Large Language Models (LLMs), including downstream tasks, such as Neural Machine Translation (NMT). With the latest research indicating that RLVR could be the preferred training method for translating legal documents due to the induced reasoning capabilities, it raises the question whether it is really attributed to the reasoning or more generally to the training paradigm. We investigate the importance of including the model's reasoning trace in the generated responses during both training and inference by systematically omitting it from one of the phases. Our experiments show that including the reasoning, specifically during inference, has a positive effect on the overall translation quality. Furthermore, we recognise that the reasoning leads to an increase in output tokens, hence we study the cost-quality tradeoff between the increased computational demands and the improved translation quality.

Large language models achieve strong reasoning performance, but often at prohibitive training cost - a challenge that is especially acute for compact models ($\leq 4 \, \mathrm{B}$ parameters) trained under limited budgets. We introduce MADA-RL, a post-training framework that specializes compact models into generator and critic roles and trains them with a debate-aware learning signal, fine-tuning only a small subset of parameters via LoRA adapters. Our central contribution is a counterfactual critic advantage: a dynamic, role-conditioned baseline that redefines the critic's advantage as its reward minus the generator ensemble's per-instance accuracy. This explicitly optimizes critics to improve over generator consensus rather than to merely reproduce a correct answer, yielding more targeted credit assignment than static mean-reward normalization. At deployment, the specialized agents are composed in a lightweight multi-round protocol. Across five mathematical reasoning benchmarks, MADA-RL raises the accuracy of the DeepSeek-R1-Distill-Qwen-1.5B model from $39.9 \, \%$ to $41.9 \, \%$ ($+2.0$ points, $p < 0.001$) using $16$ times fewer trainable parameters than fully fine-tuned baselines, placing it on the accuracy-trainable-parameter Pareto front. It approaches, but does not surpass, the strongest baselines (DeepScaleR, STILL-3), which are trained on substantially larger datasets; we analyse this gap and the associated inference-time cost directly. A controlled study isolates the source of MADA-RL's gains: the counterfactual advantage produces the highest critic improvement rate of any model evaluated, indicating that trained critics learn to correct generator errors rather than to imitate them.

Large reasoning models often solve problems through long chain-of-thought (CoT) traces, yet much of this computation is spent on redundant derivations, repeated self-verification, and detours that do not improve the final answer. Existing on-policy self-distillation methods reduce this cost by matching a student model to a concise copy of itself on prefixes sampled from the student's own rollouts. We show that this objective has an initialization bottleneck. Since supervision is applied only to visited prefixes, training from a verbose base model places the KL loss on contexts that are often noisy, redundant, or already off track. In such regions, a concise teacher can provide only local corrections, while the student continues to explore trajectories that an efficient reasoner should avoid. In this paper, we propose BIRD(Bootstrapped Iterative Self-Reasoning Distillation), a two-stage self-reasoning distillation method that improves the rollout distribution before on-policy training. BIRD first samples concise solutions from the base model under a brevity instruction, keeps only answer-correct traces, and performs a lightweight prompt-switch SFT step. The traces are generated with the brevity instruction but learned under the original task prompt, turning instruction-induced conciseness into a default reasoning behavior. Starting from this warm model, BIRD then applies on-policy reverse-KL distillation with a concise self-teacher, now on cleaner and more informative prefixes. Across Qwen3 series models, BIRD achieves a stronger accuracy-efficiency trade-off than prompting and cold-start on-policy distillation on MATH-500 and AIME benchmarks. On Qwen3-8B, it improves MATH-500 accuracy from 86.2% to 92.0% while reducing the average response length from 3,099 to 1,115 tokens. These results highlight prefix support as a central factor in efficient reasoning distillation.