Efficient Language Model Reasoning

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23 papers in the last four weeks, up 188% on the four weeks before. 0.2% of all new papers.

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Oct 8, 2026cs.AI

When Should Agents Think? Adaptive Reasoning via Cross-Turn Estimation

Large language model (LLM)-based agents have demonstrated strong capabilities on complex tasks. They typically perform reasoning before each action throughout an interaction trajectory. However, reasoning may not be necessary at every turn, as reasoning produced earlier can continue to support subsequent actions. A key challenge is therefore to determine when existing reasoning remains sufficient and when a new reasoning step is needed, without relying on costly generation-based verification. We find that decreases in the likelihood of subsequent reference actions after removing additional reasoning closely track whether those actions remain recoverable given earlier reasoning, providing an effective and lightweight signal for estimating cross-turn action support. Based on this observation, we propose Reasoning Adaptation through Cross-Turn Estimation (RACE), a training approach for adaptive agent reasoning. RACE introduces a Likelihood-Guided Progressive Reasoning Cover Detection (LoGiC) procedure that progressively identifies reasoning turns whose removal has limited impact on the current and subsequent reference actions. The resulting removal signals are incorporated into both supervised fine-tuning and agentic reinforcement learning, enabling the policy to learn when to reason and when to act directly. Extensive experiments on four representative agent benchmarks show that RACE substantially reduces reasoning cost while maintaining or improving task performance.

Yiruo Cheng, Shen Huang, Xiaoshuai Song +5

Gaoling School of Artificial Intelligence, Renmin University of China · Alibaba Token Hub, Alibaba Group

Agentic Reasoning Efficient Language Model Reasoning

Oct 8, 2026cs.AI

Scaling to Tens of Thousands of Test-Time Iterations with Loop-Native Attention Residuals

In this paper, we argue that looped Transformers need their own residual connections to prevent performance degradation as the number of iterations grows. We observe that increasing loop iterations can reduce reasoning accuracy: noisy state updates overwrite correct intermediate deductions and even undo completed solutions. This leaves subsequent iterations to recover lost information from an already degraded representation: once an error arises in an earlier loop, often as a result of long-range propagation through the recurrence, later loops find it difficult to correct. In this paper, we introduce InfiLoop, a loop-native residual connection that learns which past computations to retain and how much to accept from each new update. InfiLoop combines content-based weighting with learned temporal decay to maintain a running summary of recurrent states. An exact streaming recurrence keeps its persistent aggregation memory constant as the loop count grows. The resulting adaptive update suppresses unreliable proposals and preserves useful intermediate states. Across extensive reasoning tasks, a 7M-parameter InfiLoop model outperforms existing recursive architectures, reaching 97.9% exact accuracy on Sudoku-Extreme, and 13.6% pass@2 on ARC-AGI-2. Notably, on Sudoku-Extreme, InfiLoop continues to improve with test-time looping beyond 20,000 effective steps, showing that added depth translates directly into stronger reasoning. Our code is available at https://github.com/pixeli99/InfiLoop.

Pengxiang Li, Dilxat Muhtar, Di He +3

The Hong Kong Polytechnic University · Independent Researcher · Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences +6

Recurrent Transformers Attention Residual Connections Neural Algorithmic Reasoning Efficient Language Model Reasoning Inference-Time Scaling

Oct 8, 2026cs.AI

From Chain-of-Thought to Loops: Non-Autoregressive Latent Reasoning via Looped Transformers

Chain-of-thought (CoT) reasoning often improves language-model performance by giving models additional computation before answering. However, explicit CoT expresses this computation as a sequence of autoregressively generated tokens. Latent reasoning replaces these tokens with compact continuous states, but most autoregressive latent-reasoning methods retain a left-to-right dependency among latent vectors. We introduce LLoCoT: a looped latent-reasoning framework that replaces left-to-right latent generation with iterative refinement of a compact latent workspace. A shared transformer is reapplied for a small number of refinement iterations, jointly updating the latent slots based on the prompt and the evolving workspace state. Using the refined state, a probabilistic head predicts a distribution from which latent tokens are sampled in parallel and used to condition an autoregressive decoder for answer generation. Training uses continuous representations derived from explicit CoT together with a final-answer prediction loss and likelihood-based supervision of the latent states. Across HumanEval and MBPP, LLoCoT achieves the highest mean among the evaluated methods, performing on par in accuracy with Reasoning SFT, our explicit-CoT baseline, while outperforming the base model, answer-only SFT and NF-CoT. Relative to Reasoning SFT, LLoCoT reduces time to the first answer token by approximately

36\times

and reasoning-phase latency by approximately

42\times

, while increasing end-to-end throughput by

9.2\%

. This design replaces serial thought generation with parallel latent-slot refinement while retaining probabilistic latent modeling and autoregressive answer decoding.

Gerard Grau García, Arnau Padrés Masdemont, Niccolò Grillo +3

Qualcomm AI Research · MIT · University of Cambridge +1

Efficient Language Model Reasoning Continuous Latent Reasoning Recurrent Transformers

Oct 7, 2026cs.LG

YANchor-4B: Effective Long-Horizon Reasoning in O(N) Time with O(1) Memory

Long-horizon reasoning demands access to earlier information at a manageable generation cost. Full-history attention incurs growing storage and computation, while recurrent compression can lose precise details. Therefore, we present YANchor-4B, a general-purpose recurrent model that preserves crucial memory as ANchors for retrieval during subsequent reasoning. Beyond

O(N)

-time generation and

O(1)

memory, YANchor enables effective long-horizon reasoning through its multidimensional memory mechanism. For example, on challenging math problems, it achieves 82.93% mean pass@1 on AIME 2024--2026 and 63.64% on HMMT, substantially outperforming linear-time, constant-state counterparts, including larger models. It also delivers several-fold higher batched long-generation throughput than Transformer and hybrid baselines on H100. Furthermore, evaluations across dozens of benchmarks demonstrate YANchor's superiority in general-purpose capabilities.

Huishan Ji, Hua Xu, Weiming Zhang +1

Rocore Matrix

Efficient Language Model Reasoning Memory-Augmented Language Models

Oct 7, 2026cs.LG

BoT-GRPO: Efficient Process-Reward RL for Reasoning via Bag-of-Token Aggregation

Reinforcement learning is now central to eliciting reasoning in large language models, while in the popular algorithm Group Relative Policy Optimization (GRPO) every token in a rollout receives the same advantage. We ask how to make process supervision efficient: accelerating convergence and improving final quality without the cost of value networks. We propose Bag-of-Tokens Group Relative Policy Optimization (BoT-GRPO), which extends GRPO to token-level reward models through a length-invariant "bag of tokens" aggregation: it collects all token-level rewards across rollouts, weights each by the inverse of its source sequence length, and computes per-token advantages relative to weighted group statistics. BoT-GRPO is critic-free, and is a drop-in replacement wherever GRPO is used when token-level reward is available. On React front-end code generation, BoT-GRPO reaches

80\%

compile rate up to

1.9\times

faster than GRPO and converges faster than modern GRPO variants (GSPO, DAPO, PURE) while reaching higher final compile and VLM-judged win rates. On a second task, AIME mathematical reasoning, BoT-GRPO delivers absolute Pass@

k

gains up to

8.1\%

over GRPO in half the steps. For both tasks we compare the algorithm's performance on reasoning vs. non-reasoning base-model families (Qwen2.5-3B, SmolLM3-3B, Phi-4-mini-reasoning). Our experiments also yield a practical recipe for the reward model itself: reward stability matters more than richness: clean, bounded, stable fine-grained signals consistently accelerate learning where noisier alternatives stall.

Yingxiang Yang, Weihang Xiao, Zhunxuan Wang +2

Amazon AGI · Virginia Tech

RL for Language Model Reasoning Group Relative Policy Optimization Efficient Language Model Reasoning Process Reward Models RL for Code Generation

Oct 7, 2026cs.AI

Efficient Reasoning with Flow Language Models

Flow Language Models (FLMs) have emerged as a continuous-state alternative to discrete diffusion language models, yet the role of their continuous representations in reasoning remains unclear. We investigate this question by comparing the reasoning efficiency of FLMs and discrete diffusion models, measured by solution accuracy under matched denoising steps. Unlike discrete diffusion, which passes categorical states between denoising steps, FLMs evolve a continuous sequence representation throughout denoising and decodes it into discrete tokens only at the end. Our theoretical analysis shows, from a superposition perspective, how information retained in these continuous states can benefit reasoning. Intermediate-state interventions provide further empirical support for this theoretical account, showing that removing information about alternative candidates reduces subsequent solution recovery. Together, these findings show that FLMs allow evidence for multiple candidates to persist and inform subsequent reasoning before a discrete answer is produced. Furthermore, our experiments on maze planning and Sudoku tasks show that FLMs achieve greater reasoning efficiency in the few-step regime: FLMs achieves higher sequence accuracy than discrete diffusion baselines at matched model sizes and small denoising steps. On maze planning tasks, FLMs can also achieve comparable accuracy with smaller models. For example, on Maze15, FLM reaches the 95% accuracy target at 64 denoising steps with 36.5% fewer parameters than MDLM. These findings point to continuous state spaces as a promising foundation for reasoning models that require fewer refinement steps.

Hanru Bai, Faissal Izermine, Oscar Davis +1

Max Planck Institute for Intelligent Systems · ETH Zurich · ELLIS Institute Tübingen +3

Efficient Language Model Reasoning Language Modeling Continuous Latent Reasoning Continuous Diffusion Language Models Algorithmic Reasoning

Oct 6, 2026cs.LG

The Dichotomy Between Pattern Recognition and Step-by-Step Reasoning

We argue that pattern recognition and step-by-step reasoning are two ends of a spectrum. A large language model (LLM) learns to reason step-by-step when data is structured such that the next token depends on a small amount of preceding context. Inference in LLMs resembles pattern recognition when the next token depends on a large amount of preceding context. If the next token depends on only the

c

most recent tokens, reasoning traces are paths on a De Bruijn graph whose nodes are

c

-length contexts and edges are next-token transitions between contexts. The set of reasoning traces of a task forms a directed acyclic subgraph of the De Bruijn graph. An LLM that has learned all edges of this subgraph can compose them to solve longer, unseen tasks, i.e., it reasons step-by-step. We prove that the number of edges is vanishingly small compared to the number of reasoning traces. Empirically, the number of training samples a transformer needs is a power law in the number of edges, so learning to reason step-by-step is sample efficient. We can induce De Bruijn structure in any task by maintaining a ``state'' that makes future reasoning independent of the past. The frequency of states in the reasoning trace determines

c

. We show, by fine-tuning Qwen2.5-1.5B-Instruct to solve equations and answer questions about stories, that frequent states (small

c

) result in higher accuracy but greater fragility to perturbations at test time. LLMs trained with a large

c

are only as good as models that perform pattern recognition without reasoning. A moderate density of states balances accuracy and robustness. We show that real-world data has De Bruijn structure: Qwen3-14B and Qwen3-32B retain over 75% of their accuracy on GSM8K, MATH-500 and GPQA-Diamond when attention is restricted to a sliding window less than 15% as long as the full reasoning trace.

Amrut Nadgir, Pratik Chaudhari, Vijay Balasubramanian

University of Pennsylvania

LLM Reasoning Efficient Language Model Reasoning Neural Algorithmic Reasoning LLM Reasoning with Graphs Language Model Robustness

Oct 6, 2026cs.AI

ThinkFuse: Trajectory-Aware Test-Time Fusion for Small Reasoning Models

Small reasoning models (SRMs) have shown strong performance on complex reasoning tasks by generating extended chain-of-thought trajectories, but they often fail to recover once their reasoning enters an erroneous path. Existing test-time fusion methods rely on local fusion signals to determine when to trigger fusion, which can be misled by transient uncertainty fluctuations and may reinforce unstable reasoning trajectories. We propose ThinkFuse, a training-free test-time fusion framework that selectively intervenes in unreliable reasoning segments. ThinkFuse compares segment-level uncertainty shifts with trajectory-level uncertainty trends to identify unstable reasoning points and fuse auxiliary reasoning paths into the primary model's trajectory. Extensive experiments demonstrate that ThinkFuse outperforms baselines on mathematical and knowledge-intensive reasoning benchmarks, with consistent gains across model-family combinations, and remains robust with a smaller primary model. Our analysis shows that ThinkFuse requires fewer fusion triggers and generates fewer tokens, highlighting the efficiency of selective triggering. Our code is available at https://github.com/js-lee-AI/ThinkFuse.

Myunghoon Kang, Jungseob Lee, Jaehyung Seo +1

Department of Computer Science and Engineering, Korea University · Department of Computer Science and Engineering, Konkuk University · Human-inspired AI Research

Efficient Language Model Reasoning LLM Reasoning

Oct 6, 2026cs.CL

SanSi: A Looped Typed Decision Model for System 1.5 Thinking

Typed decision models answer a declared question without generating text: a decision head returns a probability for each of the declared options in a single forward pass. A single pass is fast, intuitive System 1 thinking. We study what lies between one pass and generated reasoning: looping, in which the same layers are recursively applied several times before one typed readout. Each loop lets the model revise its hidden state before it commits to an answer, without generating a token; we call this System 1.5 thinking. We propose SanSi, which turns a pre-trained looped language model into a typed decision model. The option probabilities are read after every loop, and every loop is trained with a proper scoring rule, so that one model serves every budget from one loop to eight in a single run. On 10,027 test decisions from 59 sources, SanSi reaches 72.0% accuracy: 13.5 points above a non-looped model of the same shape trained with the same recipe, 5.3 points above a newer non-looped model of its size, and 1.8 points below one with three times the parameters. On two depth-controlled tasks, loops extend the solvable depth beyond the depths seen in training, where the larger single-pass model fails. Used as the judge for policy optimization with reinforcement learning, without gold answers, SanSi raises the generator's F1 by 7.7 points.

Shuyu Gan, Young-Jun Lee, Dongyeop Kang

University of Minnesota

Efficient Language Model Reasoning Implicit Reasoning in Language Models LLM Decision-Making Recursive Language Models

Oct 5, 2026cs.AI

COMPASS: Finding Where Reasoning Lives in Language Models

Explicitly eliciting reasoning substantially improves LLM performance. Existing approaches require a predefined characterization of reasoning, whether through CoT prompt design, contrastive CoT directions, or via SAE derived reasoning features. For mathematical reasoning with verifiable answers, we show that a much simpler signal suffices, which is the correctness of the model's own direct answer attempts. This signal yields a latent direction that elicits reasoning. This direction is decodable within the activations of most attention heads, but only a small subset of them can be effectively intervened. We introduce COMPASS, an inference-time steering method that identifies these heads using a logit-space attribution score and steers their activations along the correctness direction, requiring only per-head activation statistics. Across three model families and multiple math benchmarks, COMPASS outperforms the activation-steering baselines we compare against, improves GSM8K accuracy by 16 percentage points on average, and approaches CoT accuracy with 20-70% fewer generated tokens. Interventions transfer without re-fitting to unseen benchmarks, and ablations show that both the correctness direction and the small set of heads carrying it are necessary, with the effect concentrated in remarkably few heads.

Pratyay Dutta, Kowshik Thopalli, Vivek Narayanaswamy

University of California, Riverside, CA 92521. Work performed during a summer internship at Lawrence Livermore National Laboratory · Lawrence Livermore National Laboratory, Livermore, CA 94550.

Efficient Language Model Reasoning Activation Steering LLM Interpretability Numerical Reasoning in Language Models

Oct 5, 2026cs.CV

CALR: Continuous Anchored Latent Reasoning via Render-of-Thought Compression

Visual latent reasoning compresses rendered derivations into compact intermediate states, reducing textual reasoning overhead. Existing approaches differ in how they represent these states: continuous methods avoid vocabulary constraints, whereas discrete methods improve accuracy through quantization into a finite codebook. Our analysis of representative continuous and discrete systems identifies two functional requirements: answers must rely on latent states, and those states must carry valid, problem-specific reasoning. Continuous latents influence answers despite collapsed reasoning content, whereas discrete latents retain recoverable intermediate reasoning that answer prediction largely bypasses. To address these challenges, we propose Continuous Anchored Latent Reasoning (CALR), which connects latent formation with answer use through functional anchoring. With reference latents from information-balanced compression, CALR couples latent-mediated answer supervision with derivation-level semantic anchoring: the former routes answer supervision through intermediate states, while the latter grounds their decoded content in problem-specific derivations. A parallel-to-autoregressive curriculum develops sequential reasoning by conditioning subsequent latent blocks on generated prefixes. Evaluations on five mathematical reasoning benchmarks across model families show substantial accuracy gains. Under matched budgets, CALR gains 26.0 percentage points over a comparable continuous latent reasoning method. Further analyses show that its latents support answer prediction and carry problem-specific intermediate reasoning.

Zhaoyang Wei, Bowen Jiang, Yanchao Hao +5

University of the Chinese Academy of Sciences · Tencent

Efficient Language Model Reasoning Latent Visual Reasoning Implicit Reasoning in Language Models Continuous Latent Reasoning LLM Mathematical Reasoning Latent Reasoning

Oct 5, 2026cs.LG

Sharpen Without Search: On-Policy Distillation of Sequence-Level Power Distribution

A language model can give a correct answer more probability than any single incorrect answer and still usually sample an incorrect one, because the incorrect answers together hold more probability. The power distribution raises each complete answer's probability to a power above one and renormalizes, shifting probability toward answers the model finds most likely (sharpening). Sampling from it improves reasoning without changing parameters, but needs many scored candidates per query. We show that a model can instead be trained to produce such answers in one generation. On-policy power distillation (OPPD) runs a sequential Monte Carlo sampler in which the model being trained generates candidates and a frozen teacher's power distribution weights them; the same probabilities weight each answer in a maximum-likelihood update. Training raises single-generation accuracy by up to 23.0 points on MATH500 and 27.3 on GSM8K over the untrained model at the same temperature, and one generation scores 2.4 and 3.5 points above published power sampling with 64 candidates, recovering 94 percent of the gain that 16 candidates give the untrained model. For context, against GRPO trained with verified rewards from the same checkpoint and budget, OPPD scores 3.8, 4.0 and 5.4 points higher on MATH500, GSM8K and AIME using no reference answers; the two are complementary, and OPPD applied after GRPO adds up to 9.3 points. Trained only on mathematics, OPPD raises HumanEval accuracy by up to 5.3 points. One loss coefficient moves the sharpening exponent the model absorbs between 1.19 and 2.02, against 1.14 for ordinary on-policy distillation, and it rises mostly on the model's own answers. Gains hold across model families and sizes, including a model already trained with verified rewards, where lowering the temperature gives nothing and OPPD adds 4.4 points on MATH500. Code: https://github.com/ArminAzizi98/OPPD.

Erfan Baghaei Potraghloo, Seyedarmin Azizi, Arya Fayyazi +4

University of Southern California, Los Angeles, USA · Intel AI, USA

Numerical Reasoning in Language Models Efficient Language Model Reasoning On-Policy Distillation

Oct 5, 2026cs.LG

What Matters for Latent Reasoning with Flow Matching

Latent reasoning lets a large language model (LLM) think in a continuous space and verbalize only the answer. We argue that an effective latent thought must meet five requirements: it should be useful, helping produce the correct answer rather than merely changing it, diverse, so that resampling yields different reasoning trajectories, explainable, so that a decoded chain of thought (CoT) reflects reasoning the answer actually follows, refinable with more inference compute, and efficient, costing less than an explicit CoT at comparable accuracy. Current methods rarely meet these requirements: they learn shortcuts from the question, distill the explicit CoT into their weights, or imitate it one token at a time. We focus on flow matching in a learned latent space, the family we argue is best placed to meet them, and identify the training choices that make it work. The result is Flow-based Latent Reasoning (FLaRe), a simple recipe covering what the latent space encodes and how to shape it, where to train the flow, how to read out the answer, and a final stage of training on the model's own verified thoughts. A probe for each requirement shows that FLaRe improves on prior latent methods in all five. It also compares favorably with them on arithmetic benchmarks, while reaching 97% of the accuracy of explicit CoT at a quarter of its latency.

Yassine Ouali, Adrian Bulat, Georgios Tzimiropoulos

Samsung AI Cambridge · Technical University of Iasi · Queen Mary University of London

Flow Matching Efficient Language Model Reasoning Continuous Latent Reasoning Latent Reasoning

Oct 5, 2026cs.CL

Test-Time Adaptation of Reasoning Strategies with Bayesian Nonparametric Memory

While modern large language models (LLMs) have been trained to reason through verbalized chains-of-thought, the generation cost grows substantially due to suboptimal paths to reach the final answer. Furthermore, as new insights are discovered while observing various input queries (e.g. through self-reflection), limited mechanisms exist for carrying forward these findings to be applied to subsequent problems. One can view the list of such strategies or behaviors as a growing cheatsheet, with elements retrieved from this memory module at inference-time. In this work, we consider structured cheatsheets, with learned clusters of behaviors. We introduce a Hierarchical Dirichlet Process Gaussian Mixture Model (HDP-GMM) over behavior embeddings, which shares components across domains while allowing domain-specific mixing weights, and uses the posterior predictive to retrieve relevant behaviors for a query; we call this a

\textit{Bayesian Cheatsheet}

. This mechanism allows for cheap adaptation in an online test-time training (TTT) setting, softly updating the mixture's sufficient statistics following each sample and enabling the creation of new components when the synthesized behaviors are sufficiently novel. We demonstrate that Bayesian Cheatsheet achieves clear performance gains relative to existing memory modules across reasoning benchmarks such as AIME'25, Omni-MATH, and PhysReason, even in the cold-start setting. We show that the Bayesian Cheatsheet is an adaptively reorganizing memory module, as behaviors can be re-assigned to components through a single step of collapsed Gibbs sampling. Our findings highlight the value of Bayesian-inspired memory modules for effective test-time adaptation and the role of structure in metacognitive reasoning.

Keshav Ramji, Tahira Naseem, Ramón Fernandez Astudillo

IBM Research AI

Memory-Augmented Language Models Bayesian Mixture Models Bayesian Inference Efficient Language Model Reasoning Test-Time Training Metacognition in Language Models

Oct 5, 2026cs.LG

Quantifying the Stability of Multi-Step Reasoning via Error Amplification

We consider the stability of multi-step reasoning processes, which have extensive applications in language models, including chain-of-thought and algorithmic reasoning. While longer sequences of reasoning can improve a model's generation capability at test time, the errors due to intermediate reasoning steps can accumulate in autoregressive generation, and thus grow substantially at the end. In this paper, we ask: What are the key factors determining the stability of multi-step reasoning? First, we show an inference error bound governed by the product of spectral norms of the Jacobians taken through the input space across generation steps. This product can be viewed as an error amplification factor, which could scale exponentially with the number of reasoning steps, serving as a quantitative measure of reasoning stability. Second, we analyze this measure in transformer models trained to predict simple tasks like linear and quadratic functions. We theoretically prove that the transformer model converges to a solution where the stability measure decays, thus yielding nearly zero inference loss over (arbitrarily) long steps. Finally, the stability analysis leads to several algorithmic implications for controlling the stability, through (i) chain-of-thought length compression that reduces the sensitivity of each step, and (ii) quantization-aware training that regularizes the input Jacobian norms. We validate the proposed algorithms by fine-tuning language models on graph-algorithmic reasoning tasks and symbolic state-tracking tasks. Across seven evaluations, our algorithms improve over baseline comparisons by 3.5% on average, and by 8.2% for longer-length inputs. Ablation analysis validates that the stability measure is drastically reduced by 3-8

\times

, confirming the regularization effect on the spectral norms of the (input space) Jacobians.

Dongyue Li, Ziniu Zhang, Minxuan Duan +1

Northeastern University Boston, MA

Efficient Language Model Reasoning CoT Compression

Oct 5, 2026cs.CL

Can Language Models Learn to Reject Their Own Bad Reasoning Steps?

Verifier-guided decoding can prevent harmful reasoning steps from contaminating subsequent generation, but typically relies on an external learned verifier. We ask whether a language model can instead reject its own bad reasoning steps. We define a prefix's recoverability as the probability that the frozen generator can complete it correctly. Diagnostics show that adjacent recoverability changes are often difficult to resolve with practical Monte Carlo budgets, while same-prefix candidates exhibit a sparse low-recoverability tail. We introduce Self-Step Rejection (SSR), which trains a lightweight LoRA acceptance gate on the generator backbone while keeping the base model frozen. SSR uses confidence-qualified first-passage supervision: steps before the first resolved crossing of a root-relative recoverability barrier are accepted, the crossing step is rejected, and unresolved steps and suffixes are excluded. Training combines pointwise classification, same-prefix pairwise learning, and group-relative policy refinement using final-answer correctness. At inference, SSR accepts candidates or resamples from the unchanged prefix under rejection budgets, without an external learned verifier. Across three reasoning models and five mathematical reasoning benchmarks, SSR improves macro-average accuracy over single-pass decoding by 5.4--10.1 points using 1.21--1.40x as many generated tokens, and achieves the highest macro-average accuracy among evaluated step-level methods. Full-solution scaling methods require 4.47--8.27x the single-pass token cost for comparable performance.

Siheng Xiong, Xiaoze Liu, Yiqiao Jin +2

Georgia Institute of Technology · Purdue University

LLM Self-Correction Language Model Decoding Efficient Language Model Reasoning LLM Reasoning Reasoning Verification

Oct 4, 2026cs.LG

Expanding LLM Reasoning

Extra inference compute is usually spent on sampling more reasoning chains. We study where inside an existing chain an additional continuation should begin. We define expansion utility, the change in correctness from restarting a chain at a stored step, and measure it at every eligible step for nine models on six benchmarks (41 model and benchmark cells). Restart position matters: steps selected on one set of continuations beat uniform placement when scored on disjoint ones, in held-out audits on 5, 16, and 38 cells (+4.25 points [+2.51, +6.63] in a fresh five-cell audit). A fixed rule that restarts from the last eligible steps, always-last, is a strong baseline: our learned router beats uniform placement but shows no detected gain over it, and on DeepSeek-R1-Distill-Qwen-14B/MATH-500 always-last exceeds the exact self-consistency frontier at matched aggregate generated output by +0.052 [+0.008, +0.098], using 0.774x the aggregate generated output of four-sample self-consistency. Cross-fitted oracle selection still finds held-out headroom beyond declared positional classes, a target for future selectors. Finally, breaking step-label ties by earliest index flips the sign of a pointwise selector's gain over uniform placement in every seed of a five-seed diagnostic with four rollouts per step; randomized ties remove the bias.

Rian Atri, Evan Luo

Keiji AI · University of California, Berkeley

LLM Inference Efficiency Inference-Time Scaling Efficient Language Model Reasoning Inference-Time Compute Allocation LLM Reasoning

Oct 1, 2026cs.CL

AURAL: Adaptive Latent Reasoning with Joint Chunk for Speech Language Models

Model intelligence and fast response jointly shape the quality of interaction with speech language models, yet remain difficult to achieve together. Explicit chain-of-thought (CoT) improves reasoning and audio understanding, but generating intermediate reasoning tokens delays responses. Describing fine-grained acoustic cues further lengthens CoT and increases latency. Latent reasoning can reduce this overhead, yet existing methods often trail CoT and remain limited by single-path supervision and reasoning budgets that do not adapt to problem difficulty. We introduce AURAL, which models a distribution over multiple plausible reasoning continuations in latent space and jointly predicts chunks of future states to reduce sequential forward passes and reasoning latency. To provide initial supervision for latent reasoning, we construct AuralReason-683K: 683K bilingual speech utterances (about 1,000 hours) with concise CoT for emotion recognition, empathetic dialogue, and general reasoning. AURAL-RL then explores beyond these traces, rewarding concise reasoning that yields high-quality answers and adapting reasoning effort to each problem. Across two backbones, AURAL-RL achieves performance comparable to CoT-RL, with larger gains over the respective supervised checkpoints on most metrics. Analysis further shows that harder questions elicit more latent reasoning steps. On Qwen2.5-Omni, it reduces time to the first answer token by 11.8x, from 1.22 to 0.10 s, versus 0.05 s for direct answering.

Yuxiang Wang, Kunyu Feng, Yuancheng Wang +12

The Chinese University of Hong Kong, Shenzhen · Tencent Hunyuan · Tsinghua University +2

RL for Language Model Reasoning Audio Reasoning Efficient Language Model Reasoning Implicit Reasoning in Language Models Speech Language Models Efficient Language Model Inference+1

Oct 1, 2026cs.AI

Learning to Ask: Information Acquisition for SLM-LLM Collaboration, under a budget

Collaboration between a small language model (SLM) and a large language model (LLM) offers an opportunity to combine the efficiency of smaller models with the strong reasoning capabilities of larger ones. Existing approaches primarily frame such collaboration as a computation allocation problem, determining which model should handle each portion of the reasoning process. In black-box API-based settings, however, this paradigm can be inefficient due to coarse-grained delegation or repeated transmission of context across model switches. In this work, we instead formulate SLM-LLM collaboration as an information acquisition problem, under an API budget constraint. The SLM remains the primary reasoner and selectively queries a black-box LLM advisor only when needed, issuing targeted queries rather than delegating the reasoning process itself. To realize this strategy, we develop a three-stage RLVR framework that learns whether to call the advisor, how to formulate useful queries, and how to integrate the collaboration into the reasoning process by jointly refining advisor invocation and information use. Across mathematical reasoning and coding tasks, our approach improves the performance--cost tradeoff over existing collaboration baselines and, in some settings, matches or exceeds oracle problem-level routing. Finally, we show that our strategy can transfer to other advisor model families, without further training.

Yongjun Kim, Xiaoxiao Li, Jaeho Lee

Pohang University of Science and Technology (POSTECH) · Department of Electrical and Computer Engineering, University of British Columbia · Vector Institute

RL for Language Model Reasoning Efficient Language Model Reasoning Multi-LLM Collaboration

Oct 1, 2026cs.AI

ReSolve: Reusing Candidate Reasoning through Selective Generative Moderation

Sampling multiple solutions spends computation on intermediate deductions and unfinished arguments as well as final answers. We introduce ReSolve, a training-free inference procedure that reuses this candidate reasoning through selective generative moderation. An answer-distribution controller invokes a model to examine existing derivations when candidates disagree or lack a parseable answer, then incorporates the generated solution into a bounded loop. Under Hybrid scoring on 130 competition-mathematics problems evaluated with two independently sampled candidate pools, ReSolve obtains 100 and 99 correct answers, compared with 91 and 92 for voting over the same four candidates, with no correct-to-incorrect changes relative to that vote in either pool. Eight-sample self-consistency obtains 94 and 96 correct answers while consuming substantially more tokens; ReSolve uses 46.3% and 47.2% fewer tokens in the two evaluations. A controlled ablation removes visible derivations while retaining answer keys, vote counts, and the per-state output-cap rule, reducing accuracy from 100 to 93 correct despite increasing computation. Selective and always-on Uniform moderation both solve 97 problems, while selectivity reduces moderation tokens by approximately 54% and total pipeline tokens by 6.2%. These results support candidate reasoning as reusable inference computation. They do not establish an accuracy advantage over additional sampling or a distinct benefit from specialized route instructions.

Bangji Yang, Jiajun Fan, Hongba Ma +6

University of Illinois at Urbana-Champaign · Tsinghua University · Rutgers University +2

Efficient Language Model Reasoning Inference-Time Compute Allocation Efficient Language Model Inference LLM Mathematical Reasoning

Sep 30, 2026cs.IT

Interpreting Reasoning of Large Language Models via Partial Information Decomposition

Large reasoning models (LRMs) have achieved substantial improvements in solving complex mathematical problems, but often produce lengthy, repetitive, or erroneous reasoning trajectories. In this work, we introduce a new interpretability framework, SLIDER, to evaluate the quality of the reasoning process. SLIDER leverages an emerging body of work from information theory called Partial Information Decomposition to disentangle the information about the final answer between two consecutive reasoning steps into non-negative components: unique information (in preceding steps or current step), redundant information, and synergistic information. Building on this decomposition, we propose the Step-wise Repetitive Reasoning Index (Step-RRI), a theoretically grounded measure that assesses whether the answer-relevant information in the current step

S_i

is predominantly redundant with the past steps

S_{<i}

, relative to its unique and synergistic contributions. To evaluate the effectiveness of Step-RRI in detecting repetitiveness, we apply SLIDER to the redundancy class of the PRMBench dataset where Step-RRI improves step-level redundancy identification accuracy by over

10

points compared to embedding-similarity and information-gain baselines. Next, we define Trajectory-RRI, an aggregate measure of repetitiveness for an individual reasoning trajectory. To demonstrate its practical relevance, we show that average Trajectory-RRI strongly correlates with actual reasoning length across QwQ-32B, DeepSeek-R1-Distill-Qwen-32B, and GPT-4.1, motivating its use as a signal for improving reasoning efficiency. Finally, we introduce Trajectory-RRI-guided data selection for fine-tuning, demonstrating that selecting training data based on Trajectory-RRI can improve a fine-tuned model's reasoning efficiency while largely preserving its task performance.

Barproda Halder, Qiuyi Zhang, Sanghamitra Dutta

University of Maryland, College Park · Elorian AI

LLM Interpretability Efficient Language Model Reasoning Large Reasoning Models

Sep 29, 2026cs.CL

LongHarness Bench: Stress-Testing Language Model Harnesses for Long-Context Reasoning

Language-model (LM) harnesses enable LMs to operate effectively over long contexts using additional compute. However, existing long-context evaluations are insufficient for distinguishing modern harnesses, reflected by saturated accuracy across harnesses and largely similar evaluation costs. In this paper, we introduce a benchmark for evaluating both the effectiveness and efficiency of long-context harnesses. Our tasks require diverse retrieval strategies, including lexical search and semantic matching, together with strategic and adaptive reasoning over global and local context. Much of the context is semantically relevant but only a small subset is useful at each step, creating both a challenging search problem and different accuracy--cost tradeoffs across processing strategies. For example, one task requires identifying every person satisfying several conditions using evidence scattered across documents; strategically checking the most selective condition first can narrow the search before verifying the remaining conditions. We evaluate multiple families of frontier language models with four state-of-the-art harnesses. Our benchmarks remain challenging even for strong model--harness combinations: the best reaches 68% macro-average accuracy across four evaluation suites. More importantly, we find that the same underlying model can exhibit markedly different efficiency under different harnesses. Our results establish efficiency as an important axis for long-context evaluation and provide a testbed for developing harnesses that process context strategically rather than exhaustively.

Quang Hieu Pham, Thuy Duong Nguyen, Jocelyn Qiaochu Chen +1

University of Alberta · Alberta Machine Intelligence Institute (Amii)

Long-Context Language Model Evaluation Long-Context Language Model Inference Efficient Language Model Reasoning Long-Context Inference

Sep 29, 2026cs.AI

HARISSA: Inference-Time Self-Checks for Efficient and Safe Local Language Model Deployment

Running a language model locally offers advantages in privacy, latency, and cost, but local hardware fits only small models, which are less capable than frontier models. The usual remedy for a hard query, escalating it to a cloud model, gives up the privacy and cost advantages of running locally. A deployment that stays local faces two decisions for hard queries instead. First, it can spend more computation on a query, e.g., reasoning before answering, which raises accuracy at a cost in latency, so it must decide which queries are worth the extra computation (efficiency). Second, some queries are beyond the local model, and delivering a wrong answer is worse than deferring the query to a human in the loop, so it must decide which answers are safe to deliver (safety). We show that both decisions can be made from the model's own hidden states. The prefill state, computed before any token is generated, predicts whether the model will answer correctly, and the answer state, at the end of the generated answer, predicts whether that answer is correct. HARISSA fine-tunes the model so that both states predict correctness, then makes both decisions with one policy that cascades through the ways of answering from cheapest to most expensive, skipping a way the prefill state predicts will fail and deferring the query when the answer it stops with is predicted wrong. On a device running a single model, HARISSA is within one accuracy point of chain-of-thought at 2.7 times lower latency. On a server holding four sizes of one model, HARISSA is more accurate than the FrugalGPT and Self-REF cascades at the same latency, and at the same deferral rate the answer state leaves fewer wrong answers than the standard confidence signals in five of six task and setting pairs.

Kenan Alkiek, Moontae Lee, David Jurgens +1

School of Information University of Michigan Ann Arbor, MI 48109, USA · SNU-LG AI Research Center Seoul, South Korea

On-Device Language Model Inference Selective Prediction Efficient Language Model Reasoning LLM Uncertainty Estimation Efficient Language Model Inference

Sep 29, 2026cs.LG

$S^3$ : Spectral Null-Space Swap Makes Reasoning Models Efficient

LLMs trained with Chain-of-thought excel in reasoning capability, but often come with excessive token cost. We find that the core of reasoning capacity lies in the Thinking model's weight component within the null space of a projection defined by the corresponding Non-thinking model's dominant singular directions, and removing the subspace component can largely improve reasoning efficiency without hurting the accuracy gained during thinking-mode post-training. Unlike existing efforts that mostly operate within the dominant subspace, we are the first to unveil the critical role of the null space and harness it for model optimization. Motivated by this finding, we propose Spectral Null-Space Swap (

S^3

), a training-free composition of paired Non-thinking and Thinking checkpoints. Our method keeps the Non-thinking model inside its own dominant subspace and takes the Thinking checkpoint outside it, improving reasoning efficiency while maintaining accuracy. We extensively evaluate

S^3

on 2B-30B dense and mixture-of-experts (MoE) architectures spanning 28 evaluation environments across mathematical, multimodal, and audio reasoning domains.

S^3

establishes new empirical Pareto Frontiers among training-free model composition strategies: across all settings, it reduces inference token overhead by an average of 27.4% compared to full Thinking models while simultaneously improving overall task accuracy by 1.0 percentage point (e.g., yielding +8.3% accuracy on HMMT25 alongside a 33.0% token speedup). We further use attention entropy for explanation and find that the retained component produces more concentrated attention, and we use a simplified analytical model about optimization to demonstrate why null-space can effectively reduce attention entropy, thereby improving the efficiency of reasoning.

Hongbo Ma, Sansheng Cao, Jiajun Fan +2

University of Illinois Urbana-Champaign · Tsinghua University · Dartmouth College +1

Efficient Language Model Reasoning Model Merging Efficient Language Model Inference Representation Geometry in Language Models Large Reasoning Models

Sep 29, 2026cs.AI

MetaCtrl: Your Large Language Models Can Reason Better and More Concisely with a Metacognitive Controller

Large reasoning models improve performance on challenging problems by allocating additional computation before answering, but longer reasoning does not always lead to better results and can introduce substantial redundant reasoning on simple problems. Conversely, aggressively shortening reasoning can degrade performance on difficult ones. Effective reasoning therefore requires dynamically deciding when additional computation is useful based on the reasoner's capabilities and evolving solution state. Existing approaches often rely on predefined budgets or intervention rules, retrain the target reasoner, or require additional supervision. We introduce MetaCtrl, a lightweight controller that adaptively regulates a frozen reasoner without predefined token budgets or reasoner retraining. We formulate reasoning regulation as a sequential metacognitive control problem: MetaCtrl observes the evolving reasoning trace and decides whether to continue, simplify, skip redundant steps, or conclude reasoning. It is trained directly with reinforcement learning using a reward that prioritizes correctness while favoring shorter trajectories among correct solutions, requiring neither supervised intervention trajectories nor problem-specific budgets. Across seven benchmarks spanning mathematics, science, and code, MetaCtrl consistently improves the accuracy of LRMs while reducing their reasoning length. On DeepSeek-R1-Distill-Qwen-7B, it improves average accuracy by 4.7 points while reducing generation length by 53.3%. Without further training, the same controller transfers to an unseen reasoner (e.g., Qwen3-14B), improving average accuracy by 2.9 points and reducing generation length by 50.3%. These results establish MetaCtrl as a plug-and-play controller for improving reasoning accuracy while substantially reducing inference-time generation. The code is available at https://github.com/binbin2xs/MetaCtrl.

Zhibin Wen, Tao Han, Lei Bai +2

Southern University of Science and Technology · The Hong Kong University of Science and Technology · Shanghai Artificial Intelligence Laboratory +1

RL for Language Model Reasoning Efficient Language Model Reasoning Efficient Language Model Inference Metacognition in Language Models Large Reasoning Models

Sep 28, 2026cs.AI

Knowing When Thinking Is Not Enough: Teaching Small Reasoning Models to Reason Beyond Their Parametric Knowledge

Scaling test-time computation is a powerful way to improve language-model reasoning, and is particularly appealing for small reasoning models (sRMs) that are cheap to serve. However, is additional thinking always the right operation? By intervening at intermediate reasoning states across two model families and multiple scales, we find that self-refinement largely consolidates probability mass onto solutions already reachable from the current state, rather than making new ones reachable. These interventions reveal two failure regimes: execution bottlenecks, where the correct path is reachable and reflection can recover it, and knowledge bottlenecks, where relevant external information makes it reachable. Motivated by this distinction, we introduce FlyBy, a selective querying framework, and train 4B and 8B variants to reason first, diagnose what remains unresolved, and, at a knowledge bottleneck, query stronger models whose parametric knowledge extends beyond its own. Supervised fine-tuning bootstraps a multi-depth query action, and cost-aware reinforcement learning calibrates whether to query, what to ask, and how much to spend. On 1,158 hard problems across six benchmarks, FlyBy-4B achieves 45.96% pass@8, surpassing Qwen3-14B (41.64%) at 2.7 times lower serving cost, while also exceeding Qwen3-8B in pass@1 (16.85% vs. 15.31%). Scaling to FlyBy-8B further improves pass@8 to 51.81%.

Chanuk Lee, Minki Kang, Sangwoo Park +3

KAIST

Cost-Aware Inference Efficient Language Model Reasoning LLM Routing LLM Reasoning

Sep 28, 2026cs.AI

Efficient Reasoning via Constrained Optimization in Latent Space

Large Reasoning Models (LRMs) have shown remarkable reasoning capabilities, yet they still suffer from overthinking, generating redundant reasoning steps which incur substantial token consumption. Existing methods, such as suppressing reflective keywords or forcing shorter reasoning lengths, attempt to mitigate this issue but inevitably truncate necessary steps and induce underthinking, thereby compromising performance. To address this dilemma, we investigate the latent representations and observe that efficient reasoning steps naturally cluster into a concentrated region in latent space, while those deviating from this region tend to produce verbose sequences. To leverage this, we keep reasoning focused within this region via a quadratic program which projects deviating hidden states back into the region. Then we propose a novel training-free framework to achieve efficient reasoning that reduces token generation costs without sacrificing performance. Extensive experiments conducted on four models ranging from 1.5B to 14B, and across six benchmarks in math reasoning, coding, and scientific QA, validate the effectiveness of our method, up to a 12.1% improvement in accuracy while reducing generated tokens by 11.8% to 52.8%. Codes are available at https://github.com/hzn18/Opt4Reasoning.

Zhinan Hou, Xingchen Li, Keyou You

Tsinghua University

Overthinking in Language Models Efficient Language Model Reasoning Quadratic Programming Efficient Language Model Inference Latent Space Optimization Large Reasoning Models

Sep 27, 2026cs.CL

On the Token Value Inequality in Efficient Reasoning

Chain-of-Thought reasoning has enabled large language models to achieve substantial performance gains on complex tasks. However, these gains come at the cost of dramatically increased token consumption. This raises a fundamental question: is every token in the reasoning trace equally valuable? We present a diagnostic and optimization framework grounded in a key empirical finding: the value of tokens within a CoT reasoning sequence is highly non-uniform, and this non-uniformity can be effectively characterized by token-level log probability signals. We show that normalized log probability helps distinguish core tokens, which carry structural and decisive reasoning content, from redundant tokens, which are exploratory, low-confidence filler that contributes less directly to the final answer. Building on these findings, we formulate the TokenProbe framework around two empirical findings and one claim: findings identify token value inequality first and then establish TokenProbe as a core-token proxy, and the claim introduces an efficient GRPO objective positing that selectively compressing redundant tokens can yield Pareto improvements in the accuracy-token efficiency space. Empirically, our method preserves reasoning quality while reducing the token usage by 76% of the baseline. Under matched reasoning-length budgets, we show that it can even outperform strong flagship baselines like Gemini-3.1-Pro. Homepage: https://runjia.tech/tokenprobe/.

Runjia Zeng, Hang Hua, Yiyang Liu +5

Rochester Institute of Technology · Purdue University · MIT-IBM Watson AI Lab +3

RL for Language Model Reasoning Efficient Language Model Reasoning Efficient Language Model Inference CoT Compression Reasoning Trace Analysis

Sep 24, 2026cs.AI

CounterRoute: Self-Routed Reasoning via Hierarchical Counterfactual Credit Assignment

Reasoning-capable language models often produce long chains of thought when direct answers suffice, wasting inference compute. Many dual-mode models leave this choice to users. Automating it is challenging because routing targets evolve with the policy, initial mode preferences destabilize exploration, and sequence-level objectives entangle routing with response learning. We introduce CounterRoute, an online reinforcement-learning framework that jointly learns routing and modeconditioned responses in one shared policy directly from a native dual-mode checkpoint, without method-specific SFT warm-up. Paired current-policy counterfactual rollouts assign cross-mode credit only to the routing token, while within-mode GRPO trains response tokens. A paired-to-self-routed curriculum stabilizes early training with forced rollouts from both modes, then increases self-routed updates to improve autonomous routing. Across nine benchmarks, CounterRoute better balances accuracy and efficiency than heuristic and learned adaptive-routing methods. Relative to always-thinking checkpoints, it improves macro-average accuracy while reducing mean generated tokens by 51% for Qwen3-8B and 41% for Qwen3-14B. On instruction-following and commonsense benchmarks where direct answering is strong, think rates fall as low as 1% while response quality improves. Despite training only on math and instruction following, its routing behavior and response quality generalize to held-out coding, science, knowledge, and commonsense benchmarks.

Ruochen Jiao, Besnik Fetahu, Zhenyu Shi +1

RL for Language Model Reasoning Efficient Language Model Reasoning LLM Routing Credit Assignment Efficient Language Model Inference Counterfactual Credit Assignment+1

Sep 23, 2026cs.CL

Towards Efficient Reasoning: Learning Causal Shortcuts for Diffusion Language Models

Diffusion Language Models (DLMs) have attracted significant attention for their strong reasoning ability. However, under a bidirectional attention mechanism, DLMs operate over an exponentially large exploration space compared to autoregressive models (ARMs), making it challenging to focus on reasoning-guiding tokens under random masking. We define causal shortcuts as token chains that cover the full sequence and provide explicit guidance towards correct reasoning trajectories. We analyze the effects of causal shortcuts on the reasoning accuracy and convergence speed of DLMs, and find that they largely improve answer convergence efficiency and generation accuracy. Motivated by this, we propose a Causal Shortcut Learning (CSL) Framework for DLMs. Specifically, we introduce a step-by-step token extraction procedure to extract causal shortcuts from data, and apply parallel prioritized masking on these tokens during training to enable efficient and accurate convergence to correct answers via causal shortcuts. Extensive experiments across multiple reasoning benchmarks and two base models demonstrate that CSL consistently outperforms existing SFT-variant baselines, achieving an average improvement of

1.92\%

over SFT-only models, and up to

4.20\%

on MATH-500. The code is available at the \href{https://github.com/ZJUDianJin/Causal-Shortcuts-Learning}{https://github.com/ZJUDianJin/Causal-Shortcuts-Learning

Dian Jin, Kairong Han, Baohong Li +5

Zhejiang University · Shanghai AI Laboratory

Efficient Language Model Reasoning Diffusion Language Models Efficient Language Model Inference