Organizations: School of Computer Science and Engineering, Beihang University · 3Hangzhou Innovation Institute, Beihang University · 2Qingdao Research Institute, Beihang University
Abstract
Test-time scaling improves the reasoning performance of large language models but often results in token-inefficient overthinking, where models continue reasoning beyond what is necessary for a correct answer. Existing dynamic early-exit methods typically rely on single-step confidence signals, which are often unreliable for detecting reasoning convergence in multi-step settings. To mitigate this limitation, we propose TRACE, a training-free framework for efficient test-time scaling that determines when to terminate reasoning based on temporal aggregation of multi-step evidence rather than instantaneous signals. TRACE detects reasoning convergence over time by aggregating two complementary signals across recent reasoning steps: answer consistency, capturing the persistence of predicted answers, and confidence trajectory, modeling the temporal evolution of model confidence. Benefiting from these two factors, TRACE can accurately determine whether the reasoning process has converged, thereby promptly halting inference and effectively avoiding redundant reasoning steps. Extensive experiments on multiple challenging benchmarks show that TRACE reduces reasoning token usage by 25-30% on average while maintaining accuracy within 1-2% of full-length reasoning, consistently outperforming existing dynamic reasoning methods.
Large Reasoning Models (LRMs) improve performance by allocating additional inference-time compute to generate extended chain-of-thought reasoning. However, recent studies reveal that sequential test-time scaling often yields diminishing or even negative returns, as longer traces exhibit increased uncertainty, error compounding, and drift from the original problem. We propose ThinkRetrieve, a test-time scaling framework that augments the reasoning traces of LRMs with dynamically retrieved solved examples at each reasoning step. Given an external corpus of problems paired with step-by-step solutions, ThinkRetrieve retrieves relevant exemplars at each intermediate step and injects them directly into the thinking trace, providing the model with guidance on how to reason rather than merely what facts are relevant. Experiments across five reasoning models (1.5B--8B parameters) on GSM-8K, MATH-500, AIME 2025, and SciQ demonstrate that ThinkRetrieve consistently improves accuracy over standard test-time scaling, with relative gains of up to 60% on AIME 2025.
Test-time scaling has become an effective paradigm for improving the reasoning ability of large language models by allocating additional computation during inference. Recent structured approaches have further advanced this paradigm by organizing inference across multiple trajectories, refinement rounds, and verification-based feedback. However, existing structured test-time scaling methods either weakly coordinate parallel reasoning trajectories or rely on noisy historical information without explicitly deciding what should be retained and reused, limiting their ability to balance exploration and exploitation. In this work, we propose TMAS, a framework for scaling test-time compute via multi-agent synergy. TMAS organizes inference as a collaborative process among specialized agents, enabling structured information flow across agents, trajectories, and refinement iterations. To support effective cross-trajectory collaboration, TMAS introduces hierarchical memories: the experience bank reuses low-level reliable intermediate conclusions and local feedback, while the guideline bank records previously explored high-level strategies to steer subsequent rollouts away from redundant reasoning patterns. Furthermore, we design a hybrid reward reinforcement learning scheme tailored to TMAS, which jointly preserves basic reasoning capability, enhances experience utilization, and encourages exploration beyond previously attempted solution strategies. Extensive experiments on challenging reasoning benchmarks show that TMAS achieves stronger iterative scaling than existing test-time scaling baselines, with hybrid reward training further improving scaling effectiveness and stability across iterations. Code and data are available at https://github.com/IQuestLab/tmas.
Scaling inference-time computation has emerged as a reliable method to improve the performance of large language models on complex reasoning and programming tasks. However, standard approaches such as independent sampling and sequential multi-turn refinement operate without token-level credit assignment, resulting in computational inefficiency, since valid reasoning prefixes are frequently discarded. In this work, we introduce Test-Time Scaling via Error Localization (TTEL), an inference-time algorithm that utilizes fixed or environment feedback to perform token-level error localization. By comparing conditional probabilities under informed feedback against a null-context baseline, TTEL isolates the step at which an error occurred. The algorithm then truncates the trajectory and branches a new generation, maximally reusing the valid prefix. Extensive evaluations demonstrate that TTEL establishes strictly dominating Pareto frontiers across sequential reasoning domains, measured by pass-at-k vs. generated-token cost. With Qwen3-8B on LiveCodeBench, TTEL attains a pass@64 of 71.0% while generating approximately half as many tokens as independent sampling (360.4k vs. 735.0k). Generalizing to math benchmarks AIME-2025 and HMMT-2025, TTEL cleanly outperforms competing test-time baselines across both Qwen3-8B and Qwen3-4B-Thinking-2507.