Chronos: Learning Temporal Dynamics of Reasoning Chains for Test-Time Scaling

Abstract

Test-Time Scaling (TTS) has emerged as an effective paradigm for improving the reasoning performance of large language models (LLMs). However, existing methods -- most notably majority voting and heuristic token-level scoring -- treat reasoning traces or tokens equally, thereby being susceptible to substantial variations in trajectory quality and localized logical failures. In this work, we introduce \textbf{Chronos}, a lightweight and plug-and-play chronological reasoning scorer that models each trajectory as a time series. Specifically, Chronos learns to capture trajectory features of token probabilities, assigns quality scores accordingly, and employs a weighted voting mechanism. Extensive evaluations on both in-domain and out-of-domain benchmarks demonstrate that Chronos consistently delivers substantial gains across a variety of models, with negligible computational overhead. Notably, Chronos@128 achieves relative improvements of 34.21\% over Pass@1 and 22.70\% over Maj@128 on HMMT25 using Qwen3-4B-Thinking-2507, highlighting its effectiveness.