@inproceedings{zhang-etal-2026-chronos,
title = "Chronos: Learning Temporal Dynamics of Reasoning Chains for Test-Time Scaling",
author = "Zhang, Kai and
Liao, Jiayi and
Li, Chengpeng and
Xie, Ziyuan and
Li, Sihang and
Wang, Xiang",
editor = "Liakata, Maria and
Moreira, Viviane P. and
Zhang, Jiajun and
Jurgens, David",
booktitle = "Findings of the {A}ssociation for {C}omputational {L}inguistics: {ACL} 2026",
month = jul,
year = "2026",
address = "San Diego, California, United States",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.findings-acl.1376/",
pages = "27651--27664",
ISBN = "979-8-89176-395-1",
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 **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."
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<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 **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.</abstract>
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%0 Conference Proceedings
%T Chronos: Learning Temporal Dynamics of Reasoning Chains for Test-Time Scaling
%A Zhang, Kai
%A Liao, Jiayi
%A Li, Chengpeng
%A Xie, Ziyuan
%A Li, Sihang
%A Wang, Xiang
%Y Liakata, Maria
%Y Moreira, Viviane P.
%Y Zhang, Jiajun
%Y Jurgens, David
%S Findings of the Association for Computational Linguistics: ACL 2026
%D 2026
%8 July
%I Association for Computational Linguistics
%C San Diego, California, United States
%@ 979-8-89176-395-1
%F zhang-etal-2026-chronos
%X 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 **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.
%U https://aclanthology.org/2026.findings-acl.1376/
%P 27651-27664
Markdown (Informal)
[Chronos: Learning Temporal Dynamics of Reasoning Chains for Test-Time Scaling](https://aclanthology.org/2026.findings-acl.1376/) (Zhang et al., Findings 2026)
ACL