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

TL;DR

Chronos tackles the problem of unreliable trajectory aggregation in test-time reasoning by treating each reasoning trace as a temporal sequence of token-level confidences. It maps decoding signals to a time series $\mathbf{s}=(s_1,...,s_{L_{tail}})$ with $s_t= - \frac{1}{k} \sum_{i=1}^{k} \log P_t(i \mid x, y_{<t})$, then processes the tail segment with multi-scale convolutional blocks inside a deep residual framework to output a quality score for each trajectory. Trajectories are ranked by these scores and a top fraction is used in a weighted voting scheme to produce final answers, yielding substantial gains over majority voting and uniform token-statistics baselines across multiple models and benchmarks. The approach achieves strong performance with negligible inference overhead, demonstrates cross-model generalization, and provides insights into hyper-parameter effects and trajectory-discrimination, making it a practical plug-in for test-time scaling in open-weight LLM settings. Overall, Chronos significantly improves reasoning accuracy in TTS by leveraging chronological dynamics, with demonstrated benefits on AIME/HMMT/GPQA benchmarks and robust scalability to increased trajectory budgets.

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.

Figures (8)

• Figure 1: Distribution of scores for correct and incorrect trajectories on AIME25. (a) Tail Confidence and (b) Chronos. All experiments use the DeepSeek-1.5B with 128 samples for 16 repeats per question.
• Figure 2: Framework of Chronos. It consists of three stages: (1) Multi-trajectory Sampling: Given an input query, we sample multiple independent inference trajectories and extract their token-level probability distributions, which are treated as temporal signals. (2) Chronological Reasoning Scoring: Chronos processes these temporal signals using multi-scale convolutions to explicitly capture sequential dependencies, producing a scalar quality score for each trajectory. (3) Weighted Majority Voting: The predicted trajectory scores are used to weight candidate answers, which are then aggregated to determine the final output.
• Figure 3: TTS performance on AIME25, HMMT25, and GPQA-D benchmarks. The x-axis represents the inference compute budget (# TFlops), corresponding to 1, 32, 64, 128 sampled trajectories per question, respectively.
• Figure 4: Cross-model generalization tests of Chronos.
• Figure 5: Hyper-parameter analysis. The plots display the AUC scores of Chronos trained and evaluated on reasoning trajectories sampled from DeepSeek-1.5B (left two panels) and Qwen3-4B (right two panels).