---
title: "Chronos — paper by Zhang et al. (2026) — summary and ideas"
description: "Parallel test-time scaling samples many reasoning traces from an LLM and combines their answers. 74.38% accuracy. 38 references."
authors: ["Kai Zhang", "Jiayi Liao", "Chengpeng Li", "Ziyuan Xie", "Sihang Li", "Xiang Wang"]
year: 2026
venue: "Findings of the Association for Computational Linguistics: ACL 2026"
source: "https://aclanthology.org/2026.findings-acl.1376/"
doi: "10.18653/v1/2026.findings-acl.1376"
licence: "CC BY 4.0 (ACL Anthology)"
licence_url: "https://creativecommons.org/licenses/by/4.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/zhang-2026-chronos-learning-temporal-dynamics-reasoning/"
---
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# Chronos: Learning Temporal Dynamics of Reasoning Chains for Test-Time Scaling

**Authors:** [Kai Zhang](https://md.research.elamur.ai/free/en/authors/kai-zhang/), Jiayi Liao, [Chengpeng Li](https://md.research.elamur.ai/free/en/authors/chengpeng-li/), Ziyuan Xie, [Sihang Li](https://md.research.elamur.ai/free/en/authors/sihang-li/) and [Xiang Wang](https://md.research.elamur.ai/free/en/authors/xiang-wang/) · **Year:** 2026 · **Venue:** [Findings of the Association for Computational Linguistics: ACL 2026](https://md.research.elamur.ai/free/en/venues/findings/) ([Findings of the Association for Computational Linguistics 2026](https://md.research.elamur.ai/free/en/venues/findings/2026/)) · **Publisher:** [Association for Computational Linguistics](https://md.research.elamur.ai/free/en/publishers/association-for-computational-linguistics/) · **Licence:** [CC BY 4.0 (ACL Anthology)](https://creativecommons.org/licenses/by/4.0/)

**Links:** [Publisher's page](https://aclanthology.org/2026.findings-acl.1376/) · [PDF](https://aclanthology.org/2026.findings-acl.1376.pdf) · [DOI 10.18653/v1/2026.findings-acl.1376](https://doi.org/10.18653/v1/2026.findings-acl.1376) · [OpenAlex](https://openalex.org/W7166837648)

**Citations:** 0 citations (OpenAlex, 2026-10-14)

## Summary
Parallel test-time scaling samples many reasoning traces from an LLM and combines their answers. Common combiners have weaknesses. Plain majority voting gives every trace the same weight. Heuristic confidence scores average token statistics into one number, which can hide a local logical slip partway through a trace. Chronos addresses this by scoring each trace with a small learned model that reads its token-probability signal as a time series.

For every decoding step, the method computes the negative mean log-probability of the top-k candidates. It keeps only the final segment of the trace and passes it through an InceptionTime-style network: a 1×1 projection, parallel convolutions with short and long kernels, and stacked residual blocks. The network outputs a quality score, and these scores weight the answer votes.

The scorer is trained on AIME problems from 2000–2023. It is tested in-domain and out-of-domain across several model sizes and consistently beats majority voting at almost no extra compute. This makes it a practical add-on for open-weight models.

## Key points
- **Benchmarks and models:** Evaluation covers AIME25, HMMT25 and GPQA-Diamond, using DeepSeek-1.5B, Qwen3-4B and DeepSeek-8B.
- **Headline result:** With Qwen3-4B-Thinking-2507 on HMMT25, Chronos@128 reaches 74.38% accuracy.
  - This compares with 55.42% for Pass@1 and 60.62% for Maj@128.
  - These are relative gains of 34.21% and 22.70%, at about 0.0005% additional inference FLOPs.
- **Score separation:** Compared with Tail Confidence, Chronos separates the score distributions of correct and incorrect traces much more cleanly.
- **Hyperparameters depend on the model:**
  - For DeepSeek-1.5B, the best setup is N_Proj = 8, N_Conv = 12 and short kernels {10, 20, 40}.
  - For Qwen3-4B, it is N_Proj = 16 with longer kernels {40, 80, 160}.
- **Limitations and code:**
  - The method needs white-box access to log-probabilities, so it cannot be applied to closed API models.
  - It was trained only on math; it transfers to GPQA, but less structured domains remain untested.
  - Code is available at github.com/Hizkai/Chronos.

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

## Institutions

- [University of Science and Technology of China](https://md.research.elamur.ai/free/en/universities/university-of-science-and-technology-of-china/) — University, Hefei, China · 145 works · 114,409 citations

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🧭 Topics (1): [🧮 Reasoning](https://md.research.elamur.ai/free/en/topics/reasoning/) · 1,685 works

## Cite

Cite as: Kai Zhang, Jiayi Liao, Chengpeng Li, Ziyuan Xie, Sihang Li and Xiang Wang. 2026. Chronos: Learning Temporal Dynamics of Reasoning Chains for Test-Time Scaling. Findings of the Association for Computational Linguistics: ACL 2026.

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@inproceedings{zhang2026chronos,
  title = {{Chronos: Learning Temporal Dynamics of Reasoning Chains for Test-Time Scaling}},
  author = {Kai Zhang, Jiayi Liao, Chengpeng Li, Ziyuan Xie, Sihang Li and Xiang Wang},
  booktitle = {Findings of the Association for Computational Linguistics: ACL 2026},
  year = {2026},
  doi = {10.18653/v1/2026.findings-acl.1376},
  url = {https://doi.org/10.18653/v1/2026.findings-acl.1376}
}
```

- [← previous ChronoLearn: A GRAG LLM-Based System for Structuring and Exploring Historical Narratives](https://md.research.elamur.ai/free/en/papers/aladdasi-2026-chronolearn-grag-llm-based-system/)
- [next → ChulaNLP at SemEval-2026 Task 6: A Hybrid BERT-LLM Framework for Political Response Clarity and Evasion Detection](https://md.research.elamur.ai/free/en/papers/peerachaidecho-2026-chulanlp-semeval-2026-task-6/)
- [↑ back to papers of 2026](https://md.research.elamur.ai/free/en/papers/2026/page/26/)

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*Updated 2 November 2026*