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Answer Convergence as a Signal for Early Stopping in Reasoning

Paper · 2025 · Xin Liu and Lu Wang

Summary

Reasoning-oriented LLMs often keep generating chain-of-thought text long after they have effectively settled on an answer, which wastes tokens and increases latency. Liu and Wang first measure how much explicit reasoning is actually needed. They split R1-distilled traces into sentence-level chunks, insert </think> after each growing prefix to force an answer, and record when the prediction stops changing. They call this measure the Answer Convergence Ratio (ACR). Across NaturalQuestions, GSM8K, MATH-500, GPQA-Diamond and AIME'24, many answers stabilise before the trace ends, and harder tasks stabilise later. Building on this, the authors propose three inference-time stopping strategies that leave model weights untouched:

  • halting once consecutive chunks yield the same answer;
  • adaptively raising the logit of </think>;
  • a lightweight predictor trained on final-layer activations, whose labels come from detected convergence rather than gold answers.

Across five open-weights LLMs, token usage drops substantially with little or no accuracy loss. The supervised variant is the most robust on difficult benchmarks. The work offers a cheap, retraining-free way to cut reasoning costs.

Key points

  • Convergence study (R1-Qwen-32B): ACR peaks near 0 for NQ, at roughly 0.8 on both GSM8K and MATH-500, and close to 0.9 on GPQA as well as AIME'24. The abstract states that math answers typically converge after roughly 60% of reasoning steps.
  • Methods:
    • Answer Consistency stops after k consecutive chunks give identical answers.
    • Think Token Adjustment boosts </think> in proportion to max-minus-mean logit, so the push toward stopping is strongest when the model is confident.
    • Learn-to-Stop is a supervised stopping predictor based on internal activations.
  • Learn-to-Stop results: up to 48% fewer tokens on NQ with QwQ-32B. On GSM8K with QwQ-32B, tokens fall from 755.1 to 418.9 (about 44%) with a 0.2-point accuracy drop. On GPQA, tokens fall by 39.2% with comparable accuracy (24.2 vs. 25.3).
  • Unsupervised methods: they work well on NQ and GSM8K; Answer Consistency saves over 40% of tokens on NQ while also improving accuracy. They become unstable on MATH-500 and GPQA. Baselines include the original model and CCoT (a prompt-level token budget).
  • Models and scaling: the models are R1-Qwen-7B/32B, R1-Llama-8B/70B and QwQ-32B. Larger models converge earlier and save more; for example, R1-Llama-70B cuts 46.4% of tokens versus 34.1% for the 8B model.
  • Limitations: convergence does not guarantee correctness, and early truncation can occasionally harm reasoning faithfulness.

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 MichiganAnn Arbor · United States70 works · 13,693 citations

 Fields, topics and concepts

📚 Shelves 5The field of science this work belongs to (OpenAlex fields).Computer Science · 16,667 worksArtificial Intelligence · 16,194 worksArts and Humanities · 16,039 worksLanguage and Linguistics · 15,891 worksComputer Vision and Pattern Recognition · 2,869 works

🧭 Topics 1Research subjects and languages the work is about.Reasoning · 1,426 works

Cite

Cite as Xin Liu and Lu Wang. 2025. Answer Convergence as a Signal for Early Stopping in Reasoning. Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing.

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.18653/v1/2025.emnlp-main.904

@inproceedings{liu2025answer,
  title = {{Answer Convergence as a Signal for Early Stopping in Reasoning}},
  author = {Xin Liu and Lu Wang},
  booktitle = {Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing},
  year = {2025},
  doi = {10.18653/v1/2025.emnlp-main.904},
  url = {https://doi.org/10.18653/v1/2025.emnlp-main.904}
}

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