Rethinking External Slow-Thinking: From Snowball Errors to Probability of Correct Reasoning

Zeyu Gan, Yun Liao, Yong Liu
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:18170-18188, 2025.

Abstract

Test-time scaling, which is also often referred to as slow-thinking, has been demonstrated to enhance multi-step reasoning in large language models (LLMs). However, despite its widespread utilization, the mechanisms underlying slow-thinking methods remain poorly understood. This paper explores the mechanisms of external slow-thinking from a theoretical standpoint. We begin by examining the snowball error effect within the LLM reasoning process and connect it to the likelihood of correct reasoning using information theory. Building on this, we show that external slow-thinking methods can be interpreted as strategies to mitigate the error probability. We further provide a comparative analysis of popular external slow-thinking approaches, ranging from simple to complex, highlighting their differences and interrelationships. Our findings suggest that the efficacy of these methods is not primarily determined by the specific framework employed, and that expanding the search scope or the model’s internal reasoning capacity may yield more sustained improvements in the long term. We open-source our code at https://github.com/ZyGan1999/Snowball-Errors-and-Probability.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-gan25a, title = {Rethinking External Slow-Thinking: From Snowball Errors to Probability of Correct Reasoning}, author = {Gan, Zeyu and Liao, Yun and Liu, Yong}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {18170--18188}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/gan25a/gan25a.pdf}, url = {https://proceedings.mlr.press/v267/gan25a.html}, abstract = {Test-time scaling, which is also often referred to as slow-thinking, has been demonstrated to enhance multi-step reasoning in large language models (LLMs). However, despite its widespread utilization, the mechanisms underlying slow-thinking methods remain poorly understood. This paper explores the mechanisms of external slow-thinking from a theoretical standpoint. We begin by examining the snowball error effect within the LLM reasoning process and connect it to the likelihood of correct reasoning using information theory. Building on this, we show that external slow-thinking methods can be interpreted as strategies to mitigate the error probability. We further provide a comparative analysis of popular external slow-thinking approaches, ranging from simple to complex, highlighting their differences and interrelationships. Our findings suggest that the efficacy of these methods is not primarily determined by the specific framework employed, and that expanding the search scope or the model’s internal reasoning capacity may yield more sustained improvements in the long term. We open-source our code at https://github.com/ZyGan1999/Snowball-Errors-and-Probability.} }
Endnote
%0 Conference Paper %T Rethinking External Slow-Thinking: From Snowball Errors to Probability of Correct Reasoning %A Zeyu Gan %A Yun Liao %A Yong Liu %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-gan25a %I PMLR %P 18170--18188 %U https://proceedings.mlr.press/v267/gan25a.html %V 267 %X Test-time scaling, which is also often referred to as slow-thinking, has been demonstrated to enhance multi-step reasoning in large language models (LLMs). However, despite its widespread utilization, the mechanisms underlying slow-thinking methods remain poorly understood. This paper explores the mechanisms of external slow-thinking from a theoretical standpoint. We begin by examining the snowball error effect within the LLM reasoning process and connect it to the likelihood of correct reasoning using information theory. Building on this, we show that external slow-thinking methods can be interpreted as strategies to mitigate the error probability. We further provide a comparative analysis of popular external slow-thinking approaches, ranging from simple to complex, highlighting their differences and interrelationships. Our findings suggest that the efficacy of these methods is not primarily determined by the specific framework employed, and that expanding the search scope or the model’s internal reasoning capacity may yield more sustained improvements in the long term. We open-source our code at https://github.com/ZyGan1999/Snowball-Errors-and-Probability.
APA
Gan, Z., Liao, Y. & Liu, Y.. (2025). Rethinking External Slow-Thinking: From Snowball Errors to Probability of Correct Reasoning. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:18170-18188 Available from https://proceedings.mlr.press/v267/gan25a.html.

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