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Rethinking External Slow-Thinking: From Snowball Errors to Probability of Correct Reasoning
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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.
Forward citations
Cited by 6 Pith papers
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PUMA detects when a reasoning model's entropy drop aligns with hidden-state momentum, truncates at that point, and reports improved accuracy-efficiency on 1.5B-32B reasoning models.
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Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought
LLM chain-of-thought length converges to an optimum because of an underfitting-overfitting tradeoff, formalized in a continuous reasoning-space framework and tested with RL.
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