Top-$n\sigma$: Not All Logits Are You Need

TL;DR

The paper introduces top-$n\sigma$, a new sampling method for large language models that filters tokens based on a statistical threshold, improving reasoning accuracy and stability across temperatures.

Contribution

It proposes top-$n\sigma$, a novel logits-based sampling technique that outperforms existing methods and maintains stable performance regardless of temperature scaling.

Findings

Outperforms existing sampling methods in reasoning tasks

Surpasses greedy decoding in accuracy

Maintains consistent performance at high temperatures

Abstract

Large language models (LLMs) typically employ greedy decoding or low-temperature sampling for reasoning tasks, reflecting a perceived trade-off between diversity and accuracy. We challenge this convention by introducing top-$n\sigma$, a novel sampling method that operates directly on pre-softmax logits by leveraging a statistical threshold. Our key insight is that logits naturally separate into a Gaussian-distributed noisy region and a distinct informative region, enabling efficient token filtering without complex probability manipulations. Unlike existing methods (e.g., top-$p$, min-$p$) that inadvertently include more noise tokens at higher temperatures, top-$n\sigma$ maintains a stable sampling space regardless of temperature scaling. We also provide a theoretical analysis of top-$n\sigma$ to better understand its behavior. The extensive experimental results across four reasoning-focused datasets demonstrate that our method not only outperforms existing sampling approaches but also surpasses greedy decoding, while maintaining consistent performance even at high temperatures.