More Test-Time Compute Can Hurt: Overestimation Bias in LLM Beam Search

TL;DR

This paper reveals that increasing beam width in large language models can actually harm output quality due to overestimation bias caused by scorer noise, and it provides a theoretical framework to determine optimal beam width based on scorer signal-to-noise ratio.

Contribution

The paper introduces a novel analysis based on Extreme Value Theory that explains when wider beam search degrades performance and offers practical diagnostics for optimal beam width selection.

Findings

Overestimation bias grows with candidate pool size.

Optimal beam width depends on scorer's signal-to-noise ratio.

Perplexity scoring benefits diminish at any width, while PRM scoring improves with larger beams.

Abstract

Wider beam search should improve LLM reasoning, but when should you stop widening? Prior work on beam width selection has focused on inference efficiency \citep{qin2025dsbd, freitag2017beam}, without analyzing whether wider search can \emph{hurt} output quality. We present an analysis, grounded in Extreme Value Theory, that answers this question. Beam selection over noisy scorer outputs introduces a systematic overestimation bias that grows with the candidate pool size, and we derive a maximum useful beam width $\hat{k}$ beyond which search degrades performance. This critical width depends on the signal-to-noise ratio of the scorer: $\hat{k}$ grows exponentially with $(\Delta/\sigma)^2$, where $\Delta > 0$ is the quality advantage of correct paths over incorrect ones and $\sigma$ is the scorer noise. We validate this theory by comparing perplexity-guided and PRM-guided beam search across three 7B-parameter models and ten domains on MR-BEN (5,975 questions). Perplexity scoring, with its high noise, yields $\hat{k} = 1$: search provides no benefit at any width tested. PRM scoring, with lower noise, yields $\hat{k} \geq 4$, with gains of up to 8.9 percentage points. The same model, the same algorithm, but different scorers place $\hat{k}$ at opposite ends of the beam width range. Our analysis identifies the scorer's signal-to-noise ratio as the key quantity governing beam width selection, and we propose diagnostic indicators for choosing the beam width in practice.