Rethinking Fine-Tuning when Scaling Test-Time Compute: Limiting Confidence Improves Mathematical Reasoning

TL;DR

This paper investigates how limiting model confidence during training can improve large language models' mathematical reasoning performance when using test-time compute strategies like pass@N, revealing the importance of co-designing training and inference.

Contribution

It introduces a modified training loss that reduces overconfidence, aligning training with pass@N, and demonstrates improved reasoning performance on math benchmarks.

Findings

Overconfidence from cross-entropy loss impairs pass@N accuracy.

Limiting confidence during training enhances mathematical reasoning.

Modified loss improves performance on MATH and MiniF2F benchmarks.

Abstract

Recent progress in large language models (LLMs) highlights the power of scaling test-time compute to achieve strong performance on complex tasks, such as mathematical reasoning and code generation. This raises a critical question: how should model training be modified to optimize performance under a subsequent test-time compute strategy and budget? To explore this, we focus on pass@N, a simple test-time strategy that searches for a correct answer in $N$ independent samples. We show, surprisingly, that training with cross-entropy (CE) loss can be ${\it misaligned}$ with pass@N in that pass@N accuracy ${\it decreases}$ with longer training. We explain the origins of this misalignment in terms of model overconfidence induced by CE, and experimentally verify our prediction of overconfidence as an impediment to scaling test-time compute via pass@N. Furthermore we suggest a principled, modified training loss that is better aligned to pass@N by limiting model confidence and rescuing pass@N test performance. Our algorithm demonstrates improved mathematical reasoning on MATH and MiniF2F benchmarks under several scenarios: (1) providing answers to math questions; and (2) proving theorems by searching over proof trees of varying shapes. Overall our work underscores the importance of co-designing two traditionally separate phases of LLM development: training-time protocols and test-time search and reasoning strategies.