Rethinking Fine-Tuning when Scaling Test-Time Compute: Limiting Confidence Improves Mathematical Reasoning
This work addresses a critical issue for LLM developers by co-designing training and test-time strategies to optimize performance under compute budgets, though it is incremental in modifying existing loss functions.
The paper tackles the problem of misalignment between cross-entropy loss training and test-time compute scaling (pass@N), showing that longer training can decrease pass@N accuracy due to model overconfidence, and proposes a modified training loss that limits confidence to improve mathematical reasoning performance on benchmarks like MATH and MiniF2F.
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.