Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for LLM Problem-Solving

Yangzhen Wu, Zhiqing Sun, Shanda Li, Sean Welleck, Yiming Yang

Keywords: Inference Scaling Law, Test-time Scaling, Compute-optimal Inference, LLM reasoning

TL;DR: We study inference scaling laws and compute-optimal inference of LLMs on mathematical problem solving.

Abstract:

While the scaling laws of large language models (LLMs) training have been extensively studied, optimal inference configurations of LLMs remain underexplored.
We study inference scaling laws (aka test-time scaling laws) and compute-optimal inference, focusing on the trade-offs between model sizes and generating additional tokens with different inference strategies. As a first step towards understanding and designing compute-optimal inference methods, we studied cost-performance trade-offs for inference strategies such as greedy search, majority voting, best-of-$n$, weighted voting, and two different tree search algorithms, using different model sizes and compute budgets. Our findings suggest that scaling inference compute with inference strategies can be more computationally efficient than scaling model parameters. Additionally, smaller models combined with advanced inference algorithms offer Pareto-optimal trade-offs in cost and performance. For example, the Llemma-7B model, when paired with our novel tree search algorithm, consistently outperforms the Llemma-34B model across all tested inference strategies on the MATH benchmark. We hope these insights contribute to a deeper understanding of inference scaling laws (test-time scaling laws) for LLMs.

Primary Area: foundation or frontier models, including LLMs

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Submission Number: 6864