Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for Problem-Solving with Language Models

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 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 indicate smaller models (e.g., Llemma-7B) can outperform larger models given the same computation budgets, and that smaller models paired with advanced inference algorithms yield Pareto-optimal cost-performance trade-offs. For instance, the Llemma-7B model, equipped with our novel tree search algorithm, consistently outperforms Llemma-34B with standard majority voting on the MATH benchmark across all FLOPs budgets. We hope these findings contribute to a broader understanding of inference scaling laws for LLMs.