S*: Test Time Scaling for Code Generation

TL;DR

This paper introduces S*, a hybrid test-time scaling framework that significantly enhances code generation accuracy and coverage in large language models by combining sequential scaling with adaptive input generation and execution-grounded comparison.

Contribution

S* is the first hybrid test-time scaling method for code generation, combining parallel and sequential scaling with a novel adaptive selection mechanism to improve model performance.

Findings

S* improves performance across various models, enabling smaller models to outperform larger ones.

S* allows non-reasoning models to surpass reasoning models in code generation.

S* boosts state-of-the-art reasoning models, nearing top benchmark performance.

Abstract

Increasing test-time compute for LLMs shows promise across domains but remains underexplored in code generation, despite extensive study in math. In this paper, we propose S*, the first hybrid test-time scaling framework that substantially improves the coverage and selection accuracy of generated code. S* extends the existing parallel scaling paradigm with sequential scaling to push performance boundaries. It further leverages a novel selection mechanism that adaptively generates distinguishing inputs for pairwise comparison, combined with execution-grounded information to robustly identify correct solutions. We evaluate across 12 Large Language Models and Large Reasoning Model and show: (1) S* consistently improves performance across model families and sizes, enabling a 3B model to outperform GPT-4o-mini; (2) S* enables non-reasoning models to surpass reasoning models - GPT-4o-mini with S* outperforms o1-preview by 3.7% on LiveCodeBench; (3) S* further boosts state-of-the-art reasoning models - DeepSeek-R1-Distill-Qwen-32B with S* achieves 85.7% on LiveCodeBench, approaching o1 (high) at 88.5%. Code will be available under https://github.com/NovaSky-AI/SkyThought.