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* augments the existing parallel scaling approach with sequential scaling to further increase the performance. 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 S* across 12 Large Language Models and Large Reasoning Models and show that: (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%. Codes, model generations and intermediate experiments results are available under Codes, model generations and intermediate ex-periments results are available under https://github.com/NovaSky-AI/SkyThought.

Processing long contexts remains a challenge for large language models (LLMs) due to the quadratic computational and memory overhead of the self-attention mechanism and the substantial KV cache sizes during generation. We propose LLoCO, a novel approach to address this problem by learning contexts offline through context compression and in-domain parameter-efficient finetuning with LoRA. Our method enables an LLM to create a concise representation of the original context and efficiently retrieve relevant information to answer questions accurately. Our approach extends the effective context window of a 4k token LLaMA2-7B model to handle up to 128k tokens. We evaluate our approach on several long-context question-answering datasets, demonstrating that LLoCO significantly outperforms in-context learning while using 30 × fewer tokens during inference. LLoCO achieves up to 7.62 × speed-up during inference and 11.52 × higher throughput during finetuning, substantially reduces the cost of long document question answering. This makes it a promising solution for efficient long context processing.