Existing RL methods for language models typically use token-level entropy, which captures uncertainty at the current position rather than over future generation. We study future entropy, i.e., uncertainty over the remaining suffix conditioned on the current prefix. By the entropy chain rule, local entropy is the expected decrease in future entropy, while the realized decrease depends on the chosen token, yielding an action-dependent future-entropy gap. We evaluate this signal at inference time with MIN-F-MC, an oracle-style probe that selects the candidate token with the lowest estimated future-entropy rate at high-entropy positions. On mathematical reasoning tasks, MIN-F-MC yields higher mean accuracy than greedy and Random TopK across the tested checkpoints and datasets. We then propose FEPO (Future Entropy Policy Optimization), which uses realized future-entropy rates at a sparse set of high-entropy positions to scale update magnitudes. Across the tested model–benchmark pairs, FEPO improves Mean@32 over GRPO.

Code LLMs have been widely used in various domains, including code generation, logical reasoning, and agent systems. However, open-access code LLMs mostly only release weights, lacking key features such as reproducible data pipelines and transparent training protocols, which are crucial for advancing deeper, more reliable investigations. To address the gap, we introduce OpenCoder, a top-tier code LLM that not only achieves performance comparable to leading models but also serves as an “open cookbook” for the research community. Unlike most prior efforts, we release not only model weights and inference code, but also the reproducible training data, complete data processing pipeline, rigorous experimental ablation results, and detailed training protocols for open scientific research. Our work identifies the key ingredients for building a top-tier code LLM: optimized heuristic rules for data cleaning and deduplication, effective recall of code-related text corpus, and high-quality synthetic data for both annealing and supervised fine-tuning stages. By offering this level of openness, we aim to broaden access to all aspects of a top-tier code LLM, with OpenCoder serving as both a powerful model and an open foundation to accelerate research and enable reproducible advancements in code intelligence. The released resource is available at https://opencoder-llm.github.io.