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.

Latent reasoning models compress chain-of-thought into hidden states, but whether these representations retain usable self-knowledge about correctness remains unclear. We study two compression-based paradigms, Latent-SFT and CoLaR, and find a sharp distinction between problem-level and trajectory-level self-knowledge. A lightweight attention probe predicts which problems the model will solve (AUC 0.805/0.853) and transfers across datasets and compression ratios, yet cannot reliably rank rollouts of the same problem; distribution-matched retraining does not recover this signal. This distinction maps directly to downstream use: selective prediction improves accuracy by 20–25pp at 50% coverage, and adaptive routing outperforms either solver while reducing token cost, whereas latent best-of-N yields negligible gains despite available oracle headroom. The problem-level signal also persists on a 7B math checkpoint but vanishes on StrategyQA. These results identify an algorithm–paradigm boundary for exploiting self-knowledge in latent reasoning. Code is available at https://github.com/Arthas777/latent-probe.