Beyond Logits: Metastable Latent Dynamics for Sample-Efficient Best-of-N Selection in LLMs

Best-of-N selection improves reasoning in large language models (LLMs) by allocating test-time compute to sample candidate trajectories, but it relies on reliable verification. Widely used proxies have complementary failure modes: logit-confidence signals can suffer from calibration collapse, where confidence becomes misaligned with correctness, while sample agreement can be costly or brittle. Instead, we analyze the model's latent dynamics during inference. Motivated by metastable dynamics in cognitive systems, we introduce Latent Velocity Entropy (LVE), a training-free metric that quantifies the temporal concentration of internal representation updates. Experiments on four reasoning benchmarks, AIME25, GPQA, MATH500, and BRUMO25, show that LVE-based selection remains informative when logit-confidence baselines fail, with the clearest gains on reasoning-dense mathematical tasks and more modest gains on knowledge-heavy GPQA. On MATH500, LogNorm-LVE reaches 92.2% Pass@1 at $N=10$ and nearly matches 10-sample majority voting with only 3 samples. Cross-model, bootstrap, and length-controlled analyses indicate that LVE is not reducible to sequence length, while also clarifying the task-dependent limits of the signal. Code is available at https://github.com/ZopenDP/LatentVelocityEntropy.