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.

Large language models can solve harder reasoning problems by generating several candidate answers and picking the best one, but this only works well if we can reliably tell which candidate is correct. Common ways to do this, such as using the model’s confidence scores or comparing many sampled answers, can fail when confidence is misleading or when agreement is hard to measure. We propose a new training-free method, Latent Velocity Entropy, which looks at how strongly the model’s internal representations change during generation. The main idea is that successful reasoning often shows a more concentrated pattern of internal updates than unsuccessful reasoning. Across four reasoning benchmarks, our method stays useful even when confidence-based baselines fail, and it performs especially well on mathematical tasks. On MATH500, our normalized variant nearly matches much more expensive majority voting while using far fewer samples.