# Early Stopping

Constrained vector search with per-category caps previously relied on a fixed visit budget or on stopping rules trained for average recall, neither of which guarantees an exact answer. CaST restricts stopping rules to a monotone class over a declared interface, calibrates them with fixed-sequence binomial tests, and derives a lower bound on the class-optimal cost via Lagrangian weak duality. On two datasets of one million items each, its replayed cost is at most 1.132 times the class optimum for risk levels 0.03 to 0.10 at 95% confidence, and at a 0.05 risk target its mean latency is lower than every other calibrated rule timed.

Constrained vector search with per-category caps previously relied on a fixed visit budget or on stopping rules trained for average recall, neither of which guarantees an exact answer. CaST restricts stopping rules to a monotone class over a declared interface, calibrates them with fixed-sequence binomial tests, and derives a lower bound on the class-optimal cost via Lagrangian weak duality. On two datasets of one million items each, its replayed cost is at most 1.132 times the class optimum for risk levels 0.03 to 0.10 at 95% confidence, and at a 0.05 risk target its mean latency is lower than every other calibrated rule timed.

Long LLM answers raise inference latency and compute cost, yet prompt-only conciseness is hard to control and early stopping can cut sentences in half. MinimalLM separates when stopping becomes desirable from whether stopping is structurally appropriate: during decoding it adjusts stop-token scores by length and uncertainty, and only lets them take effect at sentence-ending punctuation, closed code fences or balanced brackets. Across three open-source models and 330 questions, generated tokens fell 47.6% with an average quality score of 8.04/10 versus 8.42/10 for unmodified models, and no structurally truncated outputs appeared.

Long LLM answers raise inference latency and compute cost, yet prompt-only conciseness is hard to control and early stopping can cut sentences in half. MinimalLM separates when stopping becomes desirable from whether stopping is structurally appropriate: during decoding it adjusts stop-token scores by length and uncertainty, and only lets them take effect at sentence-ending punctuation, closed code fences or balanced brackets. Across three open-source models and 330 questions, generated tokens fell 47.6% with an average quality score of 8.04/10 versus 8.42/10 for unmodified models, and no structurally truncated outputs appeared.