The Verifier is the Curriculum: Precision Sets the Return on Search in Code Self-Distillation

Abstract

Post-training a code generator against a learned judge can optimize proxy features that raise the score without improving the artifact. We study the opposite signal: a deterministic, judge-free filter that asks only whether a generated project launches cleanly under a headless engine (strict-launch). Under this gate, rejection-sampling self-distillation compounds out-of-family generalization: on GameCraft-Bench a 14B model raises the per-candidate clean-launch rate on four held-out families from 8.8% to 42.2% and coverage at 32 candidates from 84% to 100%, the gold references' own ceiling, beating the supervised model on every one of the 25 held-out tasks. The gate costs one engine invocation per candidate: no reward model, no judge. At a fixed admitted count, what governs the loop is verifier precision. Swapping in a lenient build check alone erases the gain (p=0.0012); a matched gold-duplication control regresses below the supervised model. Under a semantic gate on APPS, dialing fuel precision from 1.0 to 0.25 at fixed candidate count prices that fuel linearly: over 23 training seeds, half-clean fuel returns +3.59 percentage points against the +3.69 a linear rate predicts. Under count-matched rejection-SFT only one direction of verifier error carries a measurable cost. Search obeys the same gate: quadrupling the harvest budget is worth +1.62pp behind a strict gate and nothing distinguishable from zero behind a partial-credit one. Recall is nearly free; search pays only through a precise gate: the verifier is the curriculum.

15 pages, 8 figures, 6 tables. v2: substantially revised and extended (new title, new APPS experiments on verifier precision, unbiased coverage estimator, three training seeds)