Teacher-Free Self-Training Amplifies but Does Not Compound: A Pass@$K$ Crossover on a Free-Verifier Domain
When a language model trains on its own verified outputs, does it acquire capability beyond its base, or merely get better at expressing capability the base already had? We make the question decidable with a teacher-free "constellation" -- a generator, a learned critic, and a free exact verifier -- on a FlashFill-style "trapdoor" DSL, where verified (problem, solution) pairs are cheap to synthesize, hard to invert, and free to check exactly. Everything runs on one 4-bit Qwen3-4B on a single 24 GB GPU, with no model in the loop larger than the base. We report three findings. (i) Critic-guided selection beats verifier-filtered best-of-$k$ by $+9.1$ pp ($6/6$ seeds), with the entire gain loc...
| Authors | Igor Lima Strozzi |
|---|---|
| Primary category | cs.LG |
| Published | 5 June 2026 |
| Last updated at source | 5 June 2026 |
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