STaR, V-STaR, Quiet-STaR — Self-Taught Reasoning

The smallest possible self-improvement loop sits inside the rationale. A model generates a chain of thought, keeps the ones that land on correct answers, and fine-tunes on those. That is STaR. V-STaR adds a verifier so inference-time selection is better. Quiet-STaR pushes the rationale down to every token. All three work. None of them are magic — the loop preserves any shortcut that happened to reach the right answer.