Optimal Stopping of Self-Refining Foundation Models

What the math gives to ML

The paper provides a concrete optimal-stopping formulation for deciding how many self-refinement iterations a foundation-model output should receive. Its transferable asset is a Bellman value function that compares accepting the current output against paying another refinement cost and taking the expected future value under stochastic score transitions. This can become an adaptive test-time-compute controller for language models, code agents, diffusion refinement, or verifier-guided reasoning, replacing fixed iteration budgets with a state-dependent stopping boundary. The key falsifiable prediction is that continuation should occur exactly where estimated expected future improvement exceeds its marginal compute cost, producing a measurable quality-cost improvement and a sharp stopping boundary in score-state space.