Finding Simple Proofs for First-Order Optimization

What the math gives to ML

The paper contributes an automated second-stage optimization over performance-estimation certificates: dense SDP/Lagrangian proofs are sparsified to identify the few interpolation inequalities and intermediate Lyapunov relations that actually support a convergence bound. The transferable asset is not proof readability itself, but the ability to search for compact, interpretable stability certificates for iterative update rules. A practical neural-network use is to run this search offline on local quadratic models of a training block or optimizer, then use the recovered active constraints to set conservative step-size or momentum rules and detect redundant state variables. This is a moderate-impact tooling and stability direction rather than a drop-in accuracy improvement.