Title: SNOV: A Scalable Near-global Optimal Verifier for   Neural Networks under Large Perturbations
Primary area: optimization
Keywords: neural network verification, global optimal, nonlinear programming, branch and bound, bound propagation, parallel computing, scalability, upper bounds, lower bounds, power flow, power grids

Abstract: Neural networks excel across many tasks, but their use in safety-critical settings (e.g., power grids) is hindered by concerns about robustness to input perturbations. Verification methods provide formal guarantees, yet existing approaches face a trade-off: exact verifiers certify global optimality but struggle to scale, while relaxation-based methods scale efficiently but yield loose bounds. We propose a hybrid verifier that achieves $\varepsilon$-global optimality by combining a nonlinear programming (NLP) local solver with convex-relaxation–based bound propagation inside a branch-and-bound framework. Convex relaxations narrow the feasible region and warm-start the NLP, while the NLP supplies tight upper bounds that guide branching and enable early termination. The proposed strong branching strategy effectively selects neurons with high sensitivity and instability, quickly tightening bounds within each branch. Parallel GPU execution further accelerates convergence. Experiments on  high-dimensional image classification benchmarks demonstrate substantial speedups, significant branch reduction, and negligible optimality gaps compared to six state-of-the-art baselines. Our results highlight the effectiveness of integrating local exact solvers with scalable relaxation methods to certify robustness of modern neural networks.

TL;DR: SNOV integrates nonlinear programming with convex relaxations in branch-and-bound, enabling scalable near-global optimal verification that unites efficiency and rigor for trustworthy AI in safety-critical domains.