# Tight Certified Robustness via Min-Max Representations of ReLU Neural Networks Source: [Tight Certified Robustness via Min-Max Representations of ReLU Neural Networks]() Collection index: [llms.txt]() Data updated: 2025-10-25T16:46:43.833Z Authors: Brendon G. Anderson, Samuel Pfrommer, Somayeh Sojoudi Published: 2023-10-07T21:07:45.000Z ## Abstract The reliable deployment of neural networks in control systems requires rigorous robustness guarantees. In this paper, we obtain tight robustness certificates over convex attack sets for min-max representations of ReLU neural networks by developing a convex reformulation of the nonconvex certification problem. This is done by "lifting" the problem to an infinite-dimensional optimization over probability measures, leveraging recent results in distributionally robust optimization to solve for an optimal discrete distribution, and proving that solutions of the original nonconvex problem are generated by the discrete distribution under mild boundedness, nonredundancy, and Slater conditions. As a consequence, optimal (worst-case) attacks against the model may be solved for exactly. This contrasts prior state-of-the-art that either requires expensive branch-and-bound schemes or loose relaxation techniques. Experiments on robust control and MNIST image classification examples highlight the benefits of our approach. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()