Convex Formulations for Training Two-Layer ReLU Neural Networks
This addresses the challenge of non-convex optimization in neural network training, offering a more interpretable approach, though it is incremental as it builds on existing convex methods for verification.
The paper tackled the problem of training two-layer ReLU neural networks by reformulating it as a convex program, and the result showed competitive test accuracy in classification tasks through a polynomial-time semidefinite relaxation.
Solving non-convex, NP-hard optimization problems is crucial for training machine learning models, including neural networks. However, non-convexity often leads to black-box machine learning models with unclear inner workings. While convex formulations have been used for verifying neural network robustness, their application to training neural networks remains less explored. In response to this challenge, we reformulate the problem of training infinite-width two-layer ReLU networks as a convex completely positive program in a finite-dimensional (lifted) space. Despite the convexity, solving this problem remains NP-hard due to the complete positivity constraint. To overcome this challenge, we introduce a semidefinite relaxation that can be solved in polynomial time. We then experimentally evaluate the tightness of this relaxation, demonstrating its competitive performance in test accuracy across a range of classification tasks.