We develop an analytical framework to characterize the set of optimal ReLU neural networks by reformulating the nonconvex training problem as a convex program. We show that the global optima of the convex parameterization are given by a polyhedral set and then extend this characterization to the optimal set of the nonconvex training objective. Since all stationary points of the ReLU training problem can be represented as optima of subsampled convex programs, our work provides a general expression for all critical points of the nonconvex objective. We then leverage our results to provide an optimal pruning algorithm for computing minimal networks, establish conditions for the regularization path of ReLU networks to be continuous, and develop sensitivity results for minimal ReLU networks.
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Optimal sets and solution paths of ReLU networks
We develop an analytical framework to characterize the set of optimal ReLU neural networks by reformulating the nonconvex training problem as a convex program. We show that the global optima of the convex parameterization are given by a polyhedral set and then extend this characterization to the optimal set of the nonconvex training objective. Since all stationary points of the ReLU training problem can be represented as optima of subsampled convex programs, our work provides a general expression for all critical points of the nonconvex objective. We then leverage our results to provide an optimal pruning algorithm for computing minimal networks, establish conditions for the regularization path of ReLU networks to be continuous, and develop sensitivity results for minimal ReLU networks.
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 Award ID(s):
 2037304
 NSFPAR ID:
 10482590
 Publisher / Repository:
 ACM Digital Library
 Date Published:
 Journal Name:
 ICML'23: Proceedings of the 40th International Conference on Machine Learning
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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