Optimal Sets and Solution Paths of ReLU Networks

• URL: http://arxiv.org/abs/2306.00119v2
• Date: Fri, 19 Jan 2024 18:30:27 GMT
• Title: Optimal Sets and Solution Paths of ReLU Networks
• Authors: Aaron Mishkin, Mert Pilanci
• Abstract summary: We develop an analytical framework to characterize the set of optimal ReLU networks. We establish conditions for the neuralization of ReLU networks to be continuous, and develop sensitivity results for ReLU networks.
• Score: 56.40911684005949
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We develop an analytical framework to characterize the set of optimal ReLU neural networks by reformulating the non-convex 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 non-convex training objective. Since all stationary points of the ReLU training problem can be represented as optima of sub-sampled convex programs, our work provides a general expression for all critical points of the non-convex 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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