Landscape analysis for shallow ReLU neural networks: complete classification of critical points for affine target functions

• URL: http://arxiv.org/abs/2103.10922v1
• Date: Fri, 19 Mar 2021 17:35:01 GMT
• Title: Landscape analysis for shallow ReLU neural networks: complete classification of critical points for affine target functions
• Authors: Patrick Cheridito, Arnulf Jentzen, Florian Rossmannek
• Abstract summary: We provide a complete classification of the critical points in the case where the target function is affine. Our approach builds on a careful analysis of the different types of hidden neurons that can occur in a ReLU neural network.
• Score: 3.9103337761169947
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we analyze the landscape of the true loss of a ReLU neural network with one hidden layer. We provide a complete classification of the critical points in the case where the target function is affine. In particular, we prove that local minima and saddle points have to be of a special form and show that there are no local maxima. Our approach is of a combinatorial nature and builds on a careful analysis of the different types of hidden neurons that can occur in a ReLU neural network.

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