Complexity Measures for Neural Networks with General Activation Functions Using Path-based Norms

• URL: http://arxiv.org/abs/2009.06132v1
• Date: Mon, 14 Sep 2020 01:15:11 GMT
• Title: Complexity Measures for Neural Networks with General Activation Functions Using Path-based Norms
• Authors: Zhong Li and Chao Ma and Lei Wu
• Abstract summary: A simple approach is proposed to obtain complexity controls for neural networks with general activation functions. We consider two-layer networks and deep residual networks, for which path-based norms are derived to control complexities.
• Score: 18.487936403345167
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A simple approach is proposed to obtain complexity controls for neural networks with general activation functions. The approach is motivated by approximating the general activation functions with one-dimensional ReLU networks, which reduces the problem to the complexity controls of ReLU networks. Specifically, we consider two-layer networks and deep residual networks, for which path-based norms are derived to control complexities. We also provide preliminary analyses of the function spaces induced by these norms and a priori estimates of the corresponding regularized estimators.

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