Nonlinear Weighted Directed Acyclic Graph and A Priori Estimates for Neural Networks

• URL: http://arxiv.org/abs/2103.16355v1
• Date: Tue, 30 Mar 2021 13:54:33 GMT
• Title: Nonlinear Weighted Directed Acyclic Graph and A Priori Estimates for Neural Networks
• Authors: Yuqing Li, Tao Luo, Chao Ma
• Abstract summary: We first present a novel graph theoretical formulation of neural network models, including fully connected, residual network(ResNet) and densely connected networks(DenseNet) We extend the error analysis of the population risk for two layer networkciteew 2019prioriTwo and ResNetcitee 2019prioriRes to DenseNet, and show further that for neural networks satisfying certain mild conditions, similar estimates can be obtained.
• Score: 9.43712471169533
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In an attempt to better understand structural benefits and generalization power of deep neural networks, we firstly present a novel graph theoretical formulation of neural network models, including fully connected, residual network~(ResNet) and densely connected networks~(DenseNet). Secondly, we extend the error analysis of the population risk for two layer network~\cite{ew2019prioriTwo} and ResNet~\cite{e2019prioriRes} to DenseNet, and show further that for neural networks satisfying certain mild conditions, similar estimates can be obtained. These estimates are a priori in nature since they depend sorely on the information prior to the training process, in particular, the bounds for the estimation errors are independent of the input dimension.

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