SGD Distributional Dynamics of Three Layer Neural Networks

• URL: http://arxiv.org/abs/2012.15036v1
• Date: Wed, 30 Dec 2020 04:37:09 GMT
• Title: SGD Distributional Dynamics of Three Layer Neural Networks
• Authors: Victor Luo, Yazhen Wang and Glenn Fung
• Abstract summary: In paper, we seek to extend the mean field results of Mei et al. from two neural networks with one hidden layer to three neural networks with two hidden layers. We will show that the SGD is captured by a set of non-linear differential equations, and prove that distributions of dynamics in the two layers are independent.
• Score: 7.025709586759655
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: With the rise of big data analytics, multi-layer neural networks have surfaced as one of the most powerful machine learning methods. However, their theoretical mathematical properties are still not fully understood. Training a neural network requires optimizing a non-convex objective function, typically done using stochastic gradient descent (SGD). In this paper, we seek to extend the mean field results of Mei et al. (2018) from two-layer neural networks with one hidden layer to three-layer neural networks with two hidden layers. We will show that the SGD dynamics is captured by a set of non-linear partial differential equations, and prove that the distributions of weights in the two hidden layers are independent. We will also detail exploratory work done based on simulation and real-world data.

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