SGD Distributional Dynamics of Three Layer Neural Networks
This work provides theoretical insights into the training dynamics of multi-layer neural networks, which is a foundational problem for machine learning researchers.
This paper extends previous mean field results for two-layer neural networks to three-layer neural networks, demonstrating that SGD dynamics can be described by a set of non-linear partial differential equations. The study also proves the independence of weight distributions in the two hidden layers.
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.