One-pass Stochastic Gradient Descent in Overparametrized Two-layer Neural Networks

TL;DR

This paper analyzes the convergence of one-pass stochastic gradient descent in overparameterized two-layer neural networks trained on streaming data, revealing the role of neural tangent kernel eigenstructure in prediction error reduction.

Contribution

It introduces a theoretical framework for understanding one-pass SGD convergence in streaming data settings for overparameterized neural networks, linking it to NTK eigen-decomposition.

Findings

Prediction error converges in expectation under overparameterization and random initialization.

Convergence rate depends on the eigen-decomposition of the neural tangent kernel.

A random kernel function converges to the NTK with high probability using VC dimension and McDiarmid's inequality.

Abstract

There has been a recent surge of interest in understanding the convergence of gradient descent (GD) and stochastic gradient descent (SGD) in overparameterized neural networks. Most previous works assume that the training data is provided a priori in a batch, while less attention has been paid to the important setting where the training data arrives in a stream. In this paper, we study the streaming data setup and show that with overparamterization and random initialization, the prediction error of two-layer neural networks under one-pass SGD converges in expectation. The convergence rate depends on the eigen-decomposition of the integral operator associated with the so-called neural tangent kernel (NTK). A key step of our analysis is to show a random kernel function converges to the NTK with high probability using the VC dimension and McDiarmid's inequality.