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

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.

References in corpus (11)

• Neural Tangent Kernel: Convergence and Generalization in Neural Networks
• A Convergence Theory for Deep Learning via Over-Parameterization
• A Mean Field View of the Landscape of Two-Layers Neural Networks
• Practical recommendations for gradient-based training of deep architectures
• On Lazy Training in Differentiable Programming
• Generalization Bounds of Stochastic Gradient Descent for Wide and Deep Neural Networks
• On the Convergence Rate of Training Recurrent Neural Networks
• What Can ResNet Learn Efficiently, Going Beyond Kernels?
• Mean-field theory of two-layers neural networks: dimension-free bounds and kernel limit
• A Generalized Neural Tangent Kernel Analysis for Two-layer Neural Networks
• On Learning Over-parameterized Neural Networks: A Functional Approximation Perspective