Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks

Abstract

Recent works have cast some light on the mystery of why deep nets fit any data and generalize despite being very overparametrized. This paper analyzes training and generalization for a simple 2-layer ReLU net with random initialization, and provides the following improvements over recent works: (i) Using a tighter characterization of training speed than recent papers, an explanation for why training a neural net with random labels leads to slower training, as originally observed in [Zhang et al. ICLR'17]. (ii) Generalization bound independent of network size, using a data-dependent complexity measure. Our measure distinguishes clearly between random labels and true labels on MNIST and CIFAR, as shown by experiments. Moreover, recent papers require sample complexity to increase (slowly) with the size, while our sample complexity is completely independent of the network size. (iii) Learnability of a broad class of smooth functions by 2-layer ReLU nets trained via gradient descent. The key idea is to track dynamics of training and generalization via properties of a related kernel.

In ICML 2019

References in corpus (5)

• Stochastic Gradient Descent Optimizes Over-parameterized Deep ReLU Networks
• Recovery Guarantees for One-hidden-layer Neural Networks
• Diverse Neural Network Learns True Target Functions
• Generalization Bounds of SGLD for Non-convex Learning: Two Theoretical Viewpoints
• Critical Points of Neural Networks: Analytical Forms and Landscape Properties

Cited by in corpus (9)

• An Improved Analysis of Training Over-parameterized Deep Neural Networks
• A Selective Overview of Deep Learning
• Generalization Guarantees for Neural Networks via Harnessing the Low-rank Structure of the Jacobian
• Gradient Dynamics of Shallow Univariate ReLU Networks
• Explicitizing an Implicit Bias of the Frequency Principle in Two-layer Neural Networks
• Analysis of the Gradient Descent Algorithm for a Deep Neural Network Model with Skip-connections
• Decoupling Gating from Linearity
• On the Learning Dynamics of Two-layer Nonlinear Convolutional Neural Networks
• On Symmetry and Initialization for Neural Networks