Analyzing Lottery Ticket Hypothesis from PAC-Bayesian Theory Perspective

TL;DR

This paper explores the lottery ticket hypothesis through PAC-Bayesian theory, revealing how flatness and initial weight distance influence generalization and robustness in neural networks.

Contribution

It provides a PAC-Bayesian analysis of winning tickets, connecting flatness, initial weights, and generalization, and revisits algorithms from this theoretical perspective.

Findings

Flat minima improve accuracy and robustness.

Distance from initial weights is crucial for winning tickets.

PAC-Bayesian bounds explain generalization behavior.

Abstract

The lottery ticket hypothesis (LTH) has attracted attention because it can explain why over-parameterized models often show high generalization ability. It is known that when we use iterative magnitude pruning (IMP), which is an algorithm to find sparse networks with high generalization ability that can be trained from the initial weights independently, called winning tickets, the initial large learning rate does not work well in deep neural networks such as ResNet. However, since the initial large learning rate generally helps the optimizer to converge to flatter minima, we hypothesize that the winning tickets have relatively sharp minima, which is considered a disadvantage in terms of generalization ability. In this paper, we confirm this hypothesis and show that the PAC-Bayesian theory can provide an explicit understanding of the relationship between LTH and generalization behavior. On the basis of our experimental findings that flatness is useful for improving accuracy and robustness to label noise and that the distance from the initial weights is deeply involved in winning tickets, we offer the PAC-Bayes bound using a spike-and-slab distribution to analyze winning tickets. Finally, we revisit existing algorithms for finding winning tickets from a PAC-Bayesian perspective and provide new insights into these methods.