On the Existence of Universal Lottery Tickets

TL;DR

This paper proves the theoretical existence of universal lottery tickets in neural networks that do not require further training, highlighting their potential for broad applicability across tasks.

Contribution

It formalizes the concept of universal lottery tickets and provides the first proof of their existence without additional training, introducing new pruning techniques and constructions.

Findings

Universal tickets exist without further training.

Explicit constructions demonstrate representational benefits.

Extensions of subset sum results support the proofs.

Abstract

The lottery ticket hypothesis conjectures the existence of sparse subnetworks of large randomly initialized deep neural networks that can be successfully trained in isolation. Recent work has experimentally observed that some of these tickets can be practically reused across a variety of tasks, hinting at some form of universality. We formalize this concept and theoretically prove that not only do such universal tickets exist but they also do not require further training. Our proofs introduce a couple of technical innovations related to pruning for strong lottery tickets, including extensions of subset sum results and a strategy to leverage higher amounts of depth. Our explicit sparse constructions of universal function families might be of independent interest, as they highlight representational benefits induced by univariate convolutional architectures.