Improving Convergence and Generalization Using Parameter Symmetries

Bo Zhao, Robert Gower, Robin Walters, Rose Yu

Submission Track: Extended Abstract

Keywords: Symmetry, optimization, generalization

TL;DR: We provide theoretical guarantees that teleportation accelerates the convergence rate, show that teleportation can be used to improve generalization, and integrate teleportation into optimization-based meta-learning.

Abstract: In overparametrized models, different parameter values may result in the same loss. Parameter space symmetries are loss-invariant transformations that change the model parameters. Teleportation applies such transformations to accelerate optimization. However, the exact mechanism behind this algorithm's success is not well understood. In this paper, we prove that teleportation gives overall faster time to convergence. Additionally, teleporting to minima with different curvatures improves generalization, which suggests a connection between the curvature of the minima and generalization ability. Finally, we show that integrating teleportation into optimization-based meta-learning improves convergence over traditional algorithms that perform only local updates. Our results showcase the versatility of teleportation and demonstrate the potential of incorporating symmetry in optimization.

Submission Number: 9