The Empirical Impact of Neural Parameter Symmetries, or Lack Thereof

TL;DR

This paper empirically investigates how reducing neural parameter symmetries affects deep learning phenomena, revealing insights into mode connectivity and Bayesian training efficiency through new architectures with fewer symmetries.

Contribution

Introduces methods to modify neural networks to reduce parameter symmetries and conducts comprehensive experiments to analyze their impact on deep learning behaviors.

Findings

Linear mode connectivity without weight space alignment

Faster Bayesian neural network training

Reduced parameter symmetries influence optimization landscapes

Abstract

Many algorithms and observed phenomena in deep learning appear to be affected by parameter symmetries -- transformations of neural network parameters that do not change the underlying neural network function. These include linear mode connectivity, model merging, Bayesian neural network inference, metanetworks, and several other characteristics of optimization or loss-landscapes. However, theoretical analysis of the relationship between parameter space symmetries and these phenomena is difficult. In this work, we empirically investigate the impact of neural parameter symmetries by introducing new neural network architectures that have reduced parameter space symmetries. We develop two methods, with some provable guarantees, of modifying standard neural networks to reduce parameter space symmetries. With these new methods, we conduct a comprehensive experimental study consisting of multiple tasks aimed at assessing the effect of removing parameter symmetries. Our experiments reveal several interesting observations on the empirical impact of parameter symmetries; for instance, we observe linear mode connectivity between our networks without alignment of weight spaces, and we find that our networks allow for faster and more effective Bayesian neural network training. Our code is available at https://github.com/cptq/asymmetric-networks