On the Symmetries of Deep Learning Models and Their Internal Representations

By Charles Godfrey et al

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Table of Contents

Abstract
1 Introduction
2 Related work
3 The symmetries of nonlinearities
3.1 Intertwiner Groups
3.2 Weight space symmetries
3.3 A "sanity test" for intertwiners
4 Intertwining group symmetries and model stitching

Summary

Symmetry is a fundamental tool in the exploration of complex systems, including in machine learning models. The paper explores the symmetries in the internal representations of deep learning models. It connects the symmetries arising from the architecture of models with the symmetries of the models' internal representation of data by calculating intertwiner groups. These intertwiner groups provide insights into weight space symmetries and are crucial for understanding how different models process the same data. The paper also discusses experiments involving neural stitching with intertwiner groups, statistical dissimilarity measures, and the impact of activation functions on interpretability. The findings suggest that a network's symmetries propagate into its internal representation of data, offering valuable insights for fields like explainable AI and deep learning systems' safety.