Gauge theory and twins paradox of disentangled representations

TL;DR

This paper introduces a geometric gauge theory perspective on disentangled representations in deep learning, linking it to quantum mechanics and relativity to clarify foundational issues.

Contribution

It presents a novel fiber bundle geometric framework for disentangled representations, connecting them to gauge theories and the twins paradox in relativity.

Findings

Disentangled representations can be modeled as gauge theories.

A geometric connection between quantum state evolution and disentanglement is established.

The approach clarifies conceptual problems in disentangled representation learning.

Abstract

Achieving disentangled representations of information is one of the key goals of deep network based machine learning system. Recently there are more discussions on this issue. In this paper, by comparing the geometric structure of disentangled representation and the geometry of the evolution of mixed states in quantum mechanics, we give a fibre bundle based geometric picture of disentangled representation which can be regarded as a kind of gauge theory. From this perspective we can build a connection between the disentangled representations and the twins paradox in relativity. This can help to clarify some problems about disentangled representation.