# A Quantum Field Theory of Representation Learning

## TL;DR

This paper applies concepts from quantum field theory and symmetry breaking to machine learning, proposing a gauge theory approach to improve convergence in temporal representation learning models.

## Contribution

It introduces a gauge theory framework for symmetry-breaking loss functions in machine learning, inspired by effective field theories in physics.

## Key findings

- Gauge invariance speeds up model convergence
- Deep analogy between superconductivity and temporal learning
- Framework connects physics concepts with machine learning optimization

## Abstract

Continuous symmetries and their breaking play a prominent role in contemporary physics. Effective low-energy field theories around symmetry breaking states explain diverse phenomena such as superconductivity, magnetism, and the mass of nucleons. We show that such field theories can also be a useful tool in machine learning, in particular for loss functions with continuous symmetries that are spontaneously broken by random initializations. In this paper, we illuminate our earlier published work (Bamler & Mandt, 2018) on this topic more from the perspective of theoretical physics. We show that the analogies between superconductivity and symmetry breaking in temporal representation learning are rather deep, allowing us to formulate a gauge theory of `charged' embedding vectors in time series models. We show that making the loss function gauge invariant speeds up convergence in such models.