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arXiv · 1907.02163

A Quantum Field Theory of Representation Learning

Robert Bamler·Stephan Mandt
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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.

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Robert Bamler, Stephan Mandt. 2019-07-04. A Quantum Field Theory of Representation Learning. https://arxiv.org/abs/1907.02163

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