Deep Neural Networks as the Semi-classical Limit of Quantum Neural Networks

TL;DR

This paper explores the relationship between quantum and classical neural networks, showing that deep neural networks are the semiclassical limit of quantum neural networks and connecting machine learning concepts with topological quantum field theories.

Contribution

It introduces a framework linking quantum neural networks to topological quantum field theories and demonstrates that deep neural networks are a semiclassical limit of quantum neural networks.

Findings

Quantum neural networks can be mapped onto spinnetworks.

Deep neural networks emerge as the semiclassical limit of quantum neural networks.

Machine learning concepts can be reinterpreted using topological quantum field theory terminology.

Abstract

Our work intends to show that: (1) Quantum Neural Networks (QNN) can be mapped onto spinnetworks, with the consequence that the level of analysis of their operation can be carried out on the side of Topological Quantum Field Theories (TQFT); (2) Deep Neural Networks (DNN) are a subcase of QNN, in the sense that they emerge as the semiclassical limit of QNN; (3) A number of Machine Learning (ML) key-concepts can be rephrased by using the terminology of TQFT. Our framework provides as well a working hypothesis for understanding the generalization behavior of DNN, relating it to the topological features of the graphs structures involved.