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

Antonino Marciano, Filippo Fabrocini*, Enrico Greco*, Kostas Terzidis

Preprint on arXive, June 2020
https://arxiv.org/abs/2007.00142

Abstract:
Our work intends to show that: (1) Quantum Neural Networks (QNN) can be mapped onto spin-networks, 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.