Deep Neural Networks as the Semi-Classical Limit of Topological Quantum Neural Networks: The Problem of Generalisation

By Antonino Marcianò et al

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Table of Contents

I. Introduction
II. Motivations and Theoretical Background
III. Novel Strategy Rooted in the Framework Provided by TQFT
IV. Generalisation within the TQNN Framework
V. Dictionary Correlating DNN and TQNN Notions
VI. Possible Perspectives Associated with the New Strategy Developed
VII. Preliminary Conclusions Based on the TQNN Models

Summary

Deep Neural Networks miss a principled model of their operation. A novel framework for supervised learning based on Topological Quantum Field Theory that looks particularly well suited for implementation on quantum processors has been recently explored. We propose the use of this framework for understanding the problem of generalization in Deep Neural Networks. More specifically, in this approach Deep Neural Networks are viewed as the semi-classical limit of Topological Quantum Neural Networks. A framework of this kind explains easily the overfitting behavior of Deep Neural Networks during the training step and the corresponding generalization capabilities. The objective of this paper is to deal with the first issue by developing and validating a principled model of generalization in DNNs...