Deep Neural Networks as the Semi-classical Limit of Topological Quantum Neural Networks: The problem of generalisation

Autor:	Marciano, Antonino, Zappala, Emanuele, Torda, Tommaso, Lulli, Matteo, Giagu, Stefano, Fields, Chris, Chen, Deen, Fabrocini, Filippo
Rok vydání:	2022
Předmět:	Quantum Physics Computer Science - Computational Geometry Computer Science - Machine Learning Mathematical Physics Mathematics - Geometric Topology
Druh dokumentu:	Working Paper
Popis:	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 using this framework to understand the problem of generalisation 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 the overfitting behavior of Deep Neural Networks during the training step and the corresponding generalisation capabilities. We explore the paradigmatic case of the perceptron, which we implement as the semiclassical limit of Topological Quantum Neural Networks. We apply a novel algorithm we developed, showing that it obtains similar results to standard neural networks, but without the need for training (optimisation). Comment: 22 pages (two columns), 9 figures. v2: Several parts rewritten, and computational results added
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2210.13741 Zobrazit plný text záznamu View this record from Arxiv