Neural Networks and Quantum Mechanics

Christian Ferko reviews correspondences between neural networks, quantum mechanics and quantum field theory. Wide networks behave like Gaussian processes and share features with free or weakly interacting fields. Focusing on one-dimensional field theories gives enough control to show, under mild assumptions, that any quantum-particle model has a neural-network representation. Architectural choices that satisfy quantum axioms then produce properties such as uncertainty relations. The presentation draws on joint work with Jim Halverson.