Emergent Quantumness in Neural Networks

• URL: http://arxiv.org/abs/2012.05082v1
• Date: Wed, 9 Dec 2020 14:32:33 GMT
• Title: Emergent Quantumness in Neural Networks
• Authors: Mikhail I. Katsnelson, Vitaly Vanchurin
• Abstract summary: We derive the Schr"odinger equation with "Planck's constant" determined by the chemical potential of hidden variables. We also discuss implications of the results for machine learning, fundamental physics and, in a more speculative way, evolutionary biology.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: It was recently shown that the Madelung equations, that is, a hydrodynamic form of the Schr\"odinger equation, can be derived from a canonical ensemble of neural networks where the quantum phase was identified with the free energy of hidden variables. We consider instead a grand canonical ensemble of neural networks, by allowing an exchange of neurons with an auxiliary subsystem, to show that the free energy must also be multivalued. By imposing the multivaluedness condition on the free energy we derive the Schr\"odinger equation with "Planck's constant" determined by the chemical potential of hidden variables. This shows that quantum mechanics provides a correct statistical description of the dynamics of the grand canonical ensemble of neural networks at the learning equilibrium. We also discuss implications of the results for machine learning, fundamental physics and, in a more speculative way, evolutionary biology.

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