Emergent Quantumness in Neural Networks

TL;DR

This paper demonstrates that quantum mechanics naturally emerges from a grand canonical ensemble of neural networks, linking neural network dynamics to fundamental physics through multivalued free energy and Schrödinger's equation.

Contribution

It introduces a grand canonical ensemble framework for neural networks, deriving quantum mechanics from neural network statistical properties and multivalued free energy conditions.

Findings

Quantum mechanics emerges from neural network ensembles.

Multivalued free energy leads to Schrödinger equation.

Planck's constant relates to the chemical potential of hidden variables.

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.