Abstract
Neural network is a dynamical system described by two different types of degrees of freedom: fast-changing non-trainable variables (e.g., state of neurons) and slow-changing trainable variables (e.g., weights and biases). We show that the non-equilibrium dynamics of trainable variables can be described by the Madelung equations, if the number of neurons is fixed, and by the Schrodinger equation, if the learning system is capable of adjusting its own parameters such as the number of neurons, step size and mini-batch size. We argue that the Lorentz symmetries and curved space-time can emerge from the interplay between stochastic entropy production and entropy destruction due to learning. We show that the non-equilibrium dynamics of non-trainable variables can be described by the geodesic equation (in the emergent space-time) for localized states of neurons, and by the Einstein equations (with cosmological constant) for the entire network. We conclude that the quantum description of trainable variables and the gravitational description of non-trainable variables are dual in the sense that they provide alternative macroscopic descriptions of the same learning system, defined microscopically as a neural network.
Highlights
Quantum mechanics is a well-defined mathematical framework that proved to be very successful for modeling a wide range of complex phenomena in high energy and condensed matter physics, but it fails to give any reasonable explanations for a phenomenon as simple as a measurement, i.e., the measurement problem
In this paper we describe how general relativity, and quantum mechanics, Lorentz invariance and space-time can all emerge from the learning dynamics of neural networks [12]
There is not a single self-consistent and paradox-free definition of macroscopic observers that could describe what is happening with quantum state during measurement or how to assign probabilities to cosmological observations
Summary
Quantum mechanics is a well-defined mathematical framework that proved to be very successful for modeling a wide range of complex phenomena in high energy and condensed matter physics, but it fails to give any reasonable explanations for a phenomenon as simple as a measurement, i.e., the measurement problem It is completely unclear what is happening with the wave-function during the measurement and what role (if any) observers play in the process. As we shall see, the very notion of locality is an emergent phenomenon that arises from the learning dynamics of neural networks General relativity is another well-defined mathematical framework that was developed for modeling a wide range of astrophysical and cosmological phenomena, but it is incomplete since it does not describe what happens in space-time singularities and it does not directly explain the indirect observations of dark matter, dark energy and cosmic inflation.
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