Towards a theory of quantum gravity from neural networks

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.

arXiv comment20 pages, minor corrections

References in corpus (15)

• The Large N Limit of Superconformal Field Theories and Supergravity
• The World as a Hologram
• Thermodynamics of Spacetime: The Einstein Equation of State
• On the Origin of Gravity and the Laws of Newton
• Thermodynamical Aspects of Gravity: New insights
• Predictability crisis in inflationary cosmology and its resolution
• The world as a neural network
• Emergent Quantum Mechanics and Emergent Symmetries
• Can quantum mechanics be an emergent phenomenon?
• Black Holes as Brains: Neural Networks with Area Law Entropy
• The Quantum as an Emergent System
• Entropic Mechanics: towards a stochastic description of quantum mechanics
• Covariant Information Theory and Emergent Gravity
• Self-organized criticality in neural networks
• The Autodidactic Universe

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