Black Holes as Brains: Neural Networks with Area Law Entropy

TL;DR

This paper introduces a quantum neural network model inspired by black hole entropy, demonstrating an area law micro-state entropy and a geometry-like structure that enables large pattern storage and retrieval.

Contribution

It constructs a gravity-inspired quantum neural network exhibiting an area law entropy and emergent geometry, bridging black hole physics and neural network theory.

Findings

Network exhibits a critical state with gapless neurons on a (d-1)-dimensional surface.

Stores exponentially many patterns within a narrow energy gap.

Micro-state entropy follows an area law, linking geometry and information capacity.

Abstract

Motivated by the potential similarities between the underlying mechanisms of the enhanced memory storage capacity in black holes and in brain networks, we construct an artificial quantum neural network based on gravity-like synaptic connections and a symmetry structure that allows to describe the network in terms of geometry of a d-dimensional space. We show that the network possesses a critical state in which the gapless neurons emerge that appear to inhabit a (d-1)-dimensional surface, with their number given by the surface area. In the excitations of these neurons, the network can store and retrieve an exponentially large number of patterns within an arbitrarily narrow energy gap. The corresponding micro-state entropy of the brain network exhibits an area law. The neural network can be described in terms of a quantum field, via identifying the different neurons with the different momentum modes of the field, while identifying the synaptic connections among the neurons with the interactions among the corresponding momentum modes. Such a mapping allows to attribute a well-defined sense of geometry to an intrinsically non-local system, such as the neural network, and vice versa, it allows to represent the quantum field model as a neural network.