Towards a Theory of Quantum Gravity from Neural Networks

Area of Science:

• Computational Neuroscience
• Theoretical Physics
• Machine Learning

Background:

• Neural networks possess distinct fast (non-trainable) and slow (trainable) variables.
• Understanding the macroscopic dynamics of these variables is crucial for advanced AI.

Purpose of the Study:

• To describe the non-equilibrium dynamics of neural network variables using established physics frameworks.
• To explore emergent phenomena like Lorentz symmetries and curved spacetime in learning systems.
• To establish a duality between quantum and gravitational descriptions of neural networks.

Main Methods:

• Applying Madelung and Schrodinger equations to trainable variables (weights, biases).
• Utilizing geodesic and Einstein equations for non-trainable variables (neuron states).
• Analyzing the interplay of entropy production and destruction during learning.

Main Results:

• Trainable variables dynamics described by Madelung/Schrodinger equations.
• Non-trainable variables dynamics described by geodesic/Einstein equations.
• Emergence of Lorentz symmetries and curved spacetime from learning dynamics.

Conclusions:

• A quantum-gravitational duality exists between trainable and non-trainable neural network variables.
• This duality offers a novel macroscopic perspective on neural network learning.
• The framework bridges concepts from quantum mechanics, general relativity, and machine learning.