Jaynes Machine: The universal microstructure of deep neural networks

TL;DR

This paper introduces a universal microstructure theory for deep neural networks, predicting a lognormal distribution of connection strengths across layers, supported by empirical data from six large-scale networks.

Contribution

It develops a novel theoretical framework called statistical teleodynamics to explain the microstructure of deep neural networks and predicts universal properties of their connection distributions.

Findings

Connection strengths follow a lognormal distribution.

Universal microstructure predicted for all layers.

Empirical validation across six large networks.

Abstract

We present a novel theory of the microstructure of deep neural networks. Using a theoretical framework called statistical teleodynamics, which is a conceptual synthesis of statistical thermodynamics and potential game theory, we predict that all highly connected layers of deep neural networks have a universal microstructure of connection strengths that is distributed lognormally ($LN({\mu}, {\sigma})$). Furthermore, under ideal conditions, the theory predicts that ${\mu}$ and ${\sigma}$ are the same for all layers in all networks. This is shown to be the result of an arbitrage equilibrium where all connections compete and contribute the same effective utility towards the minimization of the overall loss function. These surprising predictions are shown to be supported by empirical data from six large-scale deep neural networks in real life. We also discuss how these results can be exploited to reduce the amount of data, time, and computational resources needed to train large deep neural networks.