Dynamic neuron approach to deep neural networks: Decoupling neurons for renormalization group analysis

TL;DR

This paper introduces a novel approach that treats neurons as degrees of freedom, revealing symmetries and enabling renormalization group analysis to better understand deep neural network behavior.

Contribution

It proposes a method to decouple neurons in deep networks, leveraging translational symmetry for renormalization group analysis, bridging deep learning and statistical physics.

Findings

Reveals translational symmetry in deep neural networks

Enables application of renormalization group transformations

Provides new insights into the scaling behavior of neural networks

Abstract

Deep neural network architectures often consist of repetitive structural elements. We introduce an approach that reveals these patterns and can be broadly applied to the study of deep learning. Similarly to how a power strip helps untangle and organize complex cable connections, this approach treats neurons as additional degrees of freedom in interactions, simplifying the structure and enhancing the intuitive understanding of interactions within deep neural networks. Furthermore, it reveals the translational symmetry of deep neural networks, which simplifies the application of the renormalization group transformation-a method that effectively analyzes the scaling behavior of the system. By utilizing translational symmetry and renormalization group transformations, we can analyze critical phenomena. This approach may open new avenues for studying deep neural networks using statistical physics.