A Scale-Invariant Diagnostic Approach Towards Understanding Dynamics of Deep Neural Networks

TL;DR

This paper presents a scale-invariant, fractal geometry-based methodology to analyze deep neural network dynamics, enhancing intrinsic explainability through chaos theory and graph-based topology reconstruction.

Contribution

It introduces a novel fractal geometry approach leveraging self-similarity and chaos theory to improve understanding and explainability of DNNs' nonlinear dynamics.

Findings

Quantifies fractal dimensions and roughness in DNNs

Uses chaos theory for better visualization of fractal evolution

Employs graph neural networks for topology reconstruction

Abstract

This paper introduces a scale-invariant methodology employing \textit{Fractal Geometry} to analyze and explain the nonlinear dynamics of complex connectionist systems. By leveraging architectural self-similarity in Deep Neural Networks (DNNs), we quantify fractal dimensions and \textit{roughness} to deeply understand their dynamics and enhance the quality of \textit{intrinsic} explanations. Our approach integrates principles from Chaos Theory to improve visualizations of fractal evolution and utilizes a Graph-Based Neural Network for reconstructing network topology. This strategy aims at advancing the \textit{intrinsic} explainability of connectionist Artificial Intelligence (AI) systems.