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

This paper introduces a scale-invariant methodology employing $\mathit{\text{Fractal}}\mathit{\text{Geometry}}$ 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 $\mathit{\text{roughness}}$ to deeply understand their dynamics and enhance the quality of $\mathit{\text{intrinsic}}$ 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 $\mathit{\text{intrinsic}}$ explainability of connectionist Artificial Intelligence (AI) systems.