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.

翻译：本文提出一种基于分形几何的尺度不变方法，用以分析和解释复杂连接主义系统的非线性动力学。通过利用深度神经网络（DNNs）中的结构自相似性，我们量化分形维度和粗糙度，以深入理解其动力学特性并提升内在解释的质量。我们的方法整合了混沌理论原理以改进分形演化的可视化，并利用基于图的神经网络来重构网络拓扑。该策略旨在推进连接主义人工智能（AI）系统的内在可解释性。