Despite significant advances in the field of deep learning in ap-plications to various areas, an explanation of the learning pro-cess of neural network models remains an important open ques-tion. The purpose of this paper is a comprehensive comparison and description of neural network architectures in terms of ge-ometry and topology. We focus on the internal representation of neural networks and on the dynamics of changes in the topology and geometry of a data manifold on different layers. In this paper, we use the concepts of topological data analysis (TDA) and persistent homological fractal dimension. We present a wide range of experiments with various datasets and configurations of convolutional neural network (CNNs) architectures and Transformers in CV and NLP tasks. Our work is a contribution to the development of the important field of explainable and interpretable AI within the framework of geometrical deep learning.

翻译：尽管深度学习在多个应用领域取得了显著进展，但神经网络模型学习过程的解释仍是重要的开放问题。本文旨在从几何与拓扑角度对神经网络架构进行全面比较与描述。我们聚焦神经网络的内部表征，以及数据流形在不同层次上的拓扑与几何变化动态。本文运用拓扑数据分析（TDA）和持续同调分形维数概念，针对多种数据集及卷积神经网络（CNN）架构与Transformer在计算机视觉（CV）和自然语言处理（NLP）任务中的不同配置开展了广泛实验。本研究为几何深度学习框架下可解释人工智能这一重要领域的发展做出了贡献。