Topology and geometry of data manifold in deep learning
This work contributes to explainable AI in computer vision, but it appears incremental as it applies existing topological concepts to deep learning without introducing a new paradigm.
The paper tackles the problem of explaining deep learning models by analyzing the topology and geometry of data manifolds across network layers, proposing a method to assess generalization ability using topological descriptors and exploring adversarial attack geometry.
Despite significant advances in the field of deep learning in applications to various fields, explaining the inner processes of deep learning models remains an important and open question. The purpose of this article is to describe and substantiate the geometric and topological view of the learning process of neural networks. Our attention is focused on the internal representation of neural networks and on the dynamics of changes in the topology and geometry of the data manifold on different layers. We also propose a method for assessing the generalizing ability of neural networks based on topological descriptors. In this paper, we use the concepts of topological data analysis and intrinsic dimension, and we present a wide range of experiments on different datasets and different configurations of convolutional neural network architectures. In addition, we consider the issue of the geometry of adversarial attacks in the classification task and spoofing attacks on face recognition systems. Our work is a contribution to the development of an important area of explainable and interpretable AI through the example of computer vision.