Topological deep learning (TDL) is an emerging area that combines the principles of
Topological data analysis (TDA) with deep learning techniques. TDA provides insight into …

Deep neural networks have achieved significant success across various fields, but their
intrinsic black-box nature hinders the further development. Addressing the interpretability …

We present a novel set of rigorous and computationally efficient topology-based complexity
notions that exhibit a strong correlation with the generalization gap in modern deep neural …

The layered structure of deep neural networks hinders the use of numerous analysis tools
and thus the development of its interpretability. Inspired by the success of functional brain …

We use topological data analysis (TDA) to study how data transforms as it passes through
successive layers of a deep neural network (DNN). We compute the persistent homology of …

Various topological methods have emerged in recent years to investigate the inner workings
of deep neural networks (DNNs) based on the structural and weight information. However …

This survey provides a comprehensive exploration of applications of Topological Data
Analysis (TDA) within neural network analysis. Using TDA tools such as persistent homology …

Overfitting reduces the generalizability of deep neural networks (DNNs). Overfitting is
generally detected by comparing the accuracies and losses of training and validation data; …

Overfitting reduces the generalizability of convolutional neural networks (CNNs). Overfitting
is generally detected by comparing the accuracies and losses of the training and validation …

Among the various generalizations of persistent topology, that based on rank functions and
leading to indexing-aware functions appears to be particularly suited to catching graph …