Higher-order interactions (HOIs) are ubiquitous in real-world complex systems and
applications. Investigation of deep learning for HOIs, thus, has become a valuable agenda …

Topological Machine Learning (TML) is an emerging field that leverages techniques from
algebraic topology to analyze complex data structures in ways that traditional machine …

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 …

Graph neural networks excel at modeling pairwise interactions, but they cannot flexibly
accommodate higher-order interactions and features. Topological deep learning (TDL) has …

The Euler Characteristic Transform (ECT) has proven to be a powerful representation,
combining geometrical and topological characteristics of shapes and graphs. However, the …

Higher-order networks capture the many-body interactions present in complex systems,
shedding light on the interplay between topology and dynamics. The theory of higher-order …

Abstract Topological Data Analysis (TDA) is a discipline that applies algebraic topology
techniques to analyze complex, multi-dimensional data. Although it is a relatively new field …

Graph Neural Networks based on the message-passing (MP) mechanism are a dominant
approach for handling graph-structured data. However, they are inherently limited to …

This dissertation develops cellular cosheaf theory for the analysis of physical structures. This
approach generalizes well known linear matrix methods to cosheaf homology. The core …

Graph Neural Networks (GNNs) excel in learning from relational datasets, processing node
and edge features in a way that preserves the symmetries of the graph domain. However …