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The Logical Expressiveness of Topological Neural Networks
Amirreza Akbari, Amauri H. Souza, Vikas Garg
Graph neural networks (GNNs) are the standard for learning on graphs, yet they have limited expressive power, often expressed in terms of the Weisfeiler-Leman (WL) hierarchy or wit…
On topological descriptors for graph products
Mattie Ji, Amauri H. Souza, Vikas Garg
Topological descriptors have been increasingly utilized for capturing multiscale structural information in relational data. In this work, we consider various filtrations on the (bo…
Positional Encoding meets Persistent Homology on Graphs
Yogesh Verma, Amauri H. Souza, Vikas Garg
The local inductive bias of message-passing graph neural networks (GNNs) hampers their ability to exploit key structural information (e.g., connectivity and cycles). Positional enc…
Graph Persistence goes Spectral
Mattie Ji, Amauri H. Souza, Vikas Garg
Including intricate topological information (e.g., cycles) provably enhances the expressivity of message-passing graph neural networks (GNNs) beyond the Weisfeiler-Leman (WL) hiera…
Topological Neural Networks go Persistent, Equivariant, and Continuous
Yogesh Verma, Amauri H Souza, Vikas Garg
Topological Neural Networks (TNNs) incorporate higher-order relational information beyond pairwise interactions, enabling richer representations than Graph Neural Networks (GNNs).…
Going beyond persistent homology using persistent homology
Johanna Immonen, Amauri H. Souza, Vikas Garg
Representational limits of message-passing graph neural networks (MP-GNNs), e.g., in terms of the Weisfeiler-Leman (WL) test for isomorphism, are well understood. Augmenting these…