4 accepted papers
Positional encodings (PEs) enhance the power of graph neural networks (GNNs), both theoretically and empirically. Two of the most popular families of PEs---spectral (e.g., Laplacian eigenspaces, effective resistance) and random walk (polynomials of the adjacency matrix)---are theoretically equivalen…
Effective resistance is a distance between vertices of a graph that is both theoretically interesting and useful in applications. We study a variant of effective resistance called the biharmonic distance. While the effective resistance measures how well-connected two vertices are, we prove several t…
The distinguishing power of graph transformers is tied to the choice of *positional encoding*: features used to augment the base transformer with information about the graph. There are two primary types of positional encoding: *absolute positional encodings (APEs)* and *relative positional encodings…
Message passing graph neural networks (GNNs) are a popular learning architectures for graph-structured data. However, one problem GNNs experience is oversquashing, where a GNN has difficulty sending information between distant nodes. Understanding and mitigating oversquashing has recently received s…