Higher Order Graph Neural Networks with P-Tensors

Explore advanced graph neural network architectures that overcome the limitations of traditional message passing neural networks (MPNNs) in this conference talk by Risi Kondor from the University of Chicago. Learn how standard MPNNs, while equivariant to vertex permutations, face severe constraints on message passing operations that ultimately limit their expressiveness. Discover the mathematical formalism of P-tensors, which guarantees equivariance for higher order MPNNs while making software implementation more transparent and efficient. Understand how P-tensors enable message passing between subgraphs rather than just individual vertices and facilitate the use of higher order messages. Examine Schur-nets, an extension of the P-tensor formalism that explicitly accounts for the automorphism structure of local topology. Gain insights into cutting-edge research that addresses fundamental challenges in graph neural network design and opens new possibilities for more expressive and powerful graph learning models.