The general theory of permutation equivarant neural networks and higher order graph variational encoders
This work provides a foundational framework for permutation equivariant networks in graph learning applications, though it builds incrementally on prior symmetric group equivariant networks.
The authors developed a general theory for permutation equivariant neural networks that handles cases where groups act by permuting rows and columns of matrices simultaneously, which is relevant for graph learning. They applied this to create a second-order graph variational encoder and demonstrated its effectiveness on link prediction in citation graphs and molecular graph generation tasks.
Previous work on symmetric group equivariant neural networks generally only considered the case where the group acts by permuting the elements of a single vector. In this paper we derive formulae for general permutation equivariant layers, including the case where the layer acts on matrices by permuting their rows and columns simultaneously. This case arises naturally in graph learning and relation learning applications. As a specific case of higher order permutation equivariant networks, we present a second order graph variational encoder, and show that the latent distribution of equivariant generative models must be exchangeable. We demonstrate the efficacy of this architecture on the tasks of link prediction in citation graphs and molecular graph generation.