Title: Permutation Equivariant Neural Networks for Antisymmetric Tensors
Primary area: learning on graphs and other geometries & topologies
Keywords: Equivariance, deep learning, permutations, antisymmetric tensors

Abstract: Antisymmetric tensors, which change sign under index swaps, appear naturally in physics, yet learning from them remains largely unexplored. We provide a complete characterisation of all linear permutation equivariant functions between antisymmetric power spaces of $\mathbb{R}^{n}$. To make this characterisation practical, we introduce a memory-efficient implementation that eliminates the need to create and store large weight matrices. We demonstrate that our approach is efficient in learning functions that depend on the antisymmetric structure of the input and outperforms models that do not incorporate this structure as an inductive bias.