Clifford Group Equivariant Simplicial Message Passing Networks
This work addresses geometric learning tasks for researchers in machine learning and computational geometry, representing an incremental advancement by combining existing techniques.
The paper tackles the problem of steerable E(n)-equivariant message passing on simplicial complexes by integrating Clifford group-equivariant layers with simplicial message passing, and it shows that the method outperforms both equivariant and simplicial graph neural networks on various geometric tasks.
We introduce Clifford Group Equivariant Simplicial Message Passing Networks, a method for steerable E(n)-equivariant message passing on simplicial complexes. Our method integrates the expressivity of Clifford group-equivariant layers with simplicial message passing, which is topologically more intricate than regular graph message passing. Clifford algebras include higher-order objects such as bivectors and trivectors, which express geometric features (e.g., areas, volumes) derived from vectors. Using this knowledge, we represent simplex features through geometric products of their vertices. To achieve efficient simplicial message passing, we share the parameters of the message network across different dimensions. Additionally, we restrict the final message to an aggregation of the incoming messages from different dimensions, leading to what we term shared simplicial message passing. Experimental results show that our method is able to outperform both equivariant and simplicial graph neural networks on a variety of geometric tasks.