CLIFFORD GROUP EQUIVARIANT SIMPLICIAL MESSAGE PASSING NETWORKS	

Cong Liu	

University of Amsterdam, AI4Science Lab, Amsterdam Machine Learning Lab	
We introduce Clifford Group Equivariant Simplicial Message Passing Networks, a method for steerable E(n)-equivariant message passing on simplicial com- plexes. Our method integrates the expressivity of Clifford group-equivariant lay- ers 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 fea- tures 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