Topo-MLP : A Simplicial Network Without Message Passing
Karthikeyan Natesan Ramamurthy Aldo Guzmán-Sáenz Mustafa Hajij
Due to their ability to model meaningful higher order relations among a set
of entities, higher order network models have emerged recently as a powerful
alternative for graph-based network models which are only capable of modeling
binary relationships. Message passing paradigm is still dominantly used to
learn representations even for higher order network models. While powerful,
message passing can have disadvantages during inference, particularly when the
higher order connectivity information is missing or corrupted. To overcome such
limitations, we propose Topo-MLP, a purely MLP-based simplicial neural network
algorithm to learn the representation of elements in a simplicial complex
without explicitly relying on message passing. Our framework utilizes a novel
Higher Order Neighborhood Contrastive (HONC) loss which implicitly incorporates
the simplicial structure into representation learning. Our proposed model's
simplicity makes it faster during inference. Moreover, we show that our model
is robust when faced with missing or corrupted connectivity structure.