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.

通过提出一种仅基于 MLP 的简化神经网络算法 Topo-MLP，可以学习简单复合物中元素的表示，而不需要明确依赖消息传递方法。该模型的简洁性使其在推理过程中更快速，并且在面对缺失或损坏的连接结构时仍然表现出鲁棒性。