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.

翻译：由于能够对实体集合中有意义的高阶关系进行建模，高阶网络模型近来已成为基于二值关系的图网络模型的强大替代方案。即便在高阶网络模型中，消息传递范式仍是学习表示的主流方法。尽管该范式功能强大，但在推理过程中，特别是当高阶连接信息缺失或受损时，消息传递可能暴露出局限性。为克服此类限制，我们提出Topo-MLP——一种基于纯MLP的单纯神经网络算法，无需显式依赖消息传递即可学习单纯复形中元素的表示。我们的框架采用新型高阶邻域对比损失函数，该损失函数通过隐式方式将单纯形结构融入表示学习过程。所提模型的简洁性使其在推理阶段速度更快。此外，我们证明该模型在面对连接结构缺失或受损时具有鲁棒性。