Simplicial Attention Networks
This addresses the problem of enhancing graph representation learning for combinatorial spaces, offering a novel method for researchers in machine learning and graph theory, though it appears incremental by building on existing simplicial neural networks.
The paper tackles the limitation of graph neural networks in modeling higher-order structures by proposing Simplicial Attention Networks (SAT), which dynamically weigh interactions between simplicies and achieve orientation equivariance, resulting in outperformance over existing convolutional SNNs and GNNs in image and trajectory classification tasks.
Graph representation learning methods have mostly been limited to the modelling of node-wise interactions. Recently, there has been an increased interest in understanding how higher-order structures can be utilised to further enhance the learning abilities of graph neural networks (GNNs) in combinatorial spaces. Simplicial Neural Networks (SNNs) naturally model these interactions by performing message passing on simplicial complexes, higher-dimensional generalisations of graphs. Nonetheless, the computations performed by most existent SNNs are strictly tied to the combinatorial structure of the complex. Leveraging the success of attention mechanisms in structured domains, we propose Simplicial Attention Networks (SAT), a new type of simplicial network that dynamically weighs the interactions between neighbouring simplicies and can readily adapt to novel structures. Additionally, we propose a signed attention mechanism that makes SAT orientation equivariant, a desirable property for models operating on (co)chain complexes. We demonstrate that SAT outperforms existent convolutional SNNs and GNNs in two image and trajectory classification tasks.