2022/04/20 by Christopher Wei Jin Goh, Goh, Christopher Wei Jin, Cristian Bodnar +4 · 10 citations
Computer Science · Materials Science · Mathematics · #Advanced Graph Neural Networks #Computational Drug Discovery Methods #Machine Learning in Materials Science #cs.LG #math.AT
paper · pdf · doi:10.48550/arxiv.2204.09455
Accepted to the ICLR 2022 Workshop on Geometrical and Topological Representation Learning
arxiv created 2022/04/20 · arxiv updated 2022/04/21
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.