Learning From Simplicial Data Based on Random Walks and 1D Convolutions
This addresses the problem of high computational costs in simplicial complex models for researchers in topological deep learning, though it is incremental as it builds on existing higher-order methods.
The paper tackles the computational cost and expressivity limitations of higher-order topological models like simplicial complexes by proposing SCRaWl, a neural network based on random walks and 1D convolutions, which outperforms other simplicial neural networks on real-world datasets.
Triggered by limitations of graph-based deep learning methods in terms of computational expressivity and model flexibility, recent years have seen a surge of interest in computational models that operate on higher-order topological domains such as hypergraphs and simplicial complexes. While the increased expressivity of these models can indeed lead to a better classification performance and a more faithful representation of the underlying system, the computational cost of these higher-order models can increase dramatically. To this end, we here explore a simplicial complex neural network learning architecture based on random walks and fast 1D convolutions (SCRaWl), in which we can adjust the increase in computational cost by varying the length and number of random walks considered while accounting for higher-order relationships. Importantly, due to the random walk-based design, the expressivity of the proposed architecture is provably incomparable to that of existing message-passing simplicial neural networks. We empirically evaluate SCRaWl on real-world datasets and show that it outperforms other simplicial neural networks.