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Cell Complex Neural Networks
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Cell complexes are topological spaces constructed from simple blocks called cells. They generalize graphs, simplicial complexes, and polyhedral complexes that form important domains for practical applications. They also provide a combinatorial formalism that allows the inclusion of complicated relationships of restrictive structures such as graphs and meshes. In this paper, we propose \textbf{Cell Complexes Neural Networks (CXNs)}, a general, combinatorial and unifying construction for performing neural network-type computations on cell complexes. We introduce an inter-cellular message passing scheme on cell complexes that takes the topology of the underlying space into account and generalizes message passing scheme to graphs. Finally, we introduce a unified cell complex encoder-decoder framework that enables learning representation of cells for a given complex inside the Euclidean spaces. In particular, we show how our cell complex autoencoder construction can give, in the special case \textbf{cell2vec}, a generalization for node2vec.
Forward citations
Cited by 5 Pith papers
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Differentiable Lifting for Topological Neural Networks
A differentiable lifting framework that samples and accepts candidate higher-order cells end-to-end outperforms static liftings on multiple TNN benchmarks.
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Heat Kernel Goes Topological
TopoHKS defines a weighted combinatorial-complex Laplacian and heat kernel descriptor, claiming maximal expressive power; the supporting uniqueness theorem is incorrect.
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CellCLAT: Preserving Topology and Trimming Redundancy in Self-Supervised Cellular Contrastive Learning
CellCLAT applies parameter-perturbation contrastive learning to cellular complexes and adaptively trims 2-cells to improve downstream graph classification.
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Representing Higher-Order Networks: A Survey of Graph-Based Frameworks
A survey organizing higher-order network formalisms into four families with a master comparison table, plus ~17 new superhypergraph-style definitions whose only supporting theorems are well-definedness checks.
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Don't be Afraid of Cell Complexes! An Introduction from an Applied Perspective
A tutorial that defines cell complexes through boundary matrices and simple cycles, proves this matches topological regular cell complexes up to dimension two, and surveys signal processing and learning applications.
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