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A Sheaf Neural Network (SNN) is a type of Graph Neural Network (GNN) that operates on a sheaf, an object that equips a graph with vector spaces over its nodes and edges and linear maps between these spaces.
Algebraic topology
Hatcher, A · 2005
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Generalizing graph neural networks beyond homophily
Zhu, J., Yan, Y., Zhao, L., Heimann, M., Akoglu, L., and Koutra, D · 2006
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The graph neural network model
Scarselli, F., Gori, M., Tsoi, A. C., Hagenbuchner, M., and Monfardini, G · 2008
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Vector diffusion maps and the connection laplacian
Singer, A. and Wu, H.-T · 2012
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Sheaves, cosheaves and applications
Curry, J. M · 2014
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Semi-supervised classification with graph convolutional networks
Kipf, T. N. and Welling, M · 2016
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Inductive representation learning on large graphs
Hamilton, W., Ying, Z., and Leskovec, J · 2017
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Graph attention networks
Velickovic, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., and Bengio, Y · 2017
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Mixhop: Higher-order graph convolutional architectures via sparsified neighborhood mixing
Abu-El-Haija, S., Perozzi, B., Kapoor, A., Alipourfard, N., Lerman, K., Harutyunyan, H., Ver Steeg, G., and Galstyan, A · 2019
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Toward a spectral theory of cellular sheaves
Hansen, J. and Ghrist, R · 2019
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The random matrix theory of the classical compact groups , volume 218
Meckes, E. S · 2019
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Graph neural networks exponentially lose expressive power for node classification
Oono, K. and Suzuki, T · 2019
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Pairnorm: Tackling oversmoothing in gnns
Zhao, L. and Akoglu, L · 2019
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Geom-gcn: Geometric graph convolutional networks
Pei, H., Wei, B., Chang, K. C.-C., Lei, Y., and Yang, B · 2020
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A deep learning approach to antibiotic discovery
Stokes, J. M., Yang, K., Swanson, K., Jin, W., Cubillos-Ruiz, A., Donghia, N. M., MacNair, C. R., French, S., Carfrae, L. A., Bloom-Ackermann, Z., Tran, V. M., Chiappino-Pepe, A., Badran, A. H., Andrews, I. W., Chory, E. J., Church, G. M., Brown, E. D., Jaakkola, T., Barzilay, R., and Collins, J. J · 2020
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Beyond low-frequency information in graph convolutional networks
Bo, D., Wang, X., Shi, C., and Shen, H · 2021
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Advancing mathematics by guiding human intuition with ai
Davies, A., Veličković, P., Buesing, L., Blackwell, S., Zheng, D., Tomašev, N., Tanburn, R., Battaglia, P., Blundell, C., Juhász, A., et al · 2021
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Opinion dynamics on discourse sheaves
Hansen, J. and Ghrist, R · 2021
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Chien, E., Peng, J., Li, P., and Milenkovic, O · 2020
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Laplacians of Cellular Sheaves: Theory and Applications
Hansen, J · 2020
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Hansen, J. and Gebhart, T · 2020
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Measuring and relieving the over-smoothing problem for graph neural networks from the topological view
Chen, D., Lin, Y., Li, W., Li, P., Zhou, J., and Sun, X
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Simple and deep graph convolutional networks
Chen, M., Wei, Z., Huang, Z., Ding, B., and Li, Y
Cited in the paper.
Beyond homophily in graph neural networks: Current limitations and effective designs
Zhu, J., Yan, Y., Zhao, L., Heimann, M., Akoglu, L., and Koutra, D
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Multi-scale attributed node embedding
Rozemberczki, B., Allen, C., and Sarkar, R · 2021
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Two sides of the same coin: Heterophily and oversmoothing in graph convolutional neural networks
Yan, Y., Hashemi, M., Swersky, K., Yang, Y., and Koutra, D · 2021
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Neural sheaf diffusion: A topological perspective on heterophily and oversmoothing in gnns
Bodnar, C., Di Giovanni, F., Chamberlain, B. P., Lio, P., and Bronstein, M. M · 2022
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