Path integral based convolution and pooling for graph neural networks. (English) Zbl 07451721


82-XX Statistical mechanics, structure of matter
Full Text: DOI arXiv


[1] Abu-El-Haija, S.; Bryan, P.; Al-Rfou, R.; Alemi, A. A., Watch your step: learning node embeddings via graph attention, 9180-9190 (2018)
[2] Abu-El-Haija, S.; Bryan, P.; Kapoor, A.; Harutyunyan, H.; Alipourfard, N.; Lerman, K.; Steeg, G. V.; Galstyan, A., Mixhop: higher-order graph convolution architectures via sparsified neighborhood mixing (2019)
[3] Abu-El-Haija, S.; Bryan, P.; Kapoor, A.; Lee, J., N-GCN: multi-scale graph convolution for semi-supervised node classification (2019)
[4] Alon, U.; Yahav, E., On the bottleneck of graph neural networks and its practical implications (2020)
[5] Anderson, P. W., Absence of diffusion in certain random lattices, Phys. Rev., 109, 1492 (1958)
[6] Atwood, J.; Don, T., Diffusion-convolutional neural networks, 1993-2001 (2016)
[7] Barabási, A-L, Network Science (2016), Cambridge: Cambridge University Press, Cambridge
[8] Battaglia, P. W., Relational inductive biases, deep learning, and graph networks (2018)
[9] Borgwardt, K. M.; Ong, C. S.; Schönauer, S.; Vishwanathan, S. V N.; Smola, A. J.; Kriegel, H-P, Protein function prediction via graph kernels, Bioinformatics, 21, i47-i56 (2005)
[10] Bronstein, M. M.; Bruna, J.; LeCun, Y.; Szlam, A.; Vandergheynst, P., Geometric deep learning: going beyond Euclidean data, IEEE Signal Process. Mag., 34, 18-42 (2017)
[11] Bruna, J.; Zaremba, W.; Szlam, A.; LeCun, Y., Spectral networks and locally connected networks on graphs (2014)
[12] Burda, Z.; Duda, J.; Luck, J. M.; Waclaw, B., Localization of the maximal entropy random walk, Phys. Rev. Lett., 102 (2009) · Zbl 1371.82043
[13] Cangea, C.; Veličković, P.; Jovanović, N.; Kipf, T.; Pietro, L., Towards sparse hierarchical graph classifiers (2018)
[14] Chen, J.; Zhu, J.; Song, L., Stochastic training of graph convolutional networks with variance reduction, 941-949 (2018)
[15] Chen, J.; Ma, T.; Xiao, C., FastGCN: fast learning with graph convolutional networks via importance sampling (2018)
[16] Defferrard, M.; Bresson, X.; Vandergheynst, P., Convolutional neural networks on graphs with fast localized spectral filtering, 3844-3852 (2016)
[17] Diehl, F.; Brunner, T.; Le, M. T.; Knoll, A., Towards graph pooling by edge contraction (2019)
[18] Dobson, P. D.; Doig, A. J., Distinguishing enzyme structures from non-enzymes without alignments, J. Mol. Biol., 330, 771-783 (2003)
[19] Duvenaud, D. K.; Maclaurin, D.; Iparraguirre, J.; Bombarell, R.; Hirzel, T.; Aspuru-Guzik, A.; Adams, R. P., Convolutional networks on graphs for learning molecular fingerprints, 2224-2232 (2015)
[20] Estrada, E.; Rodriguez-Velazquez, J. A., Subgraph centrality in complex networks, Phys. Rev. E, 71 (2005)
[21] Fey, M.; Lenssen, J. E., Fast graph representation learning with pytorch geometric (2019)
[22] Feynman, R. P., Space-time approach to non-relativistic quantum mechanics, Rev. Mod. Phys., 20, 367-387 (1948) · Zbl 1371.81126
[23] Feynman, R. P.; Hibbs, A. R.; Styer, D. F., Quantum Mechanics and Path Integrals (2010), New York: Dover, New York
[24] Flam-Shepherd, D.; Wu, T.; Friederich, P.; Aspuru-Guzik, A., Neural message passing on high order paths (2020)
[25] Gao, H.; Ji, S., Graph U-nets, 2083-2092 (2019)
[26] Gilmer, J.; Schoenholz, S. S.; Riley, P. F.; Vinyals, O.; Dahl, G. E., Neural message passing for quantum chemistry, 1263-1272 (2017)
[27] Grover, A.; Leskovec, J., node2vec: scalable feature learning for networks, 855-864 (2016)
[28] Hamilton, W.; Ying, Z.; Leskovec, J., Inductive representation learning on large graphs, 1024-1034 (2017)
[29] Hansen, J-P; McDonald, I. R., Theory of Simple Liquids (1990), London: Academic, London · Zbl 0756.00004
[30] Hu, W.; Fey, M.; Zitnik, M.; Dong, Y.; Ren, H.; Liu, B.; Catasta, M.; Leskovec, J., Open graph benchmark: datasets for machine learning on graphs (2020)
[31] Kazius, J.; McGuire, R.; Bursi, R., Derivation and validation of toxicophores for mutagenicity prediction, J. Med. Chem., 48, 312-320 (2005)
[32] Kersting, K.; Kriege, N. M.; Morris, C.; Mutzel, P.; Neumann, M., Benchmark data sets for graph kernels (2020)
[33] Kipf, T. N.; Welling, M., Semi-supervised classification with graph convolutional networks (2017)
[34] Kleinert, H., Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets (2009), Singapore: World Scientific, Singapore · Zbl 1169.81001
[35] Klicpera, J.; Weißenberger, S.; Günnemann, S., Diffusion improves graph learning, 13354-13366 (2019)
[36] Knyazev, B.; Taylor, G. W.; Mohamed, R. A., Understanding attention and generalization in graph neural networks (2019)
[37] Lee, J.; Lee, I.; Kang, J., Self-attention graph pooling, 3734-3743 (2019)
[38] Li, R-H; Xu, Y. J.; Liu, J., Link prediction: the power of maximal entropy random walk, 1147-1156 (2011)
[39] Li, Y.; Tarlow, D.; Brockschmidt, M.; Zemel, R., Gated graph sequence neural networks (2016)
[40] Liao, R.; Zhao, Z.; Urtasun, R.; Zemel, R. S., Lanczosnet: multi-scale deep graph convolutional networks (2019)
[41] Yao, M.; Wang, S.; Aggarwal, C. C.; Tang, J., Graph convolutional networks with EigenPooling, 723-731 (2019)
[42] Zheng, M.; Li, M.; Yu, G. W., PAN: path integral based convolution for deep graph neural networks (2019)
[43] Monti, F.; Boscaini, D.; Masci, J.; Rodola, E.; Svoboda, J.; Bronstein, M. M., Geometric deep learning on graphs and manifolds using mixture model CNNs, 5425-5434 (2017)
[44] Newman, M., Networks (2018), New York: Oxford University Press, New York
[45] Noutahi, E.; Beani, D.; Horwood, J.; Tossou, P., Towards interpretable sparse graph representation learning with Laplacian pooling (2019)
[46] Ochab, J. K.; Burda, Z., Maximal entropy random walk in community detection, Eur. Phys. J. Spec. Top., 216, 73-81 (2013)
[47] Bryan, P.; Al-Rfou, R.; Skiena, S., Deepwalk: online learning of social representations, 701-710 (2014)
[48] Ranjan, E.; Sanyal, S.; Talukdar, P. P., ASAP: adaptive structure aware pooling for learning hierarchical graph representations (2020)
[49] Riesen, K.; Bunke, H., IAM graph database repository for graph based pattern recognition and machine learning, 287-297 (2008), Berlin: Springer, Berlin
[50] Franco, S.; Gori, M.; Tsoi, A. C.; Hagenbuchner, M.; Monfardini, G., The graph neural network model, IEEE Trans. Neural Netw., 20, 61-80 (2009)
[51] Such, F. P.; Sah, S.; Dominguez, M. A.; Pillai, S.; Zhang, C.; Michael, A.; Cahill, N. D.; Ptucha, R., Robust spatial filtering with graph convolutional neural networks, IEEE J. Sel. Top. Signal Process., 11, 884-896 (2017)
[52] Tang, J.; Qu, M.; Wang, M.; Zhang, M.; Yan, J.; Mei, Q., Line: large-scale information network embedding, 1067-1077 (2015)
[53] Veličković, P.; Cucurull, G.; Casanova, A.; Romero, A.; Lio, P.; Bengio, Y., Graph attention networks (2018)
[54] Vinyals, O.; Bengio, S.; Kudlur, M., Order matters: sequence to sequence for sets (2015)
[55] Wale, N.; Watson, I. A.; Karypis, G., Comparison of descriptor spaces for chemical compound retrieval and classification, Knowl. Inf. Syst., 14, 347-375 (2008)
[56] Wang, Y. G.; Li, M.; Zheng, M.; Guido, M.; Zhuang, X.; Fan, Y., Haar graph pooling (2020)
[57] Wu, F.; Souza, A.; Zhang, T.; Fifty, C.; Tao, Y.; Weinberger, K., Simplifying graph convolutional networks, 6861-6871 (2019)
[58] Wu, F.; Zhang, T.; de Souza, A. H Jr; Fifty, C.; Tao, Y.; Weinberger, K. Q., Simplifying graph convolutional networks (2019)
[59] Wu, Z.; Pan, S.; Chen, F.; Long, G.; Zhang, C.; Philip, S. Y., A comprehensive survey on graph neural networks, IEEE Trans. Neural Netw. Learn. Syst., 32, 4-24 (2021)
[60] Xu, B.; Shen, H.; Qi, C.; Qiu, Y.; Cheng, X., Graph wavelet neural network (2019)
[61] Xu, K.; Hu, W.; Leskovec, J.; Jegelka, S., How powerful are graph neural networks? (2019)
[62] Yang, Z.; Cohen, W. W.; Salakhutdinov, R., Revisiting semi-supervised learning with graph embeddings (2016)
[63] Ying, Z.; You, J.; Morris, C.; Ren, X.; Hamilton, W.; Leskovec, J., Hierarchical graph representation learning with differentiable pooling, 4800-4810 (2018)
[64] Yuan, H.; Ji, S., Structpool: structured graph pooling via conditional random fields (2020)
[65] Zhang, M.; Cui, Z.; Neumann, M.; Chen, Y., An end-to-end deep learning architecture for graph classification (2018)
[66] Zhang, Z.; Cui, P.; Zhu, W., Deep learning on graphs: a survey, IEEE Trans. Knowl. Data Eng., 34, 249-270 (2020)
[67] Zhou, J.; Cui, G.; Zhang, Z.; Cheng, Y.; Liu, Z.; Sun, M., Graph neural networks: a review of methods and applications (2018)
[68] Zinn-Justin, J., Path integral, Scholarpedia, 4, 8674 (2009)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.