Skip to main content

2024 | OriginalPaper | Buchkapitel

Rewiring Networks for Graph Neural Network Training Using Discrete Geometry

verfasst von : Jakub Bober, Anthea Monod, Emil Saucan, Kevin N. Webster

Erschienen in: Complex Networks & Their Applications XII

Verlag: Springer Nature Switzerland

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Information over-squashing occurs under inefficient information propagation between distant nodes on networks, which can significantly impact graph neural network (GNN) training. Rewiring is a preprocessing procedure applied to the input network to mitigate this problem. In this paper, we investigate discrete analogues of various notions of curvature to model information flow on networks and rewire them. We show that classical notions of curvature achieve state-of-the-art performance in GNN training accuracy on a wide variety of real-world datasets. Moreover, these classical notions exhibit a clear advantage in computational runtime by several orders of magnitude.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Alon, U., Yahav, E.: On the bottleneck of graph neural networks and its practical implications. arXiv preprint arXiv:2006.05205 (2020) Alon, U., Yahav, E.: On the bottleneck of graph neural networks and its practical implications. arXiv preprint arXiv:​2006.​05205 (2020)
2.
Zurück zum Zitat Barkanass, V., Jost, J., Saucan, E.: Geometric sampling of networks. J. Complex Netw. 10(4), cnac014 (2022) Barkanass, V., Jost, J., Saucan, E.: Geometric sampling of networks. J. Complex Netw. 10(4), cnac014 (2022)
3.
Zurück zum Zitat Bronstein, M.M., Bruna, J., LeCun, Y., Szlam, A., Vandergheynst, P.: Geometric deep learning: going beyond euclidean data. IEEE Signal Process. Mag. 34(4), 18–42 (2017)CrossRef Bronstein, M.M., Bruna, J., LeCun, Y., Szlam, A., Vandergheynst, P.: Geometric deep learning: going beyond euclidean data. IEEE Signal Process. Mag. 34(4), 18–42 (2017)CrossRef
4.
Zurück zum Zitat Chow, B., Knopf, D.: The Ricci Flow: An Introduction: An Introduction, vol. 1. American Mathematical Soc. (2004) Chow, B., Knopf, D.: The Ricci Flow: An Introduction: An Introduction, vol. 1. American Mathematical Soc. (2004)
5.
Zurück zum Zitat Craven, M., McCallum, A., PiPasquo, D., Mitchell, T., Freitag, D.: Learning to extract symbolic knowledge from the world wide web. Technical report, Carnegie-Mellon Univ Pittsburgh PA School of Computer Science (1998) Craven, M., McCallum, A., PiPasquo, D., Mitchell, T., Freitag, D.: Learning to extract symbolic knowledge from the world wide web. Technical report, Carnegie-Mellon Univ Pittsburgh PA School of Computer Science (1998)
6.
Zurück zum Zitat Forman, R.: Bochner’s method for cell complexes and combinatorial ricci curvature. Discret. Comput. Geom. 29(3), 323–374 (2003)MathSciNetCrossRef Forman, R.: Bochner’s method for cell complexes and combinatorial ricci curvature. Discret. Comput. Geom. 29(3), 323–374 (2003)MathSciNetCrossRef
7.
Zurück zum Zitat Gilmer, J., , S.S., Riley, P.F., Vinyals, O., Dahl, G.E.: Neural message passing for quantum chemistry. In: Precup, D., Teh, Y.W. (eds.), Proceedings of the 34th International Conference on Machine Learning, vol. 70. Proceedings of Machine Learning Research, 06–11 Aug, pages 1263–1272. PMLR (2017) Gilmer, J., , S.S., Riley, P.F., Vinyals, O., Dahl, G.E.: Neural message passing for quantum chemistry. In: Precup, D., Teh, Y.W. (eds.), Proceedings of the 34th International Conference on Machine Learning, vol. 70. Proceedings of Machine Learning Research, 06–11 Aug, pages 1263–1272. PMLR (2017)
8.
Zurück zum Zitat Haantjes, J.: Distance geometry. curvature in abstract metric spaces. Proc. Kon. Ned. Akad. V. Wetenseh., Amsterdam 50, 302–314 (194 Haantjes, J.: Distance geometry. curvature in abstract metric spaces. Proc. Kon. Ned. Akad. V. Wetenseh., Amsterdam 50, 302–314 (194
9.
10.
11.
Zurück zum Zitat McCallum, A.K., Nigam, K., Rennie, J., Seymore, K.: Automating the construction of internet portals with machine learning. Inf. Retrieval 3(2), 127–163 (2000)CrossRef McCallum, A.K., Nigam, K., Rennie, J., Seymore, K.: Automating the construction of internet portals with machine learning. Inf. Retrieval 3(2), 127–163 (2000)CrossRef
13.
Zurück zum Zitat Namata, G., London, B., Getoor, L., Huang, B., Edu, U.: Query-driven active surveying for collective classification. In: 10th International Workshop on Mining and Learning with Graphs, vol. 8, p. 1 (2012) Namata, G., London, B., Getoor, L., Huang, B., Edu, U.: Query-driven active surveying for collective classification. In: 10th International Workshop on Mining and Learning with Graphs, vol. 8, p. 1 (2012)
14.
Zurück zum Zitat Rozemberczki, B., Allen, C., Sarkar, R.: Multi-scale attributed node embedding. J. Complex Netw. 9(2), cnab014 (2021) Rozemberczki, B., Allen, C., Sarkar, R.: Multi-scale attributed node embedding. J. Complex Netw. 9(2), cnab014 (2021)
15.
Zurück zum Zitat Samal, A., Sreejith, R., Gu, J., Liu, S., Saucan, E.: Comparative analysis of two discretizations of ricci curvature for complex networks. Sci. Rep. 8, 8650 (2018) Samal, A., Sreejith, R., Gu, J., Liu, S., Saucan, E.: Comparative analysis of two discretizations of ricci curvature for complex networks. Sci. Rep. 8, 8650 (2018)
16.
Zurück zum Zitat Sen, P., Namata, G., Bilgic, M., Getoor, L., Galligher, B., Eliassi-Rad, T.: Collective classification in network data. AI Mag. 29(3), 93–93 (2008) Sen, P., Namata, G., Bilgic, M., Getoor, L., Galligher, B., Eliassi-Rad, T.: Collective classification in network data. AI Mag. 29(3), 93–93 (2008)
17.
Zurück zum Zitat Shchur, O., Mumme, M., Bojchevski, A., Günnemann, S.: Pitfalls of graph neural network evaluation. arXiv preprint arXiv:1811.05868 (2018) Shchur, O., Mumme, M., Bojchevski, A., Günnemann, S.: Pitfalls of graph neural network evaluation. arXiv preprint arXiv:​1811.​05868 (2018)
18.
Zurück zum Zitat Sigbeku, J., Saucan, E., Monod, A.: Curved markov chain monte carlo for network learning. In: Benito, R.M., Cherifi, C., Cherifi, H., Moro, E., Rocha, L.M., Sales-Pardo, M. (eds.) Complex Networks & Their Applications X. pp, pp. 461–473. Springer International Publishing, Cham (2022). https://doi.org/10.1007/978-3-030-93413-2_39CrossRef Sigbeku, J., Saucan, E., Monod, A.: Curved markov chain monte carlo for network learning. In: Benito, R.M., Cherifi, C., Cherifi, H., Moro, E., Rocha, L.M., Sales-Pardo, M. (eds.) Complex Networks & Their Applications X. pp, pp. 461–473. Springer International Publishing, Cham (2022). https://​doi.​org/​10.​1007/​978-3-030-93413-2_​39CrossRef
19.
Zurück zum Zitat Sreejith, R., Mohanraj, K., Jost, J., Saucan, E., Samal, A.: Forman curvature for complex networks. J. Stat. Mech: Theory Exp. 2016(6), 063206 (2016)MathSciNetCrossRef Sreejith, R., Mohanraj, K., Jost, J., Saucan, E., Samal, A.: Forman curvature for complex networks. J. Stat. Mech: Theory Exp. 2016(6), 063206 (2016)MathSciNetCrossRef
20.
Zurück zum Zitat Tang, J., Sun, J., Wang, C., Yang, Z.: Social influence analysis in large-scale networks. In: Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 807–816 (2009) Tang, J., Sun, J., Wang, C., Yang, Z.: Social influence analysis in large-scale networks. In: Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 807–816 (2009)
21.
Zurück zum Zitat Topping, J., Di Giovanni, F., Chamberlain, B.P., Dong, X., Bronstein, M.M.: Understanding over-squashing and bottlenecks on graphs via curvature. arXiv preprint arXiv:2111.14522 (2021) Topping, J., Di Giovanni, F., Chamberlain, B.P., Dong, X., Bronstein, M.M.: Understanding over-squashing and bottlenecks on graphs via curvature. arXiv preprint arXiv:​2111.​14522 (2021)
Metadaten
Titel
Rewiring Networks for Graph Neural Network Training Using Discrete Geometry
verfasst von
Jakub Bober
Anthea Monod
Emil Saucan
Kevin N. Webster
Copyright-Jahr
2024
DOI
https://doi.org/10.1007/978-3-031-53468-3_19

Premium Partner