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Revisiting Attention-Based Graph Neural Networks for Graph Classification

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Parallel Problem Solving from Nature – PPSN XVII (PPSN 2022)

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Abstract

The attention mechanism is widely used in GNNs to improve performances. However, we argue that it breaks the prerequisite for a GNN model to obtain the maximum expressive power of distinguishing different graph structures. This paper performs theoretical analyses of attention-based GNN models’ expressive power on graphs with both node and edge features. We propose an enhanced graph attention network (EGAT) framework based on the analysis to deal with this problem. We add a degree-related scale term to the attention coefficients and adjust the message extraction function to enhance the expressive power, which is critical in the graph classification task. Furthermore, we introduce a virtual node connected with all nodes to augment the node representation update process with global information. To prove the effectiveness of our EGAT framework, we first construct synthetic datasets to validate our theoretical proposal, then we apply EGAT to two Open Graph Benchmark (OGB) graph classification tasks to empirically demonstrate that our model also performs well in real applications.

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References

  1. Aggarwal, C.C., Bar-Noy, A., Shamoun, S.: On sensor selection in linked information networks. Comput. Networks 126, 100–113 (2017). https://doi.org/10.1016/j.comnet.2017.05.024

  2. Allamanis, M.: The adverse effects of code duplication in machine learning models of code. In: Masuhara, H., Petricek, T. (eds.) Proceedings of the 2019 ACM SIGPLAN International Symposium on New Ideas, New Paradigms, and Reflections on Programming and Software, Onward! 2019, Athens, Greece, 23–24 October 2019, pp. 143–153. ACM (2019). https://doi.org/10.1145/3359591.3359735

  3. Babai, L., Kucera, L.: Canonical labelling of graphs in linear average time. In: 20th Annual Symposium on Foundations of Computer Science, San Juan, Puerto Rico, 29–31 October 1979, pp. 39–46. IEEE Computer Society (1979). https://doi.org/10.1109/SFCS.1979.8

  4. Backstrom, L., Leskovec, J.: Supervised random walks: predicting and recommending links in social networks. In: King, I., Nejdl, W., Li, H. (eds.) Proceedings of the Forth International Conference on Web Search and Web Data Mining, WSDM 2011, Hong Kong, China, 9–12 February, 2011, pp. 635–644. ACM (2011). https://doi.org/10.1145/1935826.1935914

  5. Battaglia, P.W., Pascanu, R., Lai, M., Rezende, D.J., Kavukcuoglu, K.: Interaction networks for learning about objects, relations and physics. In: Lee, D.D., Sugiyama, M., von Luxburg, U., Guyon, I., Garnett, R. (eds.) Advances in Neural Information Processing Systems 29: Annual Conference on Neural Information Processing Systems 2016, 5–10 December 2016, Barcelona, Spain, pp. 4502–4510 (2016). https://proceedings.neurips.cc/paper/2016/hash/3147da8ab4a0437c15ef51a5cc7f2dc4-Abstract.html

  6. Beaini, D., Passaro, S., Létourneau, V., Hamilton, W.L., Corso, G., Liò, P.: Directional graph networks. CoRR abs/2010.02863 (2020). https://arxiv.org/abs/2010.02863

  7. Brossard, R., Frigo, O., Dehaene, D.: Graph convolutions that can finally model local structure. CoRR abs/2011.15069 (2020). https://arxiv.org/abs/2011.15069

  8. Cai, J., Fürer, M., Immerman, N.: An optimal lower bound on the number of variables for graph identifications. Comb. 12(4), 389–410 (1992). https://doi.org/10.1007/BF01305232

  9. Corso, G., Cavalleri, L., Beaini, D., Liò, P., Velickovic, P.: Principal neighbourhood aggregation for graph nets. In: Larochelle, H., Ranzato, M., Hadsell, R., Balcan, M., Lin, H. (eds.) Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020, NeurIPS 2020, 6–12 December 2020, virtual (2020). https://proceedings.neurips.cc/paper/2020/hash/99cad265a1768cc2dd013f0e740300ae-Abstract.html

  10. Defferrard, M., Bresson, X., Vandergheynst, P.: Convolutional neural networks on graphs with fast localized spectral filtering. In: Lee, D.D., Sugiyama, M., von Luxburg, U., Guyon, I., Garnett, R. (eds.) Advances in Neural Information Processing Systems 29: Annual Conference on Neural Information Processing Systems 2016, 5–10 December, 2016, Barcelona, Spain, pp. 3837–3845 (2016). https://proceedings.neurips.cc/paper/2016/hash/04df4d434d481c5bb723be1b6df1ee65-Abstract.html

  11. Deng, S., Huang, L., Xu, G., Wu, X., Wu, Z.: On deep learning for trust-aware recommendations in social networks. IEEE Trans. Neural Networks Learn. Syst. 28(5), 1164–1177 (2017). https://doi.org/10.1109/TNNLS.2016.2514368

  12. Duvenaud, D., et al.: Convolutional networks on graphs for learning molecular fingerprints. In: Cortes, C., Lawrence, N.D., Lee, D.D., Sugiyama, M., Garnett, R. (eds.) Advances in Neural Information Processing Systems 28: Annual Conference on Neural Information Processing Systems 2015, 7–12 December 2015, Montreal, Quebec, Canada, pp. 2224–2232 (2015). https://proceedings.neurips.cc/paper/2015/hash/f9be311e65d81a9ad8150a60844bb94c-Abstract.html

  13. Hamilton, W.L., Ying, Z., Leskovec, J.: Inductive representation learning on large graphs. In: Guyon, I., von Luxburg, U., Bengio, S., Wallach, H.M., Fergus, R., Vishwanathan, S.V.N., Garnett, R. (eds.) Advances in Neural Information Processing Systems 30: Annual Conference on Neural Information Processing Systems 2017, 4–9 December 2017, Long Beach, CA, USA, pp. 1024–1034 (2017). https://proceedings.neurips.cc/paper/2017/hash/5dd9db5e033da9c6fb5ba83c7a7ebea9-Abstract.html

  14. Hornik, K.: Approximation capabilities of multilayer feedforward networks. Neural Networks 4(2), 251–257 (1991). https://doi.org/10.1016/0893-6080(91)90009-T

  15. Hornik, K., Stinchcombe, M.B., White, H.: Multilayer feedforward networks are universal approximators. Neural Networks 2(5), 359–366 (1989). https://doi.org/10.1016/0893-6080(89)90020-8

  16. Hu, W., et al.: Open graph benchmark: Datasets for machine learning on graphs. In: Larochelle, H., Ranzato, M., Hadsell, R., Balcan, M., Lin, H. (eds.) Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020, NeurIPS 2020, 6–12 December, 2020, virtual (2020). https://proceedings.neurips.cc/paper/2020/hash/fb60d411a5c5b72b2e7d3527cfc84fd0-Abstract.html

  17. Hu, Z., Dong, Y., Wang, K., Sun, Y.: Heterogeneous graph transformer. In: Huang, Y., King, I., Liu, T., van Steen, M. (eds.) WWW ’20: The Web Conference 2020, Taipei, Taiwan, 20–24 April, 2020, pp. 2704–2710. ACM / IW3C2 (2020). https://doi.org/10.1145/3366423.3380027

  18. Husain, H., Wu, H., Gazit, T., Allamanis, M., Brockschmidt, M.: Codesearchnet challenge: evaluating the state of semantic code search. CoRR abs/1909.09436 (2019). http://arxiv.org/abs/1909.09436

  19. Kearnes, S.M., McCloskey, K., Berndl, M., Pande, V.S., Riley, P.: Molecular graph convolutions: moving beyond fingerprints. J. Comput. Aided Mol. Des. 30(8), 595–608 (2016). https://doi.org/10.1007/s10822-016-9938-8

  20. Kingma, D.P., Ba, J.: Adam: A method for stochastic optimization. In: Bengio, Y., LeCun, Y. (eds.) 3rd International Conference on Learning Representations, ICLR 2015, San Diego, CA, USA, 7–9 May, 2015, Conference Track Proceedings (2015). http://arxiv.org/abs/1412.6980

  21. Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. In: 5th International Conference on Learning Representations, ICLR 2017, Toulon, France, April 24–26, 2017, Conference Track Proceedings. OpenReview.net (2017). https://openreview.net/forum?id=SJU4ayYgl

  22. Landrum: Rdkit: Open-source cheminformatics (2006)

    Google Scholar 

  23. Lee, J.B., Kong, X., Bao, Y., Moore, C.M.: Identifying deep contrasting networks from time series data: application to brain network analysis. In: Chawla, N.V., Wang, W. (eds.) Proceedings of the 2017 SIAM International Conference on Data Mining, Houston, Texas, USA, 27–29 April, 2017, pp. 543–551. SIAM (2017). https://doi.org/10.1137/1.9781611974973.61

  24. Lee, J.B., Rossi, R.A., Kong, X.: Graph classification using structural attention. In: Guo, Y., Farooq, F. (eds.) Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, KDD 2018, London, UK, 19–23 August 2018, pp. 1666–1674. ACM (2018). https://doi.org/10.1145/3219819.3219980

  25. Li, G., Xiong, C., Thabet, A.K., Ghanem, B.: Deepergcn: All you need to train deeper gcns. CoRR abs/2006.07739 (2020). https://arxiv.org/abs/2006.07739

  26. Li, J., Cai, D., He, X.: Learning graph-level representation for drug discovery. CoRR abs/1709.03741 (2017). http://arxiv.org/abs/1709.03741

  27. Liu, Q., Xiang, B., Yuan, N.J., Chen, E., Xiong, H., Zheng, Y., Yang, Y.: An influence propagation view of pagerank. ACM Trans. Knowl. Discov. Data 11(3), 30:1–30:30 (2017). https://doi.org/10.1145/3046941

  28. Morris, C., Ritzert, M., Fey, M., Hamilton, W.L., Lenssen, J.E., Rattan, G., Grohe, M.: Weisfeiler and leman go neural: Higher-order graph neural networks. In: The Thirty-Third AAAI Conference on Artificial Intelligence, AAAI 2019, The Thirty-First Innovative Applications of Artificial Intelligence Conference, IAAI 2019, The Ninth AAAI Symposium on Educational Advances in Artificial Intelligence, EAAI 2019, Honolulu, Hawaii, USA, January 27 - February 1, 2019, pp. 4602–4609. AAAI Press (2019). https://doi.org/10.1609/aaai.v33i01.33014602

  29. Pei, J., Jiang, D., Zhang, A.: On mining cross-graph quasi-cliques. In: Grossman, R., Bayardo, R.J., Bennett, K.P. (eds.) Proceedings of the Eleventh ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Chicago, Illinois, USA, 21–24 August 2005, pp. 228–238. ACM (2005). https://doi.org/10.1145/1081870.1081898

  30. Pham, T., Tran, T., Dam, K.H., Venkatesh, S.: Graph classification via deep learning with virtual nodes. CoRR abs/1708.04357 (2017). http://arxiv.org/abs/1708.04357

  31. Rong, Y., Huang, W., Xu, T., Huang, J.: Dropedge: towards deep graph convolutional networks on node classification. In: 8th International Conference on Learning Representations, ICLR 2020, Addis Ababa, Ethiopia, 26–30, April 2020. OpenReview.net (2020). https://openreview.net/forum?id=Hkx1qkrKPr

  32. Scarselli, F., Gori, M., Tsoi, A.C., Hagenbuchner, M., Monfardini, G.: Computational capabilities of graph neural networks. IEEE Trans. Neural Networks 20(1), 81–102 (2009). https://doi.org/10.1109/TNN.2008.2005141

  33. Schlichtkrull, M., Kipf, T.N., Bloem, P., van den Berg, R., Titov, I., Welling, M.: Modeling relational data with graph convolutional networks. In: Gangemi, A., Navigli, R., Vidal, M.-E., Hitzler, P., Troncy, R., Hollink, L., Tordai, A., Alam, M. (eds.) ESWC 2018. LNCS, vol. 10843, pp. 593–607. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-93417-4_38

    Chapter  Google Scholar 

  34. Velickovic, P., Cucurull, G., Casanova, A., Romero, A., Liò, P., Bengio, Y.: Graph attention networks. In: 6th International Conference on Learning Representations, ICLR 2018, Vancouver, BC, Canada, 30 April–3 May 2018, Conference Track Proceedings. OpenReview.net (2018). https://openreview.net/forum?id=rJXMpikCZ

  35. Wang, M., et al.: Deep graph library: towards efficient and scalable deep learning on graphs. CoRR abs/1909.01315 (2019). http://arxiv.org/abs/1909.01315

  36. Wang, X., et al.: Heterogeneous graph attention network. In: Liu, L., White, R.W., Mantrach, A., Silvestri, F., McAuley, J.J., Baeza-Yates, R., Zia, L. (eds.) The World Wide Web Conference, WWW 2019, San Francisco, CA, USA, 13–17 May 2019, pp. 2022–2032. ACM (2019). https://doi.org/10.1145/3308558.3313562

  37. Wu, Z., et al.: Moleculenet: a benchmark for molecular machine learning. CoRR abs/1703.00564 (2017). http://arxiv.org/abs/1703.00564

  38. Xu, K., Hu, W., Leskovec, J., Jegelka, S.: How powerful are graph neural networks? In: 7th International Conference on Learning Representations, ICLR 2019, New Orleans, LA, USA, 6–9 May 2019. OpenReview.net (2019). https://openreview.net/forum?id=ryGs6iA5Km

  39. Zaheer, M., Kottur, S., Ravanbakhsh, S., Póczos, B., Salakhutdinov, R., Smola, A.J.: Deep sets. In: Guyon, I., et al. (eds.) Advances in Neural Information Processing Systems 30: Annual Conference on Neural Information Processing Systems 2017, 4–9 December 2017, Long Beach, CA, USA, pp. 3391–3401 (2017). https://proceedings.neurips.cc/paper/2017/hash/f22e4747da1aa27e363d86d40ff442fe-Abstract.html

  40. Zheng, Y., Capra, L., Wolfson, O., Yang, H.: Introduction to the special section on urban computing. ACM Trans. Intell. Syst. Technol. 5(3), 37:1–37:2 (2014). https://doi.org/10.1145/2642650

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The work is partly supported by Delta Research Program.

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Correspondence to Ying Li .

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Tao, Y., Li, Y., Wu, Z. (2022). Revisiting Attention-Based Graph Neural Networks for Graph Classification. In: Rudolph, G., Kononova, A.V., Aguirre, H., Kerschke, P., Ochoa, G., Tušar, T. (eds) Parallel Problem Solving from Nature – PPSN XVII. PPSN 2022. Lecture Notes in Computer Science, vol 13398. Springer, Cham. https://doi.org/10.1007/978-3-031-14714-2_31

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