Exponentially Improving the Complexity of Simulating the Weisfeiler-Lehman Test with Graph Neural Networks

Anders Aamand; Justin Y. Chen; Piotr Indyk; Shyam Narayanan; Ronitt Rubinfeld; Nicholas Schiefer; Sandeep Silwal; Tal Wagner

Exponentially Improving the Complexity of Simulating the Weisfeiler-Lehman Test with Graph Neural Networks

Anders Aamand, Justin Y. Chen, Piotr Indyk, Shyam Narayanan, Ronitt Rubinfeld, Nicholas Schiefer, Sandeep Silwal, Tal Wagner

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Recent work shows that the expressive power of Graph Neural Networks (GNNs) in distinguishing non-isomorphic graphs is exactly the same as that of the Weisfeiler-Lehman (WL) graph test. In particular, they show that the WL test can be simulated by GNNs. However, those simulations involve neural networks for the “combine” function of size polynomial or even exponential in the number of graph nodes n, as well as feature vectors of length linear in n. We present an improved simulation of the WL test on GNNs with exponentially lower complexity. In particular, the neural network implementing the combine function in each node has only polylog(n) parameters, and the feature vectors exchanged by the nodes of GNN consists of only O(log n) bits. We also give logarithmic lower bounds for the feature vector length and the size of the neural networks, showing the (near)-optimality of our construction.

Original language	English
Title of host publication	Advances in Neural Information Processing Systems 35 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022
Editors	S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, A. Oh
Publisher	Neural information processing systems foundation
ISBN (Electronic)	9781713871088
State	Published - 2022
Externally published	Yes
Event	36th Conference on Neural Information Processing Systems, NeurIPS 2022 - New Orleans, United States Duration: 28 Nov 2022 → 9 Dec 2022

Publication series

Name	Advances in Neural Information Processing Systems
Volume	35

Conference

Conference	36th Conference on Neural Information Processing Systems, NeurIPS 2022
Country/Territory	United States
City	New Orleans
Period	28/11/22 → 9/12/22

All Science Journal Classification (ASJC) codes

Computer Networks and Communications
Information Systems
Signal Processing

Cite this

Aamand, A., Chen, J. Y., Indyk, P., Narayanan, S., Rubinfeld, R., Schiefer, N., Silwal, S., & Wagner, T. (2022). Exponentially Improving the Complexity of Simulating the Weisfeiler-Lehman Test with Graph Neural Networks. In S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, & A. Oh (Eds.), Advances in Neural Information Processing Systems 35 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022 (Advances in Neural Information Processing Systems; Vol. 35). Neural information processing systems foundation.

Aamand, Anders ; Chen, Justin Y. ; Indyk, Piotr et al. / Exponentially Improving the Complexity of Simulating the Weisfeiler-Lehman Test with Graph Neural Networks. Advances in Neural Information Processing Systems 35 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022. editor / S. Koyejo ; S. Mohamed ; A. Agarwal ; D. Belgrave ; K. Cho ; A. Oh. Neural information processing systems foundation, 2022. (Advances in Neural Information Processing Systems).

@inproceedings{a71f7b998e2a45bf8eca12445e1bb2a7,

title = "Exponentially Improving the Complexity of Simulating the Weisfeiler-Lehman Test with Graph Neural Networks",

abstract = "Recent work shows that the expressive power of Graph Neural Networks (GNNs) in distinguishing non-isomorphic graphs is exactly the same as that of the Weisfeiler-Lehman (WL) graph test. In particular, they show that the WL test can be simulated by GNNs. However, those simulations involve neural networks for the “combine” function of size polynomial or even exponential in the number of graph nodes n, as well as feature vectors of length linear in n. We present an improved simulation of the WL test on GNNs with exponentially lower complexity. In particular, the neural network implementing the combine function in each node has only polylog(n) parameters, and the feature vectors exchanged by the nodes of GNN consists of only O(log n) bits. We also give logarithmic lower bounds for the feature vector length and the size of the neural networks, showing the (near)-optimality of our construction.",

author = "Anders Aamand and Chen, {Justin Y.} and Piotr Indyk and Shyam Narayanan and Ronitt Rubinfeld and Nicholas Schiefer and Sandeep Silwal and Tal Wagner",

note = "Publisher Copyright: {\textcopyright} 2022 Neural information processing systems foundation. All rights reserved.; 36th Conference on Neural Information Processing Systems, NeurIPS 2022 ; Conference date: 28-11-2022 Through 09-12-2022",

year = "2022",

language = "الإنجليزيّة",

series = "Advances in Neural Information Processing Systems",

publisher = "Neural information processing systems foundation",

editor = "S. Koyejo and S. Mohamed and A. Agarwal and D. Belgrave and K. Cho and A. Oh",

booktitle = "Advances in Neural Information Processing Systems 35 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022",

address = "الولايات المتّحدة",

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Aamand, A, Chen, JY, Indyk, P, Narayanan, S, Rubinfeld, R, Schiefer, N, Silwal, S & Wagner, T 2022, Exponentially Improving the Complexity of Simulating the Weisfeiler-Lehman Test with Graph Neural Networks. in S Koyejo, S Mohamed, A Agarwal, D Belgrave, K Cho & A Oh (eds), Advances in Neural Information Processing Systems 35 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022. Advances in Neural Information Processing Systems, vol. 35, Neural information processing systems foundation, 36th Conference on Neural Information Processing Systems, NeurIPS 2022, New Orleans, United States, 28/11/22.

Exponentially Improving the Complexity of Simulating the Weisfeiler-Lehman Test with Graph Neural Networks. / Aamand, Anders; Chen, Justin Y.; Indyk, Piotr et al.
Advances in Neural Information Processing Systems 35 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022. ed. / S. Koyejo; S. Mohamed; A. Agarwal; D. Belgrave; K. Cho; A. Oh. Neural information processing systems foundation, 2022. (Advances in Neural Information Processing Systems; Vol. 35).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Exponentially Improving the Complexity of Simulating the Weisfeiler-Lehman Test with Graph Neural Networks

AU - Aamand, Anders

AU - Chen, Justin Y.

AU - Indyk, Piotr

AU - Narayanan, Shyam

AU - Rubinfeld, Ronitt

AU - Schiefer, Nicholas

AU - Silwal, Sandeep

AU - Wagner, Tal

PY - 2022

Y1 - 2022

N2 - Recent work shows that the expressive power of Graph Neural Networks (GNNs) in distinguishing non-isomorphic graphs is exactly the same as that of the Weisfeiler-Lehman (WL) graph test. In particular, they show that the WL test can be simulated by GNNs. However, those simulations involve neural networks for the “combine” function of size polynomial or even exponential in the number of graph nodes n, as well as feature vectors of length linear in n. We present an improved simulation of the WL test on GNNs with exponentially lower complexity. In particular, the neural network implementing the combine function in each node has only polylog(n) parameters, and the feature vectors exchanged by the nodes of GNN consists of only O(log n) bits. We also give logarithmic lower bounds for the feature vector length and the size of the neural networks, showing the (near)-optimality of our construction.

AB - Recent work shows that the expressive power of Graph Neural Networks (GNNs) in distinguishing non-isomorphic graphs is exactly the same as that of the Weisfeiler-Lehman (WL) graph test. In particular, they show that the WL test can be simulated by GNNs. However, those simulations involve neural networks for the “combine” function of size polynomial or even exponential in the number of graph nodes n, as well as feature vectors of length linear in n. We present an improved simulation of the WL test on GNNs with exponentially lower complexity. In particular, the neural network implementing the combine function in each node has only polylog(n) parameters, and the feature vectors exchanged by the nodes of GNN consists of only O(log n) bits. We also give logarithmic lower bounds for the feature vector length and the size of the neural networks, showing the (near)-optimality of our construction.

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M3 - منشور من مؤتمر

T3 - Advances in Neural Information Processing Systems

BT - Advances in Neural Information Processing Systems 35 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022

A2 - Koyejo, S.

A2 - Mohamed, S.

A2 - Agarwal, A.

A2 - Belgrave, D.

A2 - Cho, K.

A2 - Oh, A.

PB - Neural information processing systems foundation

T2 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022

Y2 - 28 November 2022 through 9 December 2022

ER -

Aamand A, Chen JY, Indyk P, Narayanan S, Rubinfeld R, Schiefer N et al. Exponentially Improving the Complexity of Simulating the Weisfeiler-Lehman Test with Graph Neural Networks. In Koyejo S, Mohamed S, Agarwal A, Belgrave D, Cho K, Oh A, editors, Advances in Neural Information Processing Systems 35 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022. Neural information processing systems foundation. 2022. (Advances in Neural Information Processing Systems).

Exponentially Improving the Complexity of Simulating the Weisfeiler-Lehman Test with Graph Neural Networks

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All Science Journal Classification (ASJC) codes

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