TY - GEN
T1 - On Provable Benefits of Depth in Training Graph Convolutional Networks
AU - Cong, Weilin
AU - Ramezani, Morteza
AU - Mahdavi, Mehrdad
N1 - Publisher Copyright:
© 2021 Neural information processing systems foundation. All rights reserved.
PY - 2021
Y1 - 2021
N2 - Graph Convolutional Networks (GCNs) are known to suffer from performance degradation as the number of layers increases, which is usually attributed to oversmoothing. Despite the apparent consensus, we observe that there exists a discrepancy between the theoretical understanding of over-smoothing and the practical capabilities of GCNs. Specifically, we argue that over-smoothing does not necessarily happen in practice, a deeper model is provably expressive, can converge to global optimum with linear convergence rate, and achieve very high training accuracy as long as properly trained. Despite being capable of achieving high training accuracy, empirical results show that the deeper models generalize poorly on the testing stage and existing theoretical understanding of such behavior remains elusive. To achieve better understanding, we carefully analyze the generalization capability of GCNs, and show that the training strategies to achieve high training accuracy significantly deteriorate the generalization capability of GCNs. Motivated by these findings, we propose a decoupled structure for GCNs that detaches weight matrices from feature propagation to preserve the expressive power and ensure good generalization performance. We conduct empirical evaluations on various synthetic and real-world datasets to validate the correctness of our theory.
AB - Graph Convolutional Networks (GCNs) are known to suffer from performance degradation as the number of layers increases, which is usually attributed to oversmoothing. Despite the apparent consensus, we observe that there exists a discrepancy between the theoretical understanding of over-smoothing and the practical capabilities of GCNs. Specifically, we argue that over-smoothing does not necessarily happen in practice, a deeper model is provably expressive, can converge to global optimum with linear convergence rate, and achieve very high training accuracy as long as properly trained. Despite being capable of achieving high training accuracy, empirical results show that the deeper models generalize poorly on the testing stage and existing theoretical understanding of such behavior remains elusive. To achieve better understanding, we carefully analyze the generalization capability of GCNs, and show that the training strategies to achieve high training accuracy significantly deteriorate the generalization capability of GCNs. Motivated by these findings, we propose a decoupled structure for GCNs that detaches weight matrices from feature propagation to preserve the expressive power and ensure good generalization performance. We conduct empirical evaluations on various synthetic and real-world datasets to validate the correctness of our theory.
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M3 - Conference contribution
AN - SCOPUS:85131823428
T3 - Advances in Neural Information Processing Systems
SP - 9936
EP - 9949
BT - Advances in Neural Information Processing Systems 34 - 35th Conference on Neural Information Processing Systems, NeurIPS 2021
A2 - Ranzato, Marc'Aurelio
A2 - Beygelzimer, Alina
A2 - Dauphin, Yann
A2 - Liang, Percy S.
A2 - Wortman Vaughan, Jenn
PB - Neural information processing systems foundation
T2 - 35th Conference on Neural Information Processing Systems, NeurIPS 2021
Y2 - 6 December 2021 through 14 December 2021
ER -