Graph Convolutional Networks (GCNs) have emerged as powerful tools for learning on network structured data. Although empirically successful, GCNs exhibit certain behaviour that has no rigorous explanation -- for instance, the performance of GCNs significantly degrades with increasing network depth, whereas it improves marginally with depth using skip connections. This paper focuses on semi-supervised learning on graphs, and explains the above observations through the lens of Neural Tangent Kernels (NTKs). We derive NTKs corresponding to infinitely wide GCNs (with and without skip connections). Subsequently, we use the derived NTKs to identify that, with suitable normalisation, network depth does not always drastically reduce the performance of GCNs -- a fact that we also validate through extensive simulation. Furthermore, we propose NTK as an efficient `surrogate model' for GCNs that does not suffer from performance fluctuations due to hyper-parameter tuning since it is a hyper-parameter free deterministic kernel. The efficacy of this idea is demonstrated through a comparison of different skip connections for GCNs using the surrogate NTKs.

翻译：图卷积网络已成为处理网络结构化数据的强大工具。尽管在实验上取得了成功，但图卷积网络表现出某些尚无严格解释的行为——例如，随着网络深度增加，GCN性能显著下降，而使用跳跃连接时性能仅随深度略有改善。本文聚焦于图的半监督学习，通过神经正切核的视角解释了上述观测现象。我们推导了对应无限宽GCN（含/不含跳跃连接）的NTK。随后，利用推导的NTK识别出：在适当归一化下，网络深度并非总会大幅降低GCN性能——这一事实也通过大量仿真得到验证。此外，我们提出将NTK作为GCN的高效“替代模型”，该模型不会因超参数调优而产生性能波动，因为它是一个无超参数的确定性核。通过使用NTK替代模型比较GCN的不同跳跃连接方式，验证了该思想的有效性。