A tighter generalization error bound for wide GCN based on loss landscape

The generalization capability of Graph Convolutional Networks (GCNs) has been researched recently. The generalization error bound based on algorithmic stability is obtained for various structures of GCN. However, the generalization error bound computed by this method increases rapidly during the iteration since the algorithmic stability exponential depends on the number of iterations, which is not consistent with the performance of GCNs in practice. Based on the fact that the property of loss landscape, such as convex, exp-concave, or Polyak-Lojasiewicz* (PL*) leads to tighter stability and better generalization error bound, this paper focuses on the semi-supervised loss landscape of wide GCN. It shows that a wide GCN has a Hessian matrix with a small norm, which can lead to a positive definite training tangent kernel. Then GCN's loss can satisfy the PL* condition and lead to a tighter uniform stability independent of the iteration compared with previous work. Therefore, the generalization error bound in this paper depends on the graph filter's norm and layers, which is consistent with the experiments' results.