We thank all reviewers for the comments and the following response will be reflected in the final version. In fact, the convergence is exponential both in theory and in practice. Duchi et al. (2008) has proposed an Thus we focus on the comparison in the graph classification task. More experiments will be added. Global methods like Geom-GCN employ additional embedding approaches to capture global information.

Non-local self-similarity in natural images has been well studied as an effective prior in image restoration. However, for single image super-resolution (SISR), most existing deep non-local methods (e.g., non-local neural networks) only exploit similar patches within the same scale of the low-resolution (LR) input image. Consequently, the restoration is limited to using the same-scale information while neglecting potential high-resolution (HR) cues from other scales. In this paper, we explore the cross-scale patch recurrence property of a natural image, i.e., similar patches tend to recur many times across different scales. This is achieved using a novel cross-scale internal graph neural network (IGNN). Specifically, we dynamically construct a cross-scale graph by searching k-nearest neighboring patches in the downsampled LR image for each query patch in the LR image.

A one-layer IGNN with hidden units as 64 is implemented on all data sets.

In this supplementary material, we provide additional details and results to the paper. Then, we give an illustration of operation details in the GraphAgg. B presents further analysis and discussions on our proposed GraphAgg module and IGNN network. A.2 Illustration of Detailed Processes in GraphAgg To further clarify the operations in the GraphAgg, we illustrate the details as shown in Figure 1. Note that we do not consider the searching window in this discussion for simplicity.

In this paper, we explore the cross-scale patch recurrence property of a natural image, i.e.,

In this paper, we explore the cross-scale patch recurrence property of a natural image, i.e.,

Graph neural networks (GNNs) (Zhou et al., 2018; Zhang et al., 2020) have been widely used on graph-structured data to obtain a meaningful representation of nodes in the graph.