Question: Why are related works including ARMA[1], AdaGNN[2], and BernNet[3], all of which are capable of learning graph spectrum filter, missing for comparison?
Evidence: We provide the methods in comparison along with the hyper-parameters ranges for each model. For all the models, we sweep the common hyper-parameters in the same ranges. Learning rate is swept over [0.001, 0.003, 0.005, 0.008, 0.01], dropout over [0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8], weight decay over [1e − 4, 5e − 4, 1e − 3, 5e − 3, 1e − 2, 5e − 2, 1e − 1], and hidden dimensions over [16, 32, 64]. For model-specific hyper-parameters, we tune over author prescribed ranges. We use undirected graphs with symmetric normalization for all graph networks in comparison. For all models, we report test accuracy for the configuration that achieves the highest validation accuracy. We report standard deviation wherever applicable.****ARMA: ARMA (Bianchi et al., 2021) is a spectral method that uses K stacks of ARMA1 filters in order to create an ARMAK filter (an ARMA filter of order K). Since (Bianchi et al., 2021) do not specify a hyperparameter range in their work, following are the ranges we have followed: GCS stacks (S): [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], stacks’ depth(T): [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]. However we only select configurations such that the number of learnable parameters are less than or equal to those in PP-GNN. The input to the ARMAConv layer are the node features and the output is the number of classes. This output is then passed through a softmax layer. We use the implementation from the official PyTorch Geometric Library 9 BernNet: BernNet (He et al., 2021) is a method that approximates any filter over the normalised Laplacian spectrum of a graph, by a Kth Order Bernstein Polynomial Approximation. We use the model specific hyper-parameters prescribed by the authors of the paper. We vary the Propagation Layer Learning Rate as follows: [0.001, 0.002, 0.01, 0.05]. We also vary the Propagation Layer Dropout as follows: [0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8]. We rely on the authors code 10 for our experiments. AdaGNN: AdaGNN (Dong et al., 2021) is a method that captures the different importance’s for varying frequency components for node representation learning. We use the model specific hyperparameters prescribed by the authors of the paper. The No. of Layers hyper-parameter is varied as follows: [2, 4, 8, 16, 32, 128]. We rely on the authors code11 for our experiments
Answer: Based on the suggestion from the reviewer, we conducted more experiments with additional baselines: ARMA [1] (which we missed) and very recent works like ADAGNN [2] and BernNet [3]. We report these results in TABLE-1. The main observation is that our model's standing remains unaffected across all datasets (other than OGBN-ArXiv). However, the improvement gap has reduced from 10% to 5%. We will include these results and modify our claims accordingly in the revised version.
 [1] Filippo Maria Bianchi, Daniele Grattarola, Lorenzo Livi, and Cesare Alippi. Graph neural networks with convolutional arma filters. TPAMI, 2021. [2] Yushun Dong, Kaize Ding, Brian Jalaian, Shuiwang Ji, and Jundong Li. Graph neural networks with adaptive frequency response filter. In CIKM, 2021. [3] Mingguo He, Zhewei Wei , Zengfeng, Hunang, and Hongteng, Xu. BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation. In NeurIPS 2021