Filling in the GAP: Achieving Robust and Adaptive GNNs through Post-Processing

1. The comparison with related literature is highly insufficient. Specifically, though the authors briefly review graph distribution shift methods in Sec 4, there is no clear discussion on how the proposed method differs from the existing methods. For example, the authors argue “our work takes a different approach ... we solve the problem focusing on edge distribution shift”, but this is one most typical graph distribution shifts. Among these methods, graph test-time adaptation methods (see [1-2] and their references/citations) are particularly related, as these methods also adapt graph data to enhance the generalization ability during the inference stage.
2. Following the above comment, in experiments, the authors only show the proposed method can enhance traditional GNNs but do not compare with any relevant literature, such as graph OOD methods. More baselines are needed to truly demonstrate the effectiveness of the proposed method over state-of-the-art baselines.
3. Besides, since the authors also emphasize the robustness of the proposed method, more discussions and comparisons of the proposed method with existing robust graph machine learning are needed.
4. The proposed method also seems to be related to graph structure learning literature [3] and more discussions and comparisons with the existing methods are needed.

[1] GraphTTA: Test Time Adaptation on Graph Neural Networks, ICML workshop 2022.
[2] Empowering Graph Representation Learning with Test-Time Graph Transformation, ICLR 2022.
[3] A Survey on Graph Structure Learning: Progress and Opportunities.

• The edge distribution shift problem is not well defined mathematically
• Lack of comparison to other robustness methods. More comprehensive comparisons should be made among other work in dynamic graph learning/GNN robustness.

• the paper does not investigate whether it is more effective than other methods to address edge distribution shifts (e.g. continual learning or graph domain adaptation), so it is not clear why a user should prefer it over those methods (see question 1 below).
• not clear whether there exist real-world scenarios where FILLER could actually be of use. Therefore, it is not clear whether this research will find application in real-world problems (see question 2 below).

1）Some formulas are missing the corresponding labels, such as ER-Advanced Layer in Lines 249-251.

2. The symbols used in critical sections are challenging to discern, such as g in Equation 1, g’ in Equation 2, g_B in Equation 4, and h_D in Lines 249-251.

3）W is calculated using the matrix pseudoinverse as shown in Equation 5. Is this a contribution of this paper? If the performance enhancement is marginal and could be considered a trick, it might be best not to highlight it. Such a technique could overcomplicate the model, hindering its popularization and application.

4）A key experimental detail is missing in Figure 1: Do the results correspond to random edge deletions?

5）It is unclear the rationale behind setting $\phi(A)=O$. Does this equate to characterizing the differences between neighboring nodes and central nodes? In my opinion, it would be more beneficial to introduce random perturbations at each training epoch to bolster the robustness.

5）Why does Figure 1 indicate an enhancement in model performance when the sparsity is excessively high, for instance, beyond 0.9?

6）Does the proposed method follow the homophily assumption? If a node transformation, $g(H^{(l-1)})$, is designed to capture the differences in changes within its neighborhood, $H^{(l-1)}_N-\tilde{H}^{(l-1)}_N$, should it be assumed that the node is similar to its neighbors?