1. There is some disconnection between Proposition 2.2 that the adjacency matrix of the line graph has the same support of some unitary matrix and the proposed method which finds the projection of a weighted adjacency matrix to the set of unitary matrices. It is unclear to me if the result in Proposition 2.3 has the same support as the adjacency matrix of the line graph.
2. The computational complexity of the proposed method is very high as it involves taking the square root of a matrix of the size $2e \times 2e$ where $e$ is the number of edges in the graph. Though the block matrix structure can be exploited, but there is no guarantee how many blocks can be found in the matrix. For example, it's likely that the proposed method cannot perform on all of the LRGB datasets.
3. The experiments are not very convincing. They only compared with the one-hop variant of some models that aims to solve the oversquashing problem. Note that the oversquashing problem is intrinsically multi-hop and I don't see the rationale weakening the baseline models to one-hop.
4. The preprocessing time that involves the computation of the block matrix is not reported.
5. It's unclear why there is a base layer GNN encoding in the proposed method. An ablation study on the necessity of the base layer GNN encoding would be helpful.
6. On the Peptide dataset, the GCN can easily achieve the accuracy of the proposed method by some proper data preprocessing or normalization. The authors should provide a comparison following [1].
[1] Tönshoff, Jan, et al. "Where did the gap go? Reassessing the long-range graph benchmark." arXiv preprint arXiv:2309.00367 (2023).
5. It's unclear why there is a base layer GNN encoding in the proposed method. An ablation study on the necessity of the base layer GNN encoding would be helpful.