Kati8/ICLR_2023_2025 huggingface dataset:
authors: Alvaro Ciudad Serrano
authors: Zinnera Tariq
authors: Stelina Tarasi
authors: Alexis Molina
reviews: 
Comments: This paper identifies the problem of the current GNN's inability to reconstruct a graph whose adjacency matrix has negative eigenvalues. It then proposes a method to manually negate several entries of the embedding vectors of nodes to allow negative eigenvalue. Experimental results show consistent improvement across datasets.
Strengths: The identified problem is interesting and allowing models to generate an adjacency matrix with negative eigenvalues is a critical task. The authors explain the intuition behind the negative eigenvalue adjacency matrix well.
Weaknesses: The presentation needs significant improvement. The use of bold/unbold letters to represent vectors is inconsistent, and some subscripts are missing.  While the core idea is interesting, it is poorly presented. As the authors emphasize the importance of the negative eigenvalues 
and mention irregularity in graphs multiple times, there is no support for how often and when negative eigenvalues appear. (Though toy examples are provided in the appendix.) Some justification should be presented, either empirically obtained from data or theoretically quantified.

The proposed method is also without in-depth analysis. While the proposed matrix multiplication does allow negative eigenvalues, the effectiveness is unclear and never justified in the paper. Also, the negate matrix is manually picked, which is not flexible for more graphs (as the authors acknowledged in the conclusion).
Recommendation: 3: reject, not good enough
Reviewer confidence: 3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.
Soundness/correctness: 1 poor
Clarity: 1 poor
reviews: 
Comments: This work introduce a graph decoder by employing the Generalized Random Dot Product Graph (GRDPG) as a generative model for graph decoding. This methodology significantly enhances the performance of encoder-decoder architectures across a range of tasks.
Strengths: 1. Clear and straightforward illustraction of method.
Weaknesses: 1. Novelty is limited.  Equation (3), the center of the method, has been proposed in [1].

2. The meaning of negative eigenvalue in adjacency matrix remains unclear. Does it corresponds to some specific substructure or some graph statistics?

3. Uncertainties are not provided in experiment results.

4. Though this work proposes a decoder, generation tasks are not included in experiments.

[1] Patrick Rubin-Delanchy, Joshua Cape, Minh Tang, and Carey E. Priebe. A statistical interpretation of spectral embedding: the generalised random dot product graph. arXiv:1709.05506, 2021.
Recommendation: 3: reject, not good enough
Reviewer confidence: 4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.
Soundness/correctness: 2 fair
Clarity: 3 good
reviews: 
Comments: This paper introduces a modification to the decoder, i.e. the dot product of the existing graph encoder-decoder framework called GRDPG. It intends to empower the decoder to represent the adjacency with negative eigenvalues. Experiments show some improvement.
Strengths: - The proposed method can be flexibly applied on any existing dot-product-based reconstruction functions.
- Experiments show some improvement somehow.
Weaknesses: - The paper is skeptically to be considered as lacking good structure, especially the connection between the dot product and its deficiency of presenting negative eigenvalues.
- Very often the sentences are repeated, presenting the same meaning, e.g. the first two paragraphs on page 2, the fourth paragraph on page 3, and so on.
- Typos are quite frequent, e.g. the third equation $p(Z|X,A \$ (also there is no index for all equations or formulas except those in the method), $Z=z_i^Tz_j$, and so on.
- The experimental results are not convincing, especially on the structure perception link prediction task, and also the random seeds and variances are missing to report.
- Overall, the quality of the paper is far below the requirements of ICLR.
Recommendation: 1: strong reject
Reviewer confidence: 4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.
Soundness/correctness: 2 fair
Clarity: 1 poor
reviews: 
Comments: In this paper, the authors propose to use a GRDPG-based decoder, instead of the classical RDPG or inner-product decoder, in the framework of GAEs and GVAEs.

The introduction of the paper is very good. However, the rest of the paper is very repetitive, and the important details are missing.

I think that four pages to describe the impact of negative eigenvalues is too much. And the paper jumps from the description of the GRDPG (Section 3) to the experiments (Section 4), without explaining the proposed method, architecture, or something.
Strengths: The introduction is very good, as said before. And the idea of using GRDPGs as decoder architecture is interesting, but I think it needs more work.
Weaknesses: Throughout the paper, the authors insist on non-bipartite graphs, as if it was a requirement or something. Even for showing the existence of graphs with negative eigenvalues, while it would have made much more sense to say, "bipartite graphs have spectra of $A$ symmetric around 0".

In this sense, Section 2.2 (and Appendix A) are not needed at all.

The GRPDG method requires knowing in advance the number of positive/negative eigenvalues, so it's very important to know how the authors addressed this. Is it always the same? Is it chosen for each dataset? How? 
If I guessed correctly, the authors try several different values of $q$ (for each dataset maybe?) and keep the result with the best performance.
The lack of information on this crucial part is not acceptable.
Recommendation: 1: strong reject
Reviewer confidence: 5: You are absolutely certain about your assessment. You are very familiar with the related work and checked the math/other details carefully.
Soundness/correctness: 2 fair
Clarity: 1 poor