Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: This paper proposes a systematical way of constructing energy functions for heterogenous graphs with multiple edge types and node types. This approach is justified from both the theoretical perspective and the experiments.

strengths_and_weaknesses: ### Strengths:
* The presentation is very clear. The authors analyzed the drawbacks of direct extention of graph regularizer from single-edge type graph and proposed a term that considers the inter-edge-type correlation as a regularizer with rigorous theory analysis.
* The results of combining proximal gradient and nice trick of gradient step rescaling (L209) makes the overall procedure sound and valid.
* The paper achieves state-of-the-art results in multiple datasets.

### Weakness:
* I only have a small presentation-level comment. It would be better if the authors can move the comparing part of their proposed $y_{si}H_t-y_{s'j}$ in Eq (8) to the introduction/abstract section to let the readers know the intuition that cross-edge-type correlation is important to heterogenous graph learning. Also it can be better if the authors can visualize what the learned $M_t$ is to justify that it's not a diagonal matrix.

#### Minor:
3. L139 (ii) "the loss can be equivalently expressed with symmetric weights" is unclear to me.
4. L143 (iv) the expression that "symmetrical w.r.t. order of nodes" is confusing. $M_t$ can be asymmetrical. Can the authors explain more on this?
questions: See above.
limitations: See above.
review_title: null

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: This work proposes a novel graph neural network architecture, HALO, for heterogeneous graphs. HALO is derived from the minimization steps of a relation-aware energy function, which addresses the oversmoothing issue in terms of heterogeneous graphs. Extensive experiments conducted on the node classification task in 8 heterogeneous graph datasets show the effectiveness of the proposed method. 
strengths_and_weaknesses: Strengths
1. The approach to solve the oversmoothing issue in terms of heterogeneous graphs is novel.
2. Paper is well-written and easy to follow.
3. The proposed model significantly outperforms other HGNN baselines in several datasets (e.g., IMDB) for node classification.

Weaknesses
1. It would be good if there was a comparison with other works that addressed the oversmoothig issue in homogeneous graphs. Then, the oversmoothing issue in heterogeneous graphs can be experimentally understood more.

questions: See the Strengths and Weaknesses.
limitations: The authors didn't address the limitations and potential negative societal impact of their work.
review_title: null

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: This paper propose a new heterogeneous GNN motivated by minimizing relation-aware energy function. In short, it tries to make connected nodes share similar labels, with a relation-dependent compatibility matrices to resolve the mistmatch between different node types. The proposed method achieves improvement on heteogenous graph benchmarks.
strengths_and_weaknesses: Strength:

1. This paper took non-trivial efforts to adopt unfolded optimization techniques (somehow force connected nodes to share similar labels) into heterogeneous GNN. There exist some challenges, such as the label and distribution mismatch across different node types, how to integrate the deterministic label adjustment with the non-linear model (the authors adopt a proximal gradient descent)

2. I appreciate how the authors try to improve the simple form in eq(7) by considering heterophily (not simply considering connected nodes to have similar labels), introducing a projection matrix H, and give a detailed and closed-form solution for the modified method.

Weakness:

1. The proposed method has many design choices, such as a naive regularization in eq (7), standard optimization, etc. Current ablation studies only change projection matrix H. It would be better if the authors could conduct more thorough ablation studies and tell us which component contributes most.

2. This paper has already conducted lots of experiments. However, it would still be good if they could also choose larger datasets such as OGB-MAG and OGBLSC-MAG and report the results. Also, it would be good to also show the model parameter and inference time (or FLOPS).



Personally I like this paper, and I think the paper could be improved if the authors could make the experiments more solid and provide more details and discussion.
questions: 1. The energy regularization seems to be similar to label propagation, and recently there exist several attempts to combine label propagation with GNN, such as [1]. Could the authors discuss their difference?

2. After reading the paper and Alg 1. I think the proposed method is more like a learning framework, and it should be agnostic to different base HGNN architecture (f in alg1)? Could the authors provide more details about it? If it's indeed model-agnostic, could the authors conduct experiments with different base function f?

3. I'm still not pretty clear why the authors choose proximal gradient descent instead of standard optimization. Could the authors provide more discussion or add some ablation study?

[1] Combining Label Propagation and Simple Models Out-performs Graph Neural Networks
limitations: The authors claim that limitation is included in supplementary but I didn't find it. I suggest the authors to add some discussion about the usage boundary and potential limitation of this method.
review_title: null

final_score: rating: 5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.
review_content: summary: This paper studies heterogeneous GNN and proposes a novel HGNN architecture HALO, derived from the minimization steps of a relation-aware energy function. HALO introduces trainable compatibility matrices to solve the mis-matches between two different node types. Experiments on 8 benchmark datasets show the effectiveness of the proposed model.
strengths_and_weaknesses: Strength:

1 The paper is well-written and easy to follow.

2 The proposed method HALO is derived by the gradient descent steps for the minimization of a relation-aware energy function, which is more explainable.

3 Experiments on 8 benchmark datasets show the superiority of the proposed method.

Weakness:

1. The proposed method HALO is a direct extension to the model proposed in [32] to heterogeneous graphs. Compared with the model in [32], HALO introduces compatibility matrices to map embeddings of nodes of different types into the same low-dimensional space. Therefore, the proposed model is a bit incremental.
2. There exist some confusions in the paper. For example, in line 133, the authors write “Eq 5 fail to capture the nuances of heterogeneous data”. I think this is incorrect because in Eq 5, node types are taken as nodes features, and edges types are also considered.
3. For experiments, I have several concerns. First, for Table 1, I even do not know what the evaluation measure is before I step into the main texts. Further, based on one metric of classification accuracy, the results is somewhat unconvincing. Finally, since alleviating the over-smoothing issue is an important contribution of the proposed model, conducting experiments on more datasets is a necessity, while in the current version, the only results on ACM seem to be cherry-pick.
4. Some important baselines are missing in this area:
(1) Representation learning for attributed multiplex heterogeneous network
(2) Graph Transformer Networks
(3) Leveraging Meta-path Contexts for Classification in Heterogeneous Information Networks
5. While 8.9 pages are not a big issue, the blank part is very easy to fill, which can make the paper more compact.

questions: Please see the comments above.
limitations: I think the high space complexity of the model is a limitation that needs to be further improved, which is omitted by the authors.
review_title: null

Meta-review: metareview: This paper studies heterogeneous GNN and proposes a novel HGNN architecture HALO. It tries to make connected nodes share similar labels, with a relation-dependent compatibility matrices to resolve the mistmatch between different node types. The key is to derive novel GNN layers from the minimization steps of a relation-aware energy function.

Authors have addressed concerns on the designed choices, experiments with larger and more datasets during the rebuttal. While the idea is extended from previous works [32, 35], reviewers generally appreciate its contributions made to heterogeneous GNNs. 
confidence: Certain
Decision: Accept