Venue: NeurIPS 2021 Conference

Reviews:

final_score: rating: 7: Good paper, accept
review_content: summary: This paper focuses on semi-supervised node classification with extremely limited labels and the authors propose a new framework termed Contrastive Graph Poisson Networks (CGPN). Specifically, they design a Graph Poisson Networks to propagate the limited labels to the entire graph and employ a Graph Neural Network (GNN) to guide the propagation. Meanwhile, labeled data and unlabeled data are also considered in the final objective function. For the labeled data, they simply use a cross-entropy loss and for the unlabeled data, they apply a pairwise contrastive loss to explore extra supervision information. 
main_review: Pros:
1. Since few studies have focused on semi-supervised classification with extremely limited labels, this paper makes an interesting attempt. The authors propose Graph Poisson Networks (GPN) to avoid the performance degradation caused by the accumulation of inaccurate label prediction with iteration propagation.
2. The proposed method contains several specially designed parts to play different roles, which well handle the given data. This method is novel to me.
2. Experimental results demonstrate the effectiveness of the proposed method.
4. This paper is clearly written and well-organized.


Cons:
1. In section 3.3, the authors employ a feature transformation module $f_{FT}$ to modify the outputs of the last two iterations. However, it is not clear whether $f_{FT}$ works.
2. In line 181, "in the last two interations". Should it be “… last two iterations …”? The authors may further re-check the typos of this paper.
3. There are only tables on Page 8. The authors may avoid that by adding some words to this page.

Overall, I think this is a decent paper with a novel method that can be accepted.

limitations_and_societal_impact: Yes
review_title: null

final_score: rating: 4: Ok but not good enough - rejection
review_content: summary: In this paper, authors propose the Graph Poisson Network (GPN) to  effectively propagate the information of limited labels to the entire graph, which is developed for semi-supervised node classification. The main contributions are as follows.

Firstly,  they integrate contrastive learning and variational inference framework into Poisson learning algorithm. This novel combination can propagate the label information more flexible.

Secondly, as they claimed, they achieve a significant improvement on semi-supervised node classification tasks.

main_review: The motivation and method of this paper is interesting. They consider the graph neural network, variational inference, and the thought of contrastive learning simultaneously, and unify them with poison learning algorithm for better semi-supervised node classification tasks.

However, there are some problems in the paper that I think it still has a long way to publish in NeurIPS.

The first problem is writing. Although the authors use the mathematical views to describe their method, the notations are confused. For example, in Eq (1) in Sec. 2.3, what does $l$ and &n& means? It seems that they define them in 3.1, but I suggest that the authors can reorganize the mathematical descriptions for better reading. Also, what does $U$ in Eq. (3) means?

The second problem is the derivations. Eq. (4) is the most important loss in this paper. But the authors do not tell us how to derive the ELBO. You mean ELBO, I think you should point out what’s the ELBO? Does it the ELBO of label likelihood like $p(Y)$?

The third problem the contrastive label loss in Eq. (9). I didn’t find the definition of $z_i$ and $z_j$. Besides, the contrastive loss pull the predictions of different node pairs away. If different node pairs has the same label, does it make sense? I think you should pull the predictions of node pairs that has different labels.

The fourth problem is the experiments. I just see some simple numerical results about performance without any other explanations to show the advantages of their method. It is better to provide more insights about what does this model learn rather than simple numerical results.

limitations_and_societal_impact: Yes
review_title: null

final_score: rating: 6: Marginally above the acceptance threshold
review_content: summary: For node classification tasks with extremely limited labeled data, this paper proposes a new GNN architecture GPN that extends Poisson learning to incorporate graph structure information and its contrastive learning method. The goal is to propagate the limited labels to the entire graph effectively to enhance classification performance. The framework consists of GNN for $p_\theta(Y|A, X)$ and GPN for $q_\phi(Y|A,X,Y_L)$ which are trained with ELBO loss and contrastive loss. GPN, inspired by GAN, is instantiated to learn attention-based edge weights used to construct a new diagonal matrix and graph Laplacian for Poisson learning. 
main_review: The main experimental results and ablation study show the proposed method effectively propagates limited labeled data.
Using both variational loss and the contrastive loss for the output of GNN $p_\theta$ and GPN $q_\phi$ is novel and interesting.
After reading this paper, I found that the notion of propagating some information is similar to APPNP [1].  It would be nice to compare the performances of APPNP in the extreme case covered by this paper.  
Additionally, the datasets on which this paper experiments are assortative so that propagating label information to the neighbors can be effective. Providing the experimental results on disassortative datasets such as Texas, Wisconsin, Actor, Squirrel, Chameleon, and Cornell would also be useful. 


The followings are some questions for several unclear things. 
- In Eq. (1) & (2), isn't  $u(x_i) \in \mathcal{R}^c$ and $L$ is an nxn matrix? How is their matrix multiplication defined?
- How many iterations we need for Eq. (7)? Doesn't it take a long time if large T is required?
- Ablation study for Eq. (8)
- Qualitative analysis for learned attention would be interesting

[1] PREDICT THEN PROPAGATE: GRAPH NEURAL NETWORKS MEET PERSONALIZED PAGERANK, ICLR2019
limitations_and_societal_impact: The negative social impact of this paper does not seem to be a concern.
review_title: null

Meta-review: This paper addresses the issue of doing label propagation on a large graph where ground truth labels are extremely sparse.  The authors purpose a hybrid strategy using poisson networks and GNNs to learn a label propagation rule.  The reviewers agree that this is a well motivated and timely paper, however the original draft was light on experiments and the reviewers wanted to see a range of additional studies.  Several of these studies were provided during the rebuttal phase.  I have reviewed these studies myself, and I feel they add some insights to the paper and should be added in the camera ready.  There is still one remaining reject vote, but I think the criticisms were largely addressed in the rebuttal.  One criticism in particular, that the authors did not spent enough time introducing the ELBO, is reasonable but I do not consider it a fatal flaw.

Decision: Accept (Poster)