Fully Hyperbolic Representation Learning on Knowledge Hypergraph

1. please elaborate on the reasons that hyperbolic space outperforms Euclidean space, such as how the distortion is reduced. The argument of the article is that the graph structure after the star extension of the hypergraph structure has a hierarchical structure and therefore has less distortion in the hyperbolic space. But the hypergraph structure and the graph structure after the star extension are bijective equivalences, so why must one need to combine the hyperbolic operation with the star extension? The writer needs to sort out the logic of the article again.
2. Is it possible to visualize star-expanded hypergraphs on hyperbolic space? This would enhance the persuasiveness of the article.
3. Can you further analyze in your experiments why your method can perform better compared to other hypergraphic learning methods?

1. Could you provide a clear step-by-step explanation of how your model starts from a hypergraph and creates node embeddings?
2. I was surprised that the position-specific embedding modifies the representation of a hyperredge in the aggregation for creating a new node representation as opposed to modifying the representation of the node in the aggregation for creating a hyperedge representation. Is there some benefit to your proposed approach compared to the one I describe here?
3. The notation for $\mathbf h_p$ is confusing. First, it is stated that $\mathbf h_p \in \mathbb R^d$, but then it is subtracted from a vector in $\mathbb H$. Secondly, the dependencies are not clear from the notation. From the text, it is clear that $\mathbf h_p$ is dependent on both a relation and a position, but in equation (4) this is left to determine from context. I assume that in equation (4), $\mathbf h_p$ is different for each $e$ and depends on the relation in $e$ as well as the position of $x_i$ in $e$, but the current notation really doesn't make this clear.
4. In section 3.3 the loss functions are presented, but it is not explained how the encodings from the message passing algorithm are converted to conditional probabilities equation (6) or confidence scores $g(x)$ in equation (7). I assume an MLP in the first case, and I see that there is a later discussion about decoders for link prediction, but details here are lacking.
5. To my understanding, m-DistMult is not particularly well-aligned to extract information from H^2GNN, yet it is shown in Figure 4 that it performs far worse when paired with UniGNN or UniSAGE. Were these encoders trained with m-DistMult as the decoder, or are these the result of simply using m-DistMult on top of frozen encoders? What is the explanation for the incredibly poor performance of UniGNN and UniSAGE when using m-DistMult?
6. In section 4.4 there is an ablation of Hyperbolic Operation (HO) and Position Information (PI) modules, which is the first time these terms are mentioned in the text. What are these modules? (This goes back to my primary question related to a clear step-by-step structure of the model.)

Typos / Suggestions

• Page 2: Additional criteria are needed to complete this statement: "The goal of representation learning is to obtain embedded representations for each node x ∈ V and relation type r ∈ R in the knowledge hypergraphs." As it stands, this could be satisfied by randomly assigning a vector to each node. The goal here should include some additional objective, eg. "... such that they can be used to reconstruct the original graph".
• Page 3: "In Figure 2, when we embed the tree structure into Euclidean space, the distance between the yellow and pink nodes on the tree is 8 nodes apart, but in reality, these tree-like structures are very close in real networks." I do not understand the latter part of this sentence. As I have understood it, the problem is typically the reverse - that embedding a tree in Euclidean space makes leaves from different paths closer than they should be, which is exactly as depicted in Figure 2 and also concordant with the sentence which follows this one in your paper.
• Page 4-5: The notation $\\{x_j\\}_{j\in e}$ doesn't make sense to me, because the integer $j$ is not in $e$. At best, I could see something like $\\{x_j \mid x_j \in e\\}$, or maybe just using $\\{x_1, \ldots, x_m\\}$ as the argument to the centroid function and putting "for $e = (r, x_1, \ldots, x_m)$" to the right or in the text above the block equation.
• Page 5: The squared Lorentzian norm is mentioned but has not been defined, it would be good to include the definition for completeness.
• Page 6: I would advise against claiming the model "significantly outperforms" the baselines when, in fact, many of the results are within 1 standard deviation of the UniSAGE baseline. Also, the accuracy range of 89.75% to 74.89% quoted in the text is incorrect based on the numbers in Table 2.

Please refer to the Weakness.