Venue: ICLR 2023 Conference

Reviews:

final_score: rating: 5: marginally below the acceptance threshold
review_content: summary_of_the_paper: This paper proposes a method to learn an embedding space, which leverages the human-designed taxonomy, for robotics tasks. It extends Gaussian Process Latent Variable Models (GPLVM) to hyperbolic latent spaces and proposes GPHLVM. The motivation for using hyperbolic space is that distances grow exponentially when moving away from the origin, and the shortest paths between distant points tend to pass through it, resembling a continuous hierarchical structure. They propose graph-distance priors and back constraints to introduce taxonomy knowledge into the GPHLVM.

The experiments are conducted on whole-body support pose taxonomy. The authors analyze the learned Hyperbolic latent embedding space and compare it with the Euclidean one. They also show that the learned embedding enables motion interpolation in the latent space.
strength_and_weaknesses: Strengths:
1. The idea of utilizing human-designed taxonomy prior in latent space learning is interesting.
2. The introduction of Hyperbolic space seems to lead to better structure than Euclidean space.


Weaknesses:
1. I feel that the experimental part is not enough to demonstrate the advantage of the proposed GPHLVM:
(a) There is only one task/dataset (whole-body support pose taxonomy) is used in the experiments. It is thus unclear whether the proposed method can be applied to other tasks as well.
(b) There are no other alternative approaches for comparison (only Gaussian counterpart for visual analysis).
(c) There is no quantitative comparison on some concrete tasks (e.g., pose classification) to demonstrate the practical benefit of the latent space.

2. An alternative design would be using a neural network to learn an embedding space. We can still apply the priors (i.e., Hyperbolic and taxonomy-aware priors) to the learned embedding space by designing various loss functions. However, this alternative approach will be more straightforward and efficient to implement. Unfortunately, we fail to find such discussion or comparison in the paper.

3. The proposed method hopes that the latent space complies with the human-designed taxonomy's hierarchical structure. However, as shown in the part of the experiments, when the human-designed taxonomy is coarse-grained, the performance of the proposed method is also limited.

4. The runtime information is missing from the text. It's unclear whether the proposed method is an efficient or computationally intractable one. 

5. The current latent space is very low-dimensional. Could the authors provide more discussion on the benefits of learning a low-dimensional latent space? Also, it's interesting to know whether the proposed method can handle high-dimensional latent space as well.

6. How shall we interpret the pairwise distance matrices in Figure 2 and compare them with the graph distances in Figure 3. To be honest, it's not easy to tell which one is closer to Figure 3.

7. The interpolated motions in Figure 4 fail to impress me. The transition is not very natural and smooth. Moreover, it includes many physically-infeasible motions. In contrast, Figure 5 shows better performance. Since only motions generated by the proposed GPHLVM are shown, it is hard to demonstrate the advantage of the proposed GPHLVM, as other methods may generate similar or better performances.
clarity,_quality,_novelty_and_reproducibility: Clarity: 8/10
Quality: 7/10
Novelty: 7/10
Reproducibility: 7/10 (if code released)
summary_of_the_review: I feel that the experimental part is not enough to demonstrate the advantage of the proposed over existing methods. The practical usage is also unclear.
review_title: null

final_score: rating: 8: accept, good paper
review_content: summary_of_the_paper: The authors propose to model robotics taxonomy data via a proposed Gaussian process hyperbolic latent variable model (GPHLVM). The GPHLVM maintains the structure of the human-designed taxonomy while embedding the taxonomy node features into a hyperbolic latent space, which naturally encodes a continuous hierarchical structure. The GPHLVM is an extension of GPLVM for hyperbolic spaces, and the authors propose using Riemannian optimization methods for training the GPHLVM and use graph-distance information as inductive bias to learn the embeddings, encouraging the embeddings to adhere to the taxonomy structure. They evaluate the approach on a whole-body support pose taxonomy dataset, and experiments show that the 2-dimensional encodings display desired structure complying with the taxonomy. Experiments also show trajectory generation by following paths in the latent space between two embeddings,
strength_and_weaknesses: * The paper is well-written: the authors include extensive technical details in the main paper and appendix.
* The approach is novel: it is the first to leverage the hyperbolic manifold in encoding hierarchical structures for robotics applications.
* The experiments are sufficient in demonstrating the approach. The visualizations in Fig. 2 demonstrate that the embeddings comply with the graph structure, and that the hyperbolic approach outperforms the Euclidean counterpart even at higher dimensions.
* Though physical constraints are not yet considered, the motion generation results look promising and indicate that the learned representations work well.
clarity,_quality,_novelty_and_reproducibility: * The writing is clear. The authors are thorough and provide extensive details in the appendix. The authors also generously provide background information (e.g. on GPLVMs, Riemannian geometry, the hyperbolic manifold, etc.)
* The work is also original, as it is the first to apply the hyperbolic manifold to learning robotics taxonomy representations to the best of my knowledge.
summary_of_the_review: The authors introduce a novel idea of embedding robotics taxonomies into a hyperbolic manifold. This is a neat idea as the hyperbolic manifold is a natural representation for hierarchical structures such as trees and graphs. The paper is well written and includes extensive technical details and analysis, and the authors demonstrate nice applications on the whole-body pose dataset, showing various motions obtained via geodesic interpolation in the latent space.
review_title: null

final_score: rating: 6: marginally above the acceptance threshold
review_content: summary_of_the_paper: The paper proposes robot taxonomy, for hierarchical classifications of the human hand postures and body poses, through Gaussian process hyperbolic latent variable models (GPHLVM) built on top of existing GPLVM and using its graph-based distance-preserving priors and back constraints. The learned hyperbolic embeddings comply with the original graph structure and encode the unseen poses better than the euclidean ones. The assumption behind hyperbolic embeddings is that (1) the distance grows exponentially from the origin and (2) the shortest paths between 2 distant points tend to pass through the origin, thereby inducing a hierarchy. The model is evaluated on whole-body support pose taxonomy of 100 human poses of standing or kneeling and compared to euclidean pose embeddings. The ablation study shows that regularization with stress prior + back constraints improves clustering in Poincare ball P^2 and results in better latent space mapping of unseen poses and classes.
strength_and_weaknesses: ### Strengths
The paper mentions the limitations and future directions for the community, such as the need to (1)  apply physical constraints on the generated motion, and (2) reduce the computational cost of the hyperbolic kernel. The lack of information on contact and object locations results in artifacts during interpolations between initial and final latent pose embeddings. 

The paper is clearly written with sufficient additional details mentioned in the background and appendix sections. 

Additional videos are provided for the generated trajectories on an augmented dataset with left & right side labels for hand and foot contacts.

### Weakness
It is unclear to understand the generated trajectories as the contacts are not visualized, only the human joints are shown.
clarity,_quality,_novelty_and_reproducibility: The paper is well-structured and written. For reproducibility, some hyperparameter and training details are provided in appendix but the code is not yet available.  

### Minor Clarifications
- Is c_i used to denote the taxonomy node and the class? What are the added classes in Fig 2. (e) part?
summary_of_the_review: Overall, the paper provides a perspective on the benefits of using hyperbolic embeddings over euclidean ones for humanoid joint pose taxonomy. The training paradigm for learning embeddings for taxonomy is driven by existing work in terms of using graph-based priors and back constraints, with modifications for the proposed hyperbolic manifold formulation.
The two advantages highlighted for the learned taxonomy are (1) generalization to unseen poses and (2) interpolation for generating trajectories. The latter, however, suffers from a lack of representation of contacts due to self-collisions and obstacles - a noted limitation of the current work.
review_title: null

Meta-review: metareview:_summary,_strengths_and_weaknesses: In this paper, robot taxonomies are embedded in GP-LVMs, extended to hyperbolic latent spaces, to enable geodesic distances.

The approach is interesting and the experimental results are OK.  But the paper does not compare with NN-based geodesics-based approaches, e.g. Tosi et al; Artavanidis et al, ICLR, 2018; Chen et al, ICML, 2020.  The comparison just with VAE and a hyperbolic VAE seems unjust, as better results exist, albeit not with hyperbolic latent spaces.   Advantages of hyperbolic latent spaces over other forms are not investigated.

The authors indicate very high training times for embedding in (relatively) low-dimensional latent spaces.  It is unclear how that generalises for more complex problems, where the inherent latent space is higher-dimensional yet lower-embedded.  Unfortunately, the rather restricted experiments give no clue to such issues.  Indeed, for the small experimental part, the results are not always convincing.
justification_for_why_not_higher_score: The experimental part  of the paper is not sufficient.  Furthermore, an at least a coarse comparison with other approaches to geodesics would be needed (NOT using hyperbolic latent spaces).  The use of hyperbolic spaces is not defended (but indeed used before).
justification_for_why_not_lower_score: n/a
Decision: Reject