Skip-gram word embeddings in hyperbolic space
Embeddings of tree-like graphs in hyperbolic space were recently shown to surpass their Euclidean counterparts in performance by a large margin. Inspired by these results, we present an algorithm for learning word embeddings in hyperbolic space from free text. An objective function based on the hyperbolic distance is derived and included in the skip-gram negative-sampling architecture from word2vec. The hyperbolic word embeddings are then evaluated on word similarity and analogy benchmarks. The results demonstrate the potential of hyperbolic word embeddings, particularly in low dimensions, though without clear superiority over their Euclidean counterparts. We further discuss subtleties in the formulation of the analogy task in curved spaces.
 This paper presents a technique for embedding words in hyperbolic space, which extends previous non-euclidean methods to non-structured data like free text. The authors provide a new gradient based method for creating the embeddings and then evaluate them on standard word embedding benchmarks. Overall the paper is very well written and well executed. They find that in the low dimensions the approach outperforms standard Euclidean space methods while in higher dimensions this advantage disappears. The results do not try to claim state of the art on all benchmarks, which I find refreshing and I appreciate the authors candor in giving an honest presentation of their results. Overall, I enjoyed this paper and am eager to see how the authors develop the approach further. However, along these same lines it would be great to have the authors provide more discussion about the next steps and potential applications for this approach. Is the interest here purely methodological? Are there potential use cases where they believe this approach might be superior to Euclidean approaches? More detail in the discussion and intro about the trajectory of this work would help the reader understand the methodological and application-specific implications. Pros: - Clearly written and results are presented in a straightforward manner. - Extension of analogy reasoning to non-euclidean spaces. Cons: - Lack of clear motivation and compelling use case. - It would be nice to have a visualization of the approach in 2-dimensions. While Figure 3 is instructive for how analogies work in this space, it would be great to visualize an entire dataset. I*m sure that the proposed embeddings would result in a very different space than euclidean embeddings (as the Poincare embedding paper showed), so it would be great to have at least one visualization of an embedded dataset. Presumably this would play to the strengths of the approach as it excels in lower dimensions. - The largest of embedding dimension tested was 100, and it is common to use much larger embeddings of 500-d. Do the trends they observe continue to larger dimensions, e.g. is the performance gap even larger in higher dimensions?
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Skip-gram word embeddings in hyperbolic space
Embeddings of tree-like graphs in hyperbolic space were recently shown to surpass their Euclidean counterparts in performance by a large margin. Inspired by these results, we present an algorithm for learning word embeddings in hyperbolic space from free text. An objective function based on the hyperbolic distance is derived and included in the skip-gram negative-sampling architecture from word2vec. The hyperbolic word embeddings are then evaluated on word similarity and analogy benchmarks. The results demonstrate the potential of hyperbolic word embeddings, particularly in low dimensions, though without clear superiority over their Euclidean counterparts. We further discuss subtleties in the formulation of the analogy task in curved spaces.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



 This paper presents a technique for embedding words in hyperbolic space, which extends previous non-euclidean methods to non-structured data like free text. The authors provide a new gradient based method for creating the embeddings and then evaluate them on standard word embedding benchmarks. Overall the paper is very well written and well executed. They find that in the low dimensions the approach outperforms standard Euclidean space methods while in higher dimensions this advantage disappears. The results do not try to claim state of the art on all benchmarks, which I find refreshing and I appreciate the authors candor in giving an honest presentation of their results. Overall, I enjoyed this paper and am eager to see how the authors develop the approach further. However, along these same lines it would be great to have the authors provide more discussion about the next steps and potential applications for this approach. Is the interest here purely methodological? Are there potential use cases where they believe this approach might be superior to Euclidean approaches? More detail in the discussion and intro about the trajectory of this work would help the reader understand the methodological and application-specific implications. Pros: - Clearly written and results are presented in a straightforward manner. - Extension of analogy reasoning to non-euclidean spaces. Cons: - Lack of clear motivation and compelling use case. - It would be nice to have a visualization of the approach in 2-dimensions. While Figure 3 is instructive for how analogies work in this space, it would be great to visualize an entire dataset. I*m sure that the proposed embeddings would result in a very different space than euclidean embeddings (as the Poincare embedding paper showed), so it would be great to have at least one visualization of an embedded dataset. Presumably this would play to the strengths of the approach as it excels in lower dimensions. - The largest of embedding dimension tested was 100, and it is common to use much larger embeddings of 500-d. Do the trends they observe continue to larger dimensions, e.g. is the performance gap even larger in higher dimensions?
assistant
 This paper presents a technique for embedding words in hyperbolic space, which extends previous non-euclidean methods to non-structured data like free text. The authors provide a new gradient based method for creating the embeddings and then evaluate them on standard word embedding benchmarks. Overall the paper is very well written and well executed. They find that in the low dimensions the approach outperforms standard Euclidean space methods while in higher dimensions this advantage disappears. The results do not try to claim state of the art on all benchmarks, which I find refreshing and I appreciate the authors candor in giving an honest presentation of their results. Overall, I enjoyed this paper and am eager to see how the authors develop the approach further. However, along these same lines it would be great to have the authors provide more discussion about the next steps and potential applications for this approach. Is the interest here purely methodological? Are there potential use cases where they believe this approach might be superior to Euclidean approaches? More detail in the discussion and intro about the trajectory of this work would help the reader understand the methodological and application-specific implications. Pros: - Clearly written and results are presented in a straightforward manner. - Extension of analogy reasoning to non-euclidean spaces. Cons: - Lack of clear motivation and compelling use case. - It would be nice to have a visualization of the approach in 2-dimensions. While Figure 3 is instructive for how analogies work in this space, it would be great to visualize an entire dataset. I*m sure that the proposed embeddings would result in a very different space than euclidean embeddings (as the Poincare embedding paper showed), so it would be great to have at least one visualization of an embedded dataset. Presumably this would play to the strengths of the approach as it excels in lower dimensions. - The largest of embedding dimension tested was 100, and it is common to use much larger embeddings of 500-d. Do the trends they observe continue to larger dimensions, e.g. is the performance gap even larger in higher dimensions?