Summary
This paper proposes a method that leverages a non-Euclidean representation space to better encode hierarchical relationships between entities. Specifically, a hyperbolic embedding space is defined, wherein items closer to the origin are higher-level concepts, and items further from the origin are lower-level concepts; items closer to each other typically have closer semantic relationships, such that it is then straightforward to translate between geometric distances and inheritance relationships between concepts—even when the relationship was not explicitly encoded in the training set.
In a series of experiments, the authors leverage sentence-Transformer models as bases to predict whether two entities have taxonomic relationships in a zero-shot manner. Comparisons are performed between the base sentence-Transformer models, the same models with task-specific fine-tuning, and the proposed hyperbolic encoding method. It is observed that the proposed method outperforms more naive methods.
Strengths
* The proposed embedding space works well as a way to categorize hierarchical relationships between inputs. It also makes it easy to tell what the relationship is between two concepts in latent space, as distances between concepts and distances to the origin both have well-defined meanings in this space.
* The method can be run with modest compute resources, making it accessible and easily scalable as sentence-Transformer models scale and improve.
* The idea is interesting and, to my knowledge, novel.
Weaknesses
1. As the authors acknowledge, it is not clear what other knowledge is lost when moving to this new latent space. While hierarchical relationships between entities are now easy to understand, does the new space also preserve properties of each independent entity? Evaluations on a wider variety of downstream tasks would be helpful for establishing what kinds of semantic information are preserved.
2. The analysis in Table 4 could have been cherry-picked. A more systematic version of the analysis in Table 4 is possible, and would be nice to see: specifically, one could search over a larger subset of WordNet, quantifying whether more deeply nested concepts correlate with higher h-norms, and whether more closely related concepts have significantly lower hyperbolic distances than unrelated but semantically similar concepts.
3. When we classify whether two entities are taxonomically related, we usually care more about whether we can leverage these relationships to improve performance on some other metric. For example, better representational quality could lead to better deductive reasoning. Consider, for example, a counterfactual reasoning task where we say “Birds have fur. Is it therefore true that sparrows have fur?” A model that better captures taxonomic relationships should be better at this task. What I’m getting at is that it would be nice to evaluate on downstream tasks that require entity classification as a key part, rather than directly evaluating entity classification (a rare task). This would demonstrate the utility of this method, and increase interest and impact among a broader audience.
Questions
1. Why sample to a consistent 1:10 ratio of positive:negative examples? Was this decision made empirically?
2. How long did it take to run your proposed method compared to standard fine-tuning? Is there a better trade-off between performance and compute?