Embedding Text in Hyperbolic Spaces
Table 6: Held out set perplexity and downstream task performance for sentence embeddings of various sizes. ∗Perplexity of the Skip-Thoughts model is not comparable to our methods since it only uses uni-directional local context.
['[BOLD] Encoder Dim', '[BOLD] Word Dim', '[BOLD] Method', '[BOLD] Perplexity', '[BOLD] CR', '[BOLD] SUBJ', '[BOLD] MPQA', '[BOLD] MR', '[BOLD] MultiNLI', '[BOLD] SNLI']
Next, following common practice for evaluating sentence representations, we evaluate the trained Poincaré encoder as a black-box feature extractor for downstream tasks. We choose four binary classification benchmarks from the original Skip-Thoughts evaluation – CR, MR, MPQA and SUBJ – and two entailment tasks – MultiNLI For the binary classification tasks we train SVM models with a kernel based on hyperbolic distance between sentences, and for the entailment tasks we train multi-layer perceptrons on top of the premise and hypothesis embeddings and their element-wise products and differences. As a baseline, we compare to embeddings trained using the Euclidean distance metric. Poincaré embeddings achieve a lower perplexity in each case, suggesting a more efficient use of the embedding space. However, both sets of embeddings perform similarly on downstream tasks, except for the MPQA opinion polarity task where Poincaré embeddings do significantly better. Training with embedding sizes greater than 1000 did not show any further improvements in our experiments.