Concatenated Power Mean Word Embeddings as Universal Cross-Lingual Sentence Representations
Table 4: Average scores (en→de and en→fr) for additional power means (based on BV ⊕ AR ⊕ FT).
['[BOLD] power mean-values', 'Σ [BOLD]  X-Ling', 'Σ [BOLD]  In-Language']
We chose several intuitive values for power mean in addition to the ones already tried out, namely p=−1 (harmonic mean), p=0.5, p=2 (quadratic mean), and p=3 (cubic mean). We notice that p=3 is the most effective power mean here and p=−1 is (by far) least effective. We discuss below why p=−1 hurts performances in this case. For all cases with p>0, additional means tend to further improve the results, but with decreasing marginal returns. This also means that improvements are not merely due to additional dimensions but due to addition of complementary information.