Norm of Word Embedding Encodes Information Gain

Momose Oyama, Sho Yokoi, Hidetoshi Shimodaira

Submission Type: Regular Long Paper

Submission Track: Interpretability, Interactivity, and Analysis of Models for NLP

Submission Track 2: Semantics: Lexical

Keywords: Word embedding, Euclidean norm, Skip-gram with Negative Sampling, Softmax function, Kullback-Leibler divergence, Information geometry, Exponential family of probability distributions

TL;DR: With the theory of information geometry, we show that the norm of word embedding approximates the KL divergence and confirm it experimentally.

Abstract:

Distributed representations of words encode lexical semantic information, but what type of information is encoded and how? Focusing on the skip-gram with negative-sampling method, we found that the squared norm of static word embedding encodes the information gain conveyed by the word; the information gain is defined by the Kullback-Leibler divergence of the co-occurrence distribution of the word to the unigram distribution.
Our findings are explained by the theoretical framework of the exponential family of probability distributions and confirmed through precise experiments that remove spurious correlations arising from word frequency. This theory also extends to contextualized word embeddings in language models or any neural networks with the softmax output layer.
We also demonstrate that both the KL divergence and the squared norm of embedding provide a useful metric of the informativeness of a word in tasks such as keyword extraction, proper-noun discrimination, and hypernym discrimination.

Submission Number: 901