Norm of Word Embedding Encodes Information Gain
This provides a theoretical explanation for embedding norms, useful for tasks like keyword extraction, but is incremental in linking known statistical concepts to existing embedding methods.
The paper shows that the squared norm of static word embeddings encodes the information gain of a word, defined by KL divergence from co-occurrence to unigram distributions, with theoretical grounding in exponential families and experimental validation removing frequency biases.
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.