Norm of word embedding encodes information gain

Distributed representations of words encode lexical semantic information, but how is that information encoded in word embeddings? Focusing on the skip-gram with negative-sampling method, we show theoretically and experimentally that the squared norm of word embedding encodes the information gain defined by the Kullback-Leibler divergence of the co-occurrence distribution of a word to the unigram distribution of the corpus. Furthermore, through experiments on tasks of keyword extraction, hypernym prediction, and part-of-speech discrimination, we confirmed that the KL divergence and the squared norm of embedding work as a measure of the informativeness of a word provided that the bias caused by word frequency is adequately corrected.