The softmax function is ubiquitous in machine learning and optimization applications. Computing the full softmax evaluation of a matrix-vector product can be computationally expensive in high-dimensional settings. In many applications, however, it is sufficient to calculate only the top few outputs of the softmax function. In this work, we present an algorithm, dubbed AdaptiveSoftmax, that adaptively computes the top k softmax values more efficiently than the full softmax computation, with probabilistic guarantees. We demonstrate the sample efficiency improvements afforded by AdaptiveSoftmax on real and synthetic data to corroborate our theoretical results.

The Word2Vec model has become a standard method for representing words as dense vectors. This is typically done as a preprocessing step, after which the learned vectors are fed into a discriminative model (typically an RNN) to generate predictions such as movie review sentiment, do machine translation, or even generate text, character by character. Previously, the bag of words model was commonly used to represent words and sentences as numerical vectors, which could then be fed into a classifier (for example Naive Bayes) to produce output predictions. Given a vocabulary of words and a document of words, a -dimensional vector would be created to represent the vector, where index denotes the number of times the th word in the vocabulary occured in the document. This model represented words as atomic units, assuming that all words were independent of each other.

We propose an approximate strategy to efficiently train neural network based language models over very large vocabularies. Our approach, called adaptive softmax, circumvents the linear dependency on the vocabulary size by exploiting the unbalanced word distribution to form clusters that explicitly minimize the expectation of computational complexity. Our approach further reduces the computational cost by exploiting the specificities of modern architectures and matrix-matrix vector operations, making it particularly suited for graphical processing units. Our experiments carried out on standard benchmarks, such as EuroParl and One Billion Word, show that our approach brings a large gain in efficiency over standard approximations while achieving an accuracy close to that of the full softmax.