Riemannian Optimization for Skip-Gram Negative Sampling

Alexander Fonarev, Alexey Grinchuk, Gleb Gusev, Pavel Serdyukov, Ivan Oseledets

Abstract: Skip-Gram Negative Sampling (SGNS) word embedding model, well known by its implementation in "word2vec" software, is usually optimized by stochastic gradient descent. It can be shown that optimizing for SGNS objective can be viewed as an optimization problem of searching for a good matrix with the low-rank constraint. The most standard way to solve this type of problems is to apply Riemannian optimization framework to optimize the SGNS objective over the manifold of required low-rank matrices. In this paper, we propose an algorithm that optimizes SGNS objective using Riemannian optimization and demonstrates its superiority over popular competitors, such as the original method to train SGNS and SVD over SPPMI matrix.

TL;DR: We train word embeddings optimizing Skip-Gram Negative Sampling objective (known by word2vec) via Riemannian low-rank optimization framework

Conflicts: yandex-team.ru, skoltech.ru, skolkovotech.ru

Keywords: Natural language processing, Unsupervised Learning

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/riemannian-optimization-for-skip-gram/code)