# Riemannian Optimization for Skip-Gram Negative Sampling

## TL;DR

This paper introduces a Riemannian optimization approach for training Skip-Gram Negative Sampling (SGNS) word embeddings, framing the problem as low-rank matrix optimization and demonstrating its advantages over traditional methods.

## Contribution

It proposes a novel Riemannian optimization algorithm for SGNS, offering a new perspective and improved performance over existing training techniques.

## Key findings

- Our method outperforms traditional SGNS training algorithms.
- The Riemannian approach yields higher-quality embeddings.
- Experimental results show faster convergence and better accuracy.

## Abstract

Skip-Gram Negative Sampling (SGNS) word embedding model, well known by its implementation in "word2vec" software, is usually optimized by stochastic gradient descent. However, the optimization of SGNS objective can be viewed as a 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.