Abstract

We present an analytical model of the statistics learned by Word2Vec and GloVe algorithms, deriving the first known closed-form solution to Word2Vec’s softmax-optimized skip-gram algorithm. Our analysis provides new insights into bias detection and the mathematical foundations of word embeddings.

Key Contributions

  • First Closed-Form Solution: Analytical solution to Word2Vec’s softmax-optimized skip-gram algorithm
  • Theoretical Framework: Mathematical model explaining what statistics these algorithms actually learn
  • Bias Detection Analysis: Systematic approach to understanding and detecting bias in word embeddings
  • Algorithm Comparison: Theoretical comparison between Word2Vec and GloVe approaches

Mathematical Innovation

This work provides the first rigorous mathematical analysis of what Word2Vec learns during training, moving beyond empirical observations to theoretical understanding. The closed-form solution offers insights into the fundamental mechanisms of distributional semantics.

Bias Detection Framework

Our analysis enables systematic detection and measurement of bias in word embeddings by understanding the mathematical relationship between input statistics and learned representations. This has important implications for fair and ethical AI applications.

Theoretical Significance

The research bridges the gap between the practical success of word embeddings and their theoretical understanding, providing a foundation for future algorithmic improvements and bias mitigation strategies.

Impact

This work has influenced subsequent research on the mathematical foundations of embedding methods and contributed to the growing field of algorithmic fairness in NLP.

Citation

@article{williams2022know,
  title={To Know by the Company Words Keep and What Else Lies in the Vicinity},
  author={Williams, Jake Ryland and Heidenreich, Hunter Scott},
  journal={arXiv preprint arXiv:2205.00148},
  year={2022}
}