On a Neural Implementation of Brenier’s Polar Factorization Apple Machine Learning Research
In 1991, Brenier proved a theorem that generalizes the polar decomposition for square matrices — factored as PSD ×times× unitary — to any vector field F:Rd→RdF:mathbb{R}^drightarrow mathbb{R}^dF:Rd→Rd. The theorem, known as the polar factorization theorem, states that any field FFF can be recovered as the… Read More »On a Neural Implementation of Brenier’s Polar Factorization Apple Machine Learning Research