Faster Orthogonal Parameterization with Householder Matrices

Alexander Mathiasen, Frederik Hvilshøj, Jakob Rødsgaard Jørgensen, Anshul Nasery, Davide Mottin

Abstract: Orthogonal matrices have been used in several Normalizing Flows (Tomczak & Welling, 2016;van den Berg et al., 2018). Orthogonal matrices are attractive since they are easy to invert and have Jacobian determinant one. Their main downside is the additional computational resources required to perform gradient descent. We identify a computational bottleneck for previous work on Householder matrices, and introduce a novel algorithm, FastH, which circumvents the bottleneck and is up to 29× faster than a previous method.