What if Neural Networks had SVDs?

Part of Advances in Neural Information Processing Systems 33 (NeurIPS 2020)

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Authors

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

Abstract

Various Neural Networks employ time-consuming matrix operations like matrix inversion. Many such matrix operations are faster to compute given the Singular Value Decomposition (SVD). Techniques from (Zhang et al., 2018; Mhammedi et al., 2017) allow using the SVD in Neural Networks without computing it. In theory, the techniques can speed up matrix operations, however, in practice, they are not fast enough. We present an algorithm that is fast enough to speed up several matrix operations. The algorithm increases the degree of parallelism of an underlying matrix multiplication H*X where H is an orthogonal matrix represented by a product of Householder matrices.