What if Neural Networks had SVDs?
This work addresses efficiency bottlenecks in neural network training and inference, offering a domain-specific improvement for computational performance.
The paper tackles the problem of slow matrix operations in neural networks by introducing a fast algorithm that leverages the Singular Value Decomposition (SVD) to speed up computations, achieving practical speed improvements for several matrix operations.
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). Previous work allows 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 $H\cdot X$ where $H$ is an orthogonal matrix represented by a product of Householder matrices. Code is available at www.github.com/AlexanderMath/fasth .