torch-householder 1.0.1

Efficient Householder Transformation in PyTorch

This package implements the Householder transformation algorithm for calculating orthogonal matrices and orthonormal frames with differentiable bindings to PyTorch. In particular, the package provides an enhanced drop-in replacement for the torch.orgqr function, which was renamed into torch.linalg.householder_product as of PyTorch 1.9.

APIs for orthogonal transformations have been around since LAPACK; however, their support in the deep learning frameworks is lacking. Recently, orthogonal constraints have become popular in deep learning as a way to regularize models and improve training dynamics, and hence the need to backpropagate through orthogonal transformations arised.

PyTorch 1.7 implements matrix exponential function torch.matrix_exp, which can be repurposed to performing the orthogonal transformation when the input matrix is skew-symmetric. This is the baseline we use in Speed and Precision evaluation.

PyTorch 1.9 renamed torch.orgqr into torch.linalg.householder_product, and added support of autograd, batching, and GPU execution.

Compared to torch.matrix_exp, the Householder transformation implemented in this package has the following advantages:

• Orders of magnitude lower memory footprint
• Ability to transform non-square matrices (orthonormal frames)
• A significant speed-up for non-square matrices
• Better numerical precision for all matrix and batch sizes

Find more details and the most up-to-date information on the project webpage: https://www.github.com/toshas/torch-householder