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
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