论文标题
QR和LQ分解矩阵反向传播算法，用于正方形，宽和深的 - 真实或复杂 - 矩阵及其软件实现
QR and LQ Decomposition Matrix Backpropagation Algorithms for Square, Wide, and Deep -- Real or Complex -- Matrices and Their Software Implementation
论文作者
论文摘要
本文介绍了用于矩阵$ a_ {m，n} $的QR分解的矩阵反向传播算法，它们是方形（m = n），宽（m <n）或deep（m> n），等级$ k = min（m，n）$。此外，我们得出了旋转（全级）QR分解以及深入输入矩阵的LQ分解的新型矩阵反向传播结果。可区分的QR分解提供了一种数值稳定的计算高效方法，可以解决机器学习和计算机视觉中经常遇到的最小二乘问题。本文列出了其他用例，例如图形学习和网络压缩。跨流行的深度学习框架（Pytorch，Tensorflow，MXNET）的软件实施结合了深度学习社区中的一般使用方法。此外，本文有助于实践者理解矩阵反向传播方法作为较大计算图的一部分。
This article presents matrix backpropagation algorithms for the QR decomposition of matrices $A_{m, n}$, that are either square (m = n), wide (m < n), or deep (m > n), with rank $k = min(m, n)$. Furthermore, we derive novel matrix backpropagation results for the pivoted (full-rank) QR decomposition and for the LQ decomposition of deep input matrices. Differentiable QR decomposition offers a numerically stable, computationally efficient method to solve least squares problems frequently encountered in machine learning and computer vision. Other use cases such as graph learning and network compression are listed in the article. Software implementation across popular deep learning frameworks (PyTorch, TensorFlow, MXNet) incorporate the methods for general use within the deep learning community. Furthermore, this article aids the practitioner in understanding the matrix backpropagation methodology as part of larger computational graphs.
