English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This article presents matrix backpropagation algorithms for the QRdecomposition 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 novelmatrix backpropagation results for the pivoted (full-rank) QR decomposition andfor the LQ decomposition of deep input matrices. Differentiable QRdecomposition offers a numerically stable, computationally efficient method tosolve least squares problems frequently encountered in machine learning andcomputer vision. Other use cases such as graph learning and network compressionare listed in the article. Software implementation across popular deep learningframeworks (PyTorch, TensorFlow, MXNet) incorporate the methods for general usewithin the deep learning community. Furthermore, this article aids thepractitioner in understanding the matrix backpropagation methodology as part oflarger computational graphs.

QR and LQ Decomposition Matrix Backpropagation Algorithms for Square,  Wide, and Deep -- Real or Complex -- Matrices and Their Software  Implementation