The early History of the Singular Value Decomposition (1993) [pdf](math.ucdavis.edu) |
The early History of the Singular Value Decomposition (1993) [pdf](math.ucdavis.edu) |
Singular values are like the fundamental frequencies of your matrix. You know how you can define any color with RGB? In a (pretty handwavy) way, singular values are like RGB color codes for us math guys.
Optimizers like Muon and Adam play around with weights' first, or second order singular values to train models.
https://www.oceanopticsbook.info/view/photometry-and-visibil...
In image processing, the SVD makes it possible to talk about all the rich spatial correlations in the image, and pick out the strongest ones and discard noise.
This is also why it's so ubiquitous in compression algorithms, and of central importance in stuff like quantum information.
I find this so annoying. I had to PR some Claude-generated gaussian elimination routine last month and making sure it got the pivoting logic correct was a waste of my time.