alt Hacker NewsFor the curious, eigenvalues only exist for square matrices. Singular values are like generalized eigenvalues.
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.
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Last statement is a bit sus... Muon computes matrix sign function which can be defined as setting singular values to 1, though you can also define it without SVD. Muon itself doesn't use SVD because it uses a faster method to compute matrix sign. Adam doesn't do anything related to SVD or singular values. Also not sure what you meant by "second order singular values"
Just going to sound really pedantic here, but RGB does not capture the entire colour space. In fact, it only captures about 35% of the colours the human eye can perceive.
https://www.oceanopticsbook.info/view/photometry-and-visibil...