Implementing efficient orthogonalization with QDWH

[valentyn1boreiko]

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QR-based Dynamically Weighted Halley (QDWH) can be used for orthogonalization and has cubic convergence (https://arxiv.org/abs/2505.21799). Would it be possible to add it as well as an alternative to Newton-Schulz?

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[snowmanwwg]

Thanks @valentyn1boreiko - is this something you want to contribute?

[skyw]

I've tested 16 steps Newton-Schulz with polar express coefficient sets. It gets very close to polar (by scipy).
Will need to see whether (or how difficult) a good GPU implementation of QDWH will be faster than ~50 matrix multiplies involved in 16 steps of NS.

[mkhona-nvidia]

QDWH will also let us implement PolarGrad by letting us compute the nuclear norm term.

[skyw]

implemented a version via SVD. It is not too slow, should be enough for evaluation purpose and motivate kernel work if turned out to be promising.