[rahimiali]

Good q. The method computes Hessian-inverse on a batch. When people say "Newton's method" they're often thinking H^{-1} g, where both the Hessian and the gradient g are on the full dataset. I thought saying "preconditioner" instead of "Newton's method" would make it clear this is solving H^{-1} g on a batch, not on the full dataset.

[hodgehog11]

Just a heads up in case you didn't know, taking the Hessian over batches is indeed referred to as Stochastic Newton, and methods of this kind have been studied for quite some time. Inverting the Hessian is often done with CG, which tends to work pretty well. The only problem is that the Hessian is often not invertible so you need a regularizer (same as here I believe). Newton methods work at scale, but no-one with the resources to try them at scale seems to be aware of them.

It's an interesting trick though, so I'd be curious to see how it compares to CG.

[1] https://arxiv.org/abs/2204.09266 [2] https://arxiv.org/abs/1601.04737 [3] https://pytorch-minimize.readthedocs.io/en/latest/api/minimi...

[semi-extrinsic]

For solving physics equations there is also Jacobian-free Newton-Krylov methods.

[throwaway198846]

I lately used these methods and BFGS worked better than CG for me.

[MontyCarloHall]

I'd call it "Stochastic Newton's Method" then. :-)

[rahimiali]

fair. thanks. i'll sleep on it and update the paper if it still sounds right tomorrow.

probably my nomenclature bias is that i started this project as a way to find new preconditioners on deep nets.