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feat: add preconditioning and coef presets to muon - #1602
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Co-authored-by: Thibaut Boissin <thibaut.boissin@irt-saintexupery.com>
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Thanks, this is great! I left a few comments.
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Thanks for the feedback! Just pushed the fixes to address the comments. Let me know if anything else needs tweaking. |
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…ex inputs The modified first Newton-Schulz step for 'schatten' preconditioning computes the Gram matrix as a = x @ x.T, which for complex x is not the Hermitian Gram matrix, so the iteration diverges and orthogonalize_via_newton_schulz returns an all-NaN array for complex parameters. Any muon(preconditioning='schatten') step on a complex model NaN-poisons the parameters on the first update. Same file, same function family: _aol_first_newton_schulz_iteration (line 217, a = x @ x.T.conj()) and _base_newton_schulz_iteration (line 247, a = x @ x.T.conj()) both take the conjugate; schatten, added alongside aol in PR google-deepmind#1602, is the only one that omitted it. .conj() is a no-op for real dtypes, so real-input behavior is unchanged. test_newton_schulz is now parameterized over frobenius, aol, and schatten so the existing real-orthogonality and complex-unitarity assertions cover all three paths; the schatten complex case fails with all-NaN output before this fix and passes after.
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…ex inputs The modified first Newton-Schulz step for 'schatten' preconditioning computes the Gram matrix as a = x @ x.T, which for complex x is not the Hermitian Gram matrix, so the iteration diverges and orthogonalize_via_newton_schulz returns an all-NaN array for complex parameters. Any muon(preconditioning='schatten') step on a complex model NaN-poisons the parameters on the first update. Same file, same function family: _aol_first_newton_schulz_iteration (line 217, a = x @ x.T.conj()) and _base_newton_schulz_iteration (line 247, a = x @ x.T.conj()) both take the conjugate; schatten, added alongside aol in PR google-deepmind#1602, is the only one that omitted it. .conj() is a no-op for real dtypes, so real-input behavior is unchanged. test_newton_schulz is now parameterized over frobenius, aol, and schatten so the existing real-orthogonality and complex-unitarity assertions cover all three paths; the schatten complex case fails with all-NaN output before this fix and passes after.
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Add Preconditioning to the Muon Optimizer
In this commit, we implement different preconditioning methods for the Muon optimizer. Notably:
These options allow the user to tweak the trade-off between convergence speed of the Newton-Schulz iterative scheme and the computational budget associated to the preconditioning method.
We also add options to choose the coefficients used in the Newton-Schulz iterations. Further development could implement the PolarExpress (https://arxiv.org/abs/2505.16932) or CAN methods (https://arxiv.org/abs/2506.10935).