Refresh-placement effects in other Kronecker-preconditioned optimizers

Determine whether refresh-placement effects and learning-rate-dependent preference reversals observed for the implemented Mousse optimizer also occur, and in what direction, for other Kronecker-preconditioned optimizers.

Background

The paper establishes the reversal primarily for Mousse, a curvature-augmented Muon optimizer. Attempts to extend the experiments to Shampoo and a capture-coupled Muon variant were inconclusive or produced behavior differing from Mousse. Consequently, the generality and direction of refresh-placement effects across other Kronecker-preconditioned optimizers remain unresolved.

References

Longer horizons and other Kronecker-preconditioned optimizers are the other open tests.

— A Refresh Interval Does Not Fully Specify a Refresh Schedule: Learning-Rate-Dependent Placement in Kronecker-Preconditioned Language Model Training  (2610.18695 - Wang et al., 13 Oct 2026) in Section 7, Discussion and Conclusion; Section 8, Limitations; Appendix C, paragraph “Other optimizers”