Assess whether Muon can be systematically improved

Ascertain whether the Muon optimizer can be systematically improved beyond its current formulation that orthogonalizes matrix-shaped gradient updates via spectral flattening.

Background

In motivating their study, the authors raise the question of whether Muon can be enhanced in a structured way. They later propose a spectral family of transformations and fractional variants to explore potential improvements, but the general question of systematic improvement is posed explicitly.

References

Consequently, it remains unclear to what extent the reported improvements can be attributed to Muon itself, how Muon relates to established adaptive optimizers such as Adam, and whether Muon can be systematically improved.

— Delving into Muon and Beyond: Deep Analysis and Extensions  (2602.04669 - Qi et al., 4 Feb 2026) in Section 1 (Introduction)