Dion3 combines Gram-based Newton-Schulz, symmetric GEMM kernels, megabatched communication, and fractional row selection so Muon-class optimizers run up to about 6x faster per step while matching or slightly improving loss.
The Polar Express: Optimal Matrix Sign Methods and their Application to the Muon Algorithm
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
fields
cs.LG 1years
2026 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Dion3: Full-Stack Orthogonal Updates
Dion3 combines Gram-based Newton-Schulz, symmetric GEMM kernels, megabatched communication, and fractional row selection so Muon-class optimizers run up to about 6x faster per step while matching or slightly improving loss.