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.
Google DeepMind, 2025.https://jax-ml.github.io/scaling-book/
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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.