Gram Newton-Schulz Cuts Muon Optimizer Step Cost at Scale

Muon's Newton-Schulz orthogonalization runs in cubic time, making optimizer steps increasingly expensive as model size grows — a key bottleneck given Muon's adoption in models like Kimi K2 and GLM-5. Gram Newton-Schulz introduces a hardware-aware algorithm to reduce this overhead, benchmarked on B300 GPUs across Llama model sizes.