arXiv:2512.04632v2 Announce Type: replace Abstract: Orthogonality-based optimizers, such as Muon, have recently shown strong performance across large-scale training and community-driven efficiency challenges. However, these methods rely on a costly gradient orthogonalization step. Even efficient iterative approximations such as Newton-Schulz remain expensive, typically requiring dozens of matrix multiplications to converge. We introduce a pre-conditioning procedure that improves the initialization of the Newton--Schulz iterations while incurring negligible overhead. Furthermore, our pre-condit
Source: arXiv cs.AI — read the full report at the original publisher.