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.
arXiv:2604. 09967v2 Announce Type: replace-cross Abstract: Muon has emerged as a promising optimizer for large-scale foundation model pre-training by exploiting the matrix structure of neural network updates through iterative orthogonalization.
arXiv:2606. 16371v1 Announce Type: new Abstract: Muon is an optimizer that computes updates using the polar factor of the momentum matrix and has shown strong empirical performance across a range of training settings.
arXiv:2606. 27153v1 Announce Type: cross Abstract: Matrix-orthogonalization-based optimizers, exemplified by Muon, have demonstrated strong convergence behavior across a wide range of modern deep learning workloads.
arXiv:2606. 00371v1 Announce Type: new Abstract: Muon optimizers improve neural-network training by replacing ill-conditioned momentum updates with approximately semi-orthogonal updates.
arXiv:2607. 20512v1 Announce Type: cross Abstract: The Muon optimizer reaches the grokking threshold on modular arithmetic faster than AdamW.
arXiv:2608. 05088v1 Announce Type: new Abstract: Muon has recently emerged as a promising alternative to AdamW for language model pretraining by orthogonalizing momentum matrices using Newton-Schulz iterations.
arXiv:2607. 22444v1 Announce Type: new Abstract: For scale-invariant deep networks, Hyperball-style optimizers have shown strong performance in large-scale training by fixing the norms of matrix-valued parameters and normalizing updates.
arXiv:2607. 20548v1 Announce Type: cross Abstract: Higher-order optimizers such as Muon and SOAP offer faster convergence than AdamW, but their computational cost and numerical stability challenges have limited adoption at scale.
arXiv:2608. 11612v1 Announce Type: cross Abstract: The Muon optimizer incurs a significant overhead cost due to its cubic-time Newton-Schulz orthogonalization step.
arXiv:2606. 27715v1 Announce Type: new Abstract: We show that for tall matrix parameters, like projection matrices in the MLP layers, the Muon update can have row norms that are arbitrarily non-uniform.
arXiv:2602. 14656v2 Announce Type: replace Abstract: Orthogonality constraints are ubiquitous in robust and probabilistic machine learning.
arXiv:2606. 14187v1 Announce Type: new Abstract: Large-scale neural network training increasingly relies on matrix-aware optimizers that exploit the structure of weight parameters beyond element-wise adaptation.