arXiv:2606.27216v1 Announce Type: cross Abstract: Muon-type optimizers construct update directions for dense neural-network weights by applying a finite Newton-Schulz map to momentum-gradient matrices. For an $H \times W$ matrix, with $r=\min\{H,W\}$ and $s=\max\{H,W\}$, $K$ steps of the full-matrix Newton-Schulz update require $O(r^2 s K)$ work and couple all rows and columns through repeated Gram matrix products. We introduce Hierarchical Muon (HiMuon), a tiled Newton-Schulz scheme for Muon-type optimization. HiMuon partitions each momentum-gradient matrix into $T \times T$ tiles, applies th
The continuous demand for more efficient AI training and the increasing scale of neural networks drive innovations in optimization algorithms.
This development can significantly reduce the computational cost and time required to train large language models and other deep learning architectures, accelerating AI progress.
The computational bottleneck for dense neural network optimization is being addressed with more efficient algorithms, potentially democratizing access to powerful AI training.
- · AI compute providers
- · Deep learning researchers
- · Companies with large AI models
- · Inefficient legacy optimization methods
Faster and cheaper training of large AI models becomes possible.
This could lead to a proliferation of more sophisticated AI applications across various industries.
Reduced compute costs might lower barriers to entry for AI development, fostering greater competition and innovation in the AI sector.
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