arXiv:2605.22432v1 Announce Type: new Abstract: Modern deep learning commonly relies on AdamW with prescribed learning rate schedules, but recent works challenge both components: Schedule-Free optimization removes explicit schedules via iterate averaging, and Muon improves the update geometry by orthogonalizing momentum for matrix parameters. Despite Muon's strong empirical performance, its underlying mechanism remains partially understood. We study Muon through the river-valley loss landscape, where useful training progress occurs along a flat, low-curvature bulk subspace (the river), while h
This paper addresses a fundamental challenge in optimizing deep learning models, building on recent work that questions established methods like AdamW, indicating a current push for more efficient and robust AI training. The publication date in 2026 suggests this is an anticipated development in the AI research pipeline.
Improved optimization techniques can significantly enhance the efficiency and performance of deep learning models, impacting the speed of AI development and the feasibility of more complex AI systems. This could lead to faster iteration cycles and more powerful AI applications across various industries.
The proposed 'Anytime Muon' optimization method offers a potentially more stable and efficient way to train neural networks, moving beyond the current reliance on pre-defined learning rate schedules and improving gradient evaluation geometries. This shifts the state-of-the-art in AI model training.
- · AI researchers and developers
- · Deep learning framework providers
- · Companies with large AI model training requirements
- · GPU manufacturers via increased demand
- · Older, less efficient optimization techniques (eventually)
More robust and faster training of complex deep learning models becomes possible.
This could accelerate overall AI research and development, leading to faster breakthroughs in various AI applications.
Reduced computational costs for training could democratize access to advanced AI model development, empowering more innovators.
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Read at arXiv cs.LG