Decoupling Variance and Scale-Invariant Updates in Adaptive Gradient Descent for Unified Vector and Matrix Optimization
arXiv:2602.06880v2 Announce Type: replace Abstract: Adaptive methods like Adam have become the $\textit{de facto}$ standard for large-scale vector and Euclidean optimization due to their coordinate-wise adaptation with a second-order nature. More recently, matrix-based spectral optimizers like Muon (Jordan et al., 2024b) show the power of treating weight matrices as matrices rather than long vectors. Linking these is hard because many natural generalizations are not feasible to implement, and we also cannot simply move the Adam adaptation to the matrix spectrum. To address this, we reformulate
The proliferation of large models and the increasing complexity of AI architectures are pushing the limits of current optimization techniques, necessitating more efficient and generalized approaches.
Improved optimization algorithms directly translate to faster training, better performance, and more efficient resource utilization for all large-scale AI models, impacting research and commercial applications.
This research introduces a unified framework that could lead to more robust, scalable, and versatile optimization methods suitable for both vector and matrix-based AI architectures.
- · AI researchers
- · Large language model developers
- · Hardware manufacturers (indirectly)
- · Cloud computing providers
- · Developers relying solely on outdated optimization methods
More efficient training of complex AI models.
Accelerated development of new AI capabilities and models across various domains.
Increased accessibility and affordability of advanced AI due to reduced computational overheads.
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Read at arXiv cs.LG