Nora is a matrix optimizer that stabilizes weight norms and angular velocities through row-wise momentum projection onto the orthogonal complement of the weights while approximating structured preconditioning with O(mn) complexity and proven scalability.
(T−1) L∞,2ηβ 1−β +T √mσ√ B s 1−β 1 +β # + T L∞,2η2 2 . (97) Dividing both sides byT ηyields 1 T T−1X t=0 E ∥Gt∥1,2 ≤ ∆ T η + 2
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Nora: Normalized Orthogonal Row Alignment for Scalable Matrix Optimizer
Nora is a matrix optimizer that stabilizes weight norms and angular velocities through row-wise momentum projection onto the orthogonal complement of the weights while approximating structured preconditioning with O(mn) complexity and proven scalability.