Preconditioned matrix norms unify steepest descent, quasi-Newton, and adaptive optimizers, revealing SGD, Adam, Muon, KL-Shampoo, SOAP, and SPlus as special cases and enabling new methods MuAdam and MuAdam-SANIA that are competitive in experiments.
Language models are few-shot learners.Advances in Neural Information Processing Systems, 33:1877–1901,
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Preconditioned Norms: A Unified Framework for Steepest Descent, Quasi-Newton and Adaptive Methods
Preconditioned matrix norms unify steepest descent, quasi-Newton, and adaptive optimizers, revealing SGD, Adam, Muon, KL-Shampoo, SOAP, and SPlus as special cases and enabling new methods MuAdam and MuAdam-SANIA that are competitive in experiments.