Adam-HNAG is a splitting-based reformulation of Adam that yields the first convergence proof for Adam-type methods, including accelerated rates, in convex smooth optimization.
Structured preconditioners in adaptive optimization: A unified analysis.arXiv preprint arXiv:2503.10537
9 Pith papers cite this work. Polarity classification is still indexing.
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UNVERDICTED 9representative citing papers
A unified stochastic convergence theory is developed for adaptive preconditioned first-order methods including AdaGrad variants, Shampoo, and Muon in nonconvex optimization.
Muon achieves higher storage capacity than SGD and matches Newton's method in one-step recovery rates for associative memory under power-law distributions, while saturating at larger critical batch sizes and showing faster initial multi-step dynamics.
Full finetuning with the pretraining optimizer reduces forgetting compared to other optimizers or LoRA while achieving comparable new-task performance.
Pro-KLShampoo projects KL-Shampoo preconditioners to a spike-and-flat parametric form on an r-dimensional subspace and recovers the full algebraic preconditioner via orthogonalization, outperforming KL-Shampoo on GPT-2 and LLaMA pre-training scales.
Proving stability of Leon's preconditioner enables the first tuning-free Nesterov-accelerated projection-free adaptive SGD variant with improved non-smooth non-convex rates.
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.
Proposes low-rank orthogonalization and derives low-rank Muon and MSGD variants that outperform standard Muon on GPT-2 and LLaMA pretraining while providing iteration complexity bounds.
Convergence analysis shows Muon outperforms gradient descent by exploiting low-rank structure in neural network Hessians.
citing papers explorer
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Adam-HNAG: A Convergent Reformulation of Adam with Accelerated Rate
Adam-HNAG is a splitting-based reformulation of Adam that yields the first convergence proof for Adam-type methods, including accelerated rates, in convex smooth optimization.
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A unified convergence theory for adaptive first-order methods in the nonconvex case, including AdaNorm, full and diagonal AdaGrad, Shampoo and Muo
A unified stochastic convergence theory is developed for adaptive preconditioned first-order methods including AdaGrad variants, Shampoo, and Muon in nonconvex optimization.
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Sharp Capacity Scaling of Spectral Optimizers in Learning Associative Memory
Muon achieves higher storage capacity than SGD and matches Newton's method in one-step recovery rates for associative memory under power-law distributions, while saturating at larger critical batch sizes and showing faster initial multi-step dynamics.
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Optimizer-Model Consistency: Full Finetuning with the Same Optimizer as Pretraining Forgets Less
Full finetuning with the pretraining optimizer reduces forgetting compared to other optimizers or LoRA while achieving comparable new-task performance.
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Pro-KLShampoo: Projected KL-Shampoo with Whitening Recovered by Orthogonalization
Pro-KLShampoo projects KL-Shampoo preconditioners to a spike-and-flat parametric form on an r-dimensional subspace and recovers the full algebraic preconditioner via orthogonalization, outperforming KL-Shampoo on GPT-2 and LLaMA pre-training scales.
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Optimal Projection-Free Adaptive SGD for Matrix Optimization
Proving stability of Leon's preconditioner enables the first tuning-free Nesterov-accelerated projection-free adaptive SGD variant with improved non-smooth non-convex rates.
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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.
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Low-rank Orthogonalization for Large-scale Matrix Optimization with Applications to Foundation Model Training
Proposes low-rank orthogonalization and derives low-rank Muon and MSGD variants that outperform standard Muon on GPT-2 and LLaMA pretraining while providing iteration complexity bounds.
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On the Convergence Analysis of Muon
Convergence analysis shows Muon outperforms gradient descent by exploiting low-rank structure in neural network Hessians.