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.
arXiv preprint arXiv:2003.02395 , year=
10 Pith papers cite this work. Polarity classification is still indexing.
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Muon outperforms Adam by reducing curvature penalty via lower Normalized Directional Sharpness, as shown via Taylor approximation on LLM training and proven on stylized quadratic problems with heterogeneous curvature.
Derives ODE limits of Adam-DA showing that first- and second-order momentum parameters reverse their convergence roles in zero-sum games compared to minimization, validated on GAN experiments.
Clipped AdamW with exponentially weighted accumulation achieves superior global convergence rates for convex stochastic generalized Lipschitz optimization compared to SGD and AdaGrad.
OptMuon combines orthogonalized momentum with trajectory-dependent AdaGrad-Norm adaptation to obtain expected-stationarity rates of order T^{-1/2} + sigma^{1/2}T^{-1/4} or T^{-1/2} + sigma^{1/3}T^{-1/3} that reduce to near-optimal deterministic first-order rates in the zero-noise regime.
SGD is reformulated via a master equation from discrete updates, producing a discrete Fokker-Planck equation that predicts non-stationary variance growth proportional to learning rate in flat Hessian directions.
ChunkFT enables full-parameter fine-tuning of Llama 3-8B on one 24 GB GPU and Llama 3-70B on two 80 GB GPUs by streaming gradients over dynamically activated sub-tensors.
Muon learns more robust and transferable features than Adam and SGD, shown via corruption robustness tests, transfer experiments, layer-wise probes, effective rank measurements, and a theoretical proof on margins in a multi-component classification problem.
Proposes Artificial Adaptive Intelligence as the regime between narrow and general AI, defined by elimination of human-specified hyperparameters, and introduces an adaptivity index plus parametric minimality principle grounded in minimum description length.
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Artificial Adaptive Intelligence: The Missing Stage Between Narrow and General Intelligence
Proposes Artificial Adaptive Intelligence as the regime between narrow and general AI, defined by elimination of human-specified hyperparameters, and introduces an adaptivity index plus parametric minimality principle grounded in minimum description length.