SignSGD provably beats SGD by a factor of d under sparse noise via matched ℓ1-norm upper and lower bounds, with an equivalent result for Muon on matrices, and this predicts faster GPT-2 pretraining.
Stochastic subgradient methods with guaranteed global stability in nonsmooth nonconvex optimization.arXiv preprint arXiv:2307.10053
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UNVERDICTED 4representative citing papers
A diameter criterion tied to a potential function certifies convergence of difference inclusions, enabling discrete proofs for first-order optimization methods with diminishing steps.
StoSignSGD resolves SignSGD divergence on non-smooth objectives via structural stochasticity, matching optimal convex rates and improving non-convex bounds while delivering 1.44-2.14x speedups in FP8 LLM pretraining.
Opt-Laws predicts LLM final training loss from LR schedules via SDE-derived convergence and escape features, with 94% Top-2 hit rate on held-out schedules and F1=0.92 for divergence detection.
citing papers explorer
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When and Why SignSGD Outperforms SGD: A Theoretical Study Based on $\ell_1$-norm Lower Bounds
SignSGD provably beats SGD by a factor of d under sparse noise via matched ℓ1-norm upper and lower bounds, with an equivalent result for Muon on matrices, and this predicts faster GPT-2 pretraining.
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Convergence of difference inclusions via a diameter criterion
A diameter criterion tied to a potential function certifies convergence of difference inclusions, enabling discrete proofs for first-order optimization methods with diminishing steps.
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StoSignSGD: Unbiased Structural Stochasticity Fixes SignSGD for Training Large Language Models
StoSignSGD resolves SignSGD divergence on non-smooth objectives via structural stochasticity, matching optimal convex rates and improving non-convex bounds while delivering 1.44-2.14x speedups in FP8 LLM pretraining.
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Optimization Hyper-parameter Laws for Large Language Models
Opt-Laws predicts LLM final training loss from LR schedules via SDE-derived convergence and escape features, with 94% Top-2 hit rate on held-out schedules and F1=0.92 for divergence detection.