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Furthermore, when combined with aggressive \\texttt{int8} quantization, PowerStep remains numerically sta","title":"PowerStep: Memory-Efficient Adaptive Optimization via $\\ell_p$-Norm Steepest Descent","url":"https://arxiv.org/abs/2605.10335","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.10335v1 Announce Type: cross \nAbstract: Adaptive optimizers, most notably Adam, have become the default standard for training large-scale neural networks such as Transformers. These methods maintain running estimates of gradient first and second moments, incurring substantial memory overhead. We introduce PowerStep, a memory-efficient optimizer that achieves coordinate-wise adaptivity without storing second-moment statistics. Motivated by steepest descent under an $\\ell_p$-norm geometry, we show that applying a nonlinear transform directly to a momentum buffer yields coordinate-wise adaptivity. 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