Memoryless stability-annealed smoothed-sign descent with weighted exponential loss converges in normalized iterates to a Burg-type barrier minimizer on a margin slice, with an explicit S_t^{-1/2} envelope.
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Adam's adaptive preconditioning and first-moment averaging improve high-probability tracking error in noise-dominated nonstationary regimes but can increase it under strong drift, where SGD achieves a smaller floor, with explicit beta-dependent bounds.
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Stability Annealing Selects the Implicit Bias of Smoothed Sign Descent: A Rate-Indexed Barrier Path on Separable Data
Memoryless stability-annealed smoothed-sign descent with weighted exponential loss converges in normalized iterates to a Burg-type barrier minimizer on a margin slice, with an explicit S_t^{-1/2} envelope.
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Adapt or Forget: Provable Tradeoffs Between Adam and SGD in Nonstationary Optimization
Adam's adaptive preconditioning and first-moment averaging improve high-probability tracking error in noise-dominated nonstationary regimes but can increase it under strong drift, where SGD achieves a smaller floor, with explicit beta-dependent bounds.