On the Two Faces of Adam in Separable Linear Classification

arXiv:2609.33904 · cs.LG · Submitted 2026-09-27 · Read on arXiv

cs.LG

Submitted: 2026-09-27

Updated: 2026-09-27

Terminology

• Adam — 1× in this paper · explained in 2 episodes

Sources

• Old Optimizer, New Norm: An Anthology
• The Implicit Bias of Adam and Muon on Smooth Homogeneous Neural Networks
• Risk and parameter convergence of logistic regression
• The Implicit Bias of Steepest Descent with Mini-batch Stochastic Gradient
• Towards Resolving the Implicit Bias of Gradient Descent for Matrix Factorization: Greedy Low-Rank Learning
• Gradient Descent Maximizes the Margin of Homogeneous Neural Networks
• Transformers as Support Vector Machines
• Flavors of Margin: Implicit Bias of Steepest Descent in Homogeneous Neural Networks
• Stability Annealing Selects the Implicit Bias of Smoothed Sign Descent: A Rate-Indexed Barrier Path on Separable Data
• Implicit Bias of AdamW: $\ell_\infty$ Norm Constrained Optimization

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