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Adam optimizer

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Provable Edge-of-Stability for Adam on a One-Dimensional Quadratic

A theoretical machine learning paper proves Adam optimizer exhibits edge-of-stability behavior in a simplified one-dimensional quadratic setting, identifying both restoring dynamics toward a stability threshold and breakdown cases where EoS fails.

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arXiv Machine Learning

Aug 24, 2026

Related Claims

01 We prove that Adam exhibits a restoring tendency toward its frozen stability threshold $2(1+\beta_1)/[\eta(1-\beta_1)]$ in broad regimes.

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