Adam at the Edge of Stability: Adaptive Feedback, Provable Oscillation, and Gradient Reversal
cs.LG, cs.AI, math.OC
Submitted: 2026-08-21
Updated: 2026-10-01
Terminology
Sources
- Understanding the unstable convergence of gradient descent
- Learning threshold neurons via the "edge of stability"
- Edge of Stochastic Stability: Revisiting the Edge of Stability for SGD
- Towards Understanding Adam Convergence on Highly Degenerate Polynomials
- Adaptive Preconditioners Trigger Loss Spikes in Adam
- Convergence and Dynamical Behavior of the ADAM Algorithm for Non-Convex Stochastic Optimization
- Local Convergence of Adaptive Gradient Descent Optimizers
- Adaptive Gradient Methods at the Edge of Stability
- On the Relation Between the Sharpest Directions of DNN Loss and the SGD Step Length
- Universal Sharpness Dynamics in Neural Network Training: Fixed Point Analysis, Edge of Stability, and Route to Chaos
- The large learning rate phase of deep learning: the catapult mechanism
- Adam Reduces a Unique Form of Sharpness: Theoretical Insights Near the Minimizer Manifold
- Analyzing Sharpness along GD Trajectory: Progressive Sharpening and Edge of Stability
- A Defense of the Quadratic Model
- State-Dependent Lyapunov Analysis of Rank-1 Matrix Factorization
- On the Convergence of Adam and Beyond
- A Rod Flow Model for Adam at the Edge of Stability
- Trajectory Alignment: Understanding the Edge of Stability Phenomenon via Bifurcation Theory
- Adam Can Converge Without Any Modification On Update Rules
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