A Journey to the Edge of Stability

arXiv:2609.32290 · cs.LG · Submitted 2026-09-26 · Read on arXiv

cs.LG

Submitted: 2026-09-26

Updated: 2026-09-26

Comments: 33 pages, 20 figures

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Gradient Flow — 32× in this paper · explained in 2 episodes
• Trace — 19× in this paper · explained in 2 episodes
• Alignment — 17× in this paper · explained in 1 episode
• Regularization — 3× in this paper · explained in 3 episodes
• Adam — 2× in this paper · explained in 2 episodes
• Consistency — 2× in this paper · explained in 3 episodes
• Generalization — 2× in this paper · explained in 13 episodes
• Adaptive Gradient Methods — 1× in this paper · explained in 1 episode
• Adaptivity — 1× in this paper · explained in 1 episode
• Aggregation — 1× in this paper · explained in 1 episode
• Cosine Similarity — 1× in this paper · explained in 3 episodes
• Loss Function — 1× in this paper · explained in 2 episodes
• Objective Function — 1× in this paper · explained in 2 episodes
• Steering — 1× in this paper · explained in 2 episodes
• Stochastic Dynamics — 1× in this paper · explained in 2 episodes
• Transformer — 1× in this paper · explained in 2 episodes

Sources

• Edge of Stochastic Stability: Revisiting the Edge of Stability for SGD
• The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System
• Greedy Alignment Principle for Optimizer Selection
• The Road Taken: The Role of Optimizers at the Edge of Stability
• Grokfast: Accelerated Grokking by Amplifying Slow Gradients
• The large learning rate phase of deep learning: the catapult mechanism
• The Origin of Edge of Stability

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