Information Geometric Self-Organization at the Edge of Stability in High-Capacity Kernel Associative Memories

arXiv:2609.16827 · cs.LG, cs.NE · Submitted 2026-09-15 · Read on arXiv

cs.LG, cs.NE

Submitted: 2026-09-15

Updated: 2026-09-25

Comments: 8 pages, 3 figures

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

Terminology

• Edge of Stability — 13× in this paper
• Gradient Descent — 10× in this paper
• Degeneracy — 8× in this paper · explained in 3 episodes
• Associative Memory — 6× in this paper · explained in 2 episodes
• Kernel Logistic Regression — 6× in this paper
• Fisher Information — 4× in this paper · explained in 3 episodes
• Fisher Information Matrix — 4× in this paper
• Regularization — 4× in this paper · explained in 3 episodes
• Loss Function — 3× in this paper · explained in 2 episodes
• Objective Function — 3× in this paper · explained in 2 episodes
• Robustness — 3× in this paper · explained in 5 episodes
• Consistency — 2× in this paper · explained in 3 episodes
• Generalization — 2× in this paper · explained in 13 episodes
• Trace — 2× in this paper · explained in 2 episodes
• Alignment — 1× in this paper · explained in 1 episode
• Anisotropy — 1× in this paper · explained in 3 episodes
• Gaussian Radial Basis Function — 1× in this paper
• Higher-order derivatives — 1× in this paper · explained in 2 episodes
• Natural Gradient Descent — 1× in this paper

Sources

• Geometry of learning dynamics: Gradient descent versus natural gradient on the ridge of optimization

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