# Spectral Concentration at the Edge of Stability: Information Geometry of Kernel Associative Memory

arXiv: https://arxiv.org/abs/2511.23083 · HTML: https://mlsanity.com/paper/2511.23083/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 12 references that are in the map.
- First posted on arXiv 28 Nov 2025.

## Builds on (most cited first, 5 of 5)

- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [Hopfield Networks is All You Need](https://mlsanity.com/paper/2008.02217/) (2020)
- [Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability](https://mlsanity.com/paper/2103.00065/) (2021)
- [Universal Statistics of Fisher Information in Deep Neural Networks: Mean Field Approach](https://mlsanity.com/paper/1806.01316/) (2018)
- [Self-Organization and Spectral Mechanism of Attractor Landscapes in High-Capacity Kernel Hopfield Networks](https://mlsanity.com/paper/2511.13053/) (2025)

## Abstract (arXiv)

High-capacity kernel Hopfield networks exhibit a textitRidge of Optimization characterized by extreme stability. While previously linked to textitSpectral Concentration, its origin remains elusive. Here, we analyze the network dynamics on a statistical manifold, revealing that the Ridge corresponds to the Edge of Stability, a critical boundary where the Fisher Information Matrix becomes singular. We demonstrate that the apparent Euclidean force antagonism is a manifestation of textitDual Equilibrium in the Riemannian space. This unifies learning dynamics and capacity via the Minimum Description Length principle, offering a geometric theory of self-organized criticality.