# Kernel Logistic Regression Learning for High-Capacity Hopfield Networks

arXiv: https://arxiv.org/abs/2504.07633 · HTML: https://mlsanity.com/paper/2504.07633/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 8 references that are in the map.
- First posted on arXiv 10 Apr 2025.

## Builds on (most cited first, 1 of 1)

- [Kernel Memory Networks: A Unifying Framework for Memory Modeling](https://mlsanity.com/paper/2208.09416/) (2022)

## Built on by (most cited first, 7 of 7)

- [Self-Organization and Spectral Mechanism of Attractor Landscapes in High-Capacity Kernel Hopfield Networks](https://mlsanity.com/paper/2511.13053/) (2025)
- [Quantitative Attractor Analysis of High-Capacity Kernel Hopfield Networks](https://mlsanity.com/paper/2505.01218/) (2025)
- [Kernel Ridge Regression for Efficient Learning of High-Capacity Hopfield Networks](https://mlsanity.com/paper/2504.12561/) (2025)
- [Quantization robustness from dense representations of sparse functions in high-capacity kernel associative memory](https://mlsanity.com/paper/2604.20333/) (2026)
- [Geometric and dynamical analysis of attractor boundaries and storage limits in kernel Hopfield networks](https://mlsanity.com/paper/2605.00366/) (2026)
- [Geometry of learning dynamics: Gradient descent versus natural gradient on the ridge of optimization](https://mlsanity.com/paper/2609.16805/) (2026)
- [Information Geometric Self-Organization at the Edge of Stability in High-Capacity Kernel Associative Memories](https://mlsanity.com/paper/2609.16827/) (2026)

## Abstract (arXiv)

Hebbian learning limits Hopfield network storage capacity (pattern-to-neuron ratio around 0.14). We propose Kernel Logistic Regression (KLR) learning. Unlike linear methods, KLR uses kernels to implicitly map patterns to high-dimensional feature space, enhancing separability. By learning dual variables, KLR dramatically improves storage capacity, achieving perfect recall even when pattern numbers exceed neuron numbers (up to ratio 1.5 shown), and enhances noise robustness. KLR demonstrably outperforms Hebbian and linear logistic regression approaches.