Kernel Logistic Regression Learning for High-Capacity Hopfield Networks

Abstract: 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.