Kernel Ridge Regression for Efficient Learning of High-Capacity Hopfield Networks

Abstract

Hebbian learning limits Hopfield network capacity. While kernel methods like Kernel Logistic Regression (KLR) improve performance via iterative learning, we propose Kernel Ridge Regression (KRR) as an alternative. KRR learns dual variables non-iteratively via a closed-form solution, offering significant learning speed advantages. We show KRR achieves comparably high storage capacity (reaching ratio 1.5 shown) and noise robustness (recalling from around 80% corrupted patterns) as KLR, while drastically reducing training time, establishing KRR as an efficient method for building high-performance associative memories.

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