AI RESEARCH
Geometric analysis of attractor boundaries and storage capacity limits in kernel Hopfield networks
arXiv CS.LG
•
ArXi:2605.00366v1 Announce Type: cross High-capacity associative memories based on Kernel Logistic Regression (KLR) exhibit strong storage capabilities, but the dynamical and geometric mechanisms underlying their stability remain poorly understood. This paper investigates the global geometry of attractor basins and the physical determinants of the storage limit in KLR-trained Hopfield networks. We combine empirical evaluations using random sequences and real-world image embeddings (CIFAR-10) with phenomenological morphing experiments and statistical Signal-to-Noise Ratio (SNR) analysis.