Phase Kernel Lifts Capacity of Dense Associative Memory
Dense associative memory underlies modern attention mechanisms; however, Modern Hopfield Networks (MHNs) with linear kernels yield overlapping attractor basins and spurious states under high memory load, limiting their theoretically exponential storage capacity in practice. We construct a class of nonlinear phase kernels that modify the energy landscape and retrieval dynamics, and prove that these kernels preserve exponential storage capacity and local fixed-point convergence under given conditions on kernel smoothness, memory separation, and memory distributions. The framework is instantiated by the Sigmoidal Phase Hopfield Network (S-Hop), which guarantees monotone energy descent and mi...
| Authors | Yifei Zhao, Ying Tang |
|---|---|
| Primary category | cs.LG |
| Published | 15 October 2026 |
| Last updated at source | 15 October 2026 |
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