S-Hop 网络用相位核提升稠密联想记忆容量
Phase Kernel Lifts Capacity of Dense Associative Memory
一群研究者给 Hopfield 网络换了个相位核，ImageNet 上检索容量直接拉到 50 倍，搞联想记忆的可以看看。
arXiv 论文提出一类非线性相位核，用于改造 Modern Hopfield Networks 的能量景观与检索动力学。论文证明在核平滑性、记忆分离度等条件下，该核能保持指数级存储容量和局部不动点收敛。基于此框架的 Sigmoidal Phase Hopfield Network（S-Hop）保证单调能量下降。在 CIFAR-10 和 TinyImageNet 上，S-Hop 单步含噪检索负载分别是 Uniform Hopfield Networks 的 8.3 倍和 4 倍，在 ImageNet 上首次失败负载达到 50 倍增益。
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 mitigates practical capacity loss. S-Hop has $8.3\times$ and $4\times$ gains in one-step noisy retrieval load over Uniform Hopfield Networks (U-Hop) on CIFAR-10 and TinyImageNet respectively, and reaches a $50\times$ gain in first-failure load for ImageNet. The results demonstrate that phase kernels provide a principled route to robust dense associative memory.
