将记忆模型从向量扩展到分布，支持图像与文本的分布存储与检索。
Dense associative memory for Gaussian distributions
- 用2-Wasserstein距离定义分布能量函数，通过最优传输加权聚合实现记忆检索
- 理论证明可存储指数级分布模式，且在分布扰动下仍能准确恢复
- 适用于图像和文本等真实数据，为生成模型与记忆学习提供新范式
密集关联记忆（DAM）通过能量函数的固定点实现模式的存储与检索，但现有模型仅限于向量表示。本文将DAM扩展至由2-Wasserstein距离度量的高斯分布。框架在存储分布上定义对数求和指数能量，并以吉布斯加权方式聚合最优传输映射进行检索。稳定点对应自洽的Wasserstein中位数，推广了经典DAM的固定点概念。理论证明其具有指数级存储容量，并在Wasserstein扰动下提供定量的检索保证。在合成数据及真实世界图像（CelebA、CIFAR-10）和文本（text8、NLI语料库）数据集上验证了方法的有效性。通过从向量到分布的推广，本工作连接了经典DAM与现代生成建模，为分布化存储与检索在记忆增强学习中的应用铺平道路。
原文摘要 · Abstract (English)
Dense associative memories (DAMs) store and retrieve patterns via energy-function based fixed points, but existing models are limited to vector representations. We extend DAMs to Gaussian densities equipped with the 2-Wasserstein distance. Our framework defines a log-sum-exp energy over stored distributions and a retrieval dynamics aggregating optimal transport maps in a Gibbs-weighted manner. Stationary points correspond to self-consistent Wasserstein barycenters, generalizing classical DAM fixed points. We prove exponential storage capacity and provide quantitative retrieval guarantees under Wasserstein perturbations. We validate the method on synthetic and real-world image (CelebA and CIFAR-10 datasets) and text (text8 and NLI corpus) datasets. By generalizing from vectors to distributions, our work bridges classical DAMs with modern generative modeling and paves way for distributional storage and retrieval in memory-augmented learning.
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