发表机构
University of Ottawa; Fudan University（渥太华大学; 复旦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对LSR稠密联想记忆的检索动态隐私问题，提出BRACE差分隐私算法，理论证明其极小极大最优性并建立中心极限定理，实验验证其检索准确性，为能量型联想记忆的隐私保护提供理论基础。
AI 中文摘要
稠密联想记忆（DAM）为记忆检索提供了基于能量的框架，与现代人工智能中的注意力机制密切相关。尽管人们对人工智能的差分隐私兴趣日益浓厚，但DAM检索动态的隐私性仍相对未被探索。本文中，我们为对数和ReLU（LSR）稠密联想记忆开发了一个差分隐私框架，其有限支持的检索动态对隐私保护计算构成了独特挑战。我们提出了边界响应自适应校正演化（BRACE）算法，这是一种用于LSR-DAM的差分隐私检索机制，可自适应校正边界敏感扰动以控制其在检索轨迹上的累积效应。理论上，我们通过推导与维度无关的终端和全轨迹检索错误率，证明了我们的方法是极小极大最优的，其对逆温度具有最优依赖性，且在增长视界 regime 下对检索视界也具有最优依赖性。我们进一步建立了中心极限定理，通过表征其渐近分布和隐私引入的额外变异性，实现了私有检索的不确定性量化。数值实验将我们提出的方法与基线差分隐私方法进行了比较，并评估了其检索准确性。总体而言，我们的结果为基于能量的联想记忆系统中的最优隐私保护检索和不确定性量化提供了理论基础。
英文摘要
Dense associative memory (DAM) provides an energy-based framework for memory retrieval with close connections to attention mechanisms in modern artificial intelligence. Despite growing interest in differential privacy for AI, the privacy of DAM retrieval dynamics remains relatively unexplored. In this paper, we develop a differential privacy framework for log-sum-ReLU (LSR) dense associative memory, whose finite-support retrieval dynamics pose distinctive challenges for privacy-preserving computation. We propose the Boundary-Responsive Adaptive Correction Evolution (BRACE) algorithm, a differentially private retrieval mechanism for LSR-DAM that adaptively corrects boundary-sensitive perturbations to control their cumulative effect over the retrieval trajectory. In theory, we prove that our method is minimax optimal by deriving dimension-independent terminal and full-trajectory retrieval error rates, with optimal dependence on the inverse temperature and, in the growing-horizon regime, the retrieval horizon. We further establish central limit theorems that enable uncertainty quantification for private retrieval by characterizing its asymptotic distribution and the additional variability introduced by privacy. Numerical experiments compare our proposed method with baseline differential privacy approaches and evaluate its retrieval accuracy. Together, our results provide a theoretical foundation for optimal privacy-preserving retrieval and uncertainty quantification in energy-based associative memory systems.
