Dense associative memory retrieval with privacy protection and error control
BRACE: Differential Privacy for Dense Associative Memory with LSR Energy
Cryptography and SecurityMachine Learning
Summary
Dense associative memory (DAM) is a way computers remember and retrieve information using energy-based methods similar to attention in AI. The authors studied how to keep this memory retrieval process private, so sensitive information isn’t accidentally revealed. They developed a method called BRACE that adds carefully controlled noise to protect privacy without losing accuracy in recalling memories. Their method also provides ways to measure the uncertainty introduced by this privacy protection. They tested BRACE and showed it works better than basic approaches while proving its best possible performance in theory.
What this means in practice
- •For data privacy engineers: Implement private retrieval methods in energy-based memory systems to safeguard user data during AI memory operations in sensitive environments.
- •For machine learning platform teams: Enhance AI platforms with scalable, provably optimal privacy controls during associative memory retrieval processes for compliance and risk reduction.
Authors
Chang Qu, Zhaoyang Shi
Abstract
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.