arXiv：cs.LG· Jianhai Zhang, Donghao Zhang, Pattarawut Charatpangoon, Bijoy Menon, M. Ethan MacDonald, Wu Qiu, Aravind Ganesh·· 4 小时前AI 评分39
有限特征联想记忆的几何容量理论
A Geometry-Based Capacity Theory for Finite-Feature Associative Memory
AI 导读
研究者提出一种基于几何的容量理论，用于压缩有限特征 Hebbian 联想记忆的精确键检索。该理论将检索干扰拆分为随特征维度下降的有限特征噪声，以及由键间核重叠决定、在无限特征极限下仍存在的结构干扰，从而无拟合预测检索质量并给出容量上限与目标质量所需的特征预算。在合成、视觉与医学图像表示上，预测的检索曲线与实验结果高度吻合。
正文
Abstract:We develop a geometry-based capacity theory for exact-key retrieval in compressed finite-feature Hebbian associative memory. For random or approximately isotropic values, retrieval interference separates into finite-feature noise, which decreases with feature dimension, and structural interference, which is determined by squared kernel overlap among stored keys and persists in the infinite-feature limit. This yields a fit-free prediction of retrieval quality, reveals a geometry-dependent capacity ceiling, and predicts the feature budget required for a target retrieval quality. When stored values are correlated, we show that retrieval depends jointly on the key kernel and value Gram matrix, and derive finite-feature approximations that account for this interaction. We validate the theory on synthetic, visual, and medical-image representations. Overall, the framework links representation geometry directly to memory capacity and distinguishes when performance can be improved by increasing the feature budget and when the representation itself must be changed. Across these settings, the predicted retrieval curves closely match empirical behavior and correctly identify changes in the preferred memory design.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.09056 [cs.LG] |
| (or arXiv:2610.09056v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.09056 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Jianhai Zhang [view email]
[v1]
Tue, 6 Oct 2026 20:07:53 UTC (1,178 KB)
来源：arXiv：cs.LG · arxiv.org