Karbasi Amin, Salavati Amir Hesam, Shokrollahi Amin, Varshney Lav R
Yale University, New Haven, CT 06511, U.S.A.
Neural Comput. 2014 Nov;26(11):2493-526. doi: 10.1162/NECO_a_00655. Epub 2014 Aug 22.
Recent advances in associative memory design through structured pattern sets and graph-based inference algorithms have allowed reliable learning and recall of an exponential number of patterns that satisfy certain subspace constraints. Although these designs correct external errors in recall, they assume neurons that compute noiselessly, in contrast to the highly variable neurons in brain regions thought to operate associatively, such as hippocampus and olfactory cortex. Here we consider associative memories with boundedly noisy internal computations and analytically characterize performance. As long as the internal noise level is below a specified threshold, the error probability in the recall phase can be made exceedingly small. More surprising, we show that internal noise improves the performance of the recall phase while the pattern retrieval capacity remains intact: the number of stored patterns does not reduce with noise (up to a threshold). Computational experiments lend additional support to our theoretical analysis. This work suggests a functional benefit to noisy neurons in biological neuronal networks.
通过结构化模式集和基于图的推理算法在联想记忆设计方面的最新进展，使得对满足特定子空间约束的指数数量的模式进行可靠的学习和回忆成为可能。尽管这些设计在回忆过程中能纠正外部错误，但它们假设神经元进行无噪声计算，这与被认为以联想方式运作的脑区（如海马体和嗅觉皮层）中高度可变的神经元不同。在此，我们考虑具有有界噪声内部计算的联想记忆，并对其性能进行分析表征。只要内部噪声水平低于指定阈值，回忆阶段的错误概率就可以变得极小。更令人惊讶的是，我们表明内部噪声在模式检索能力保持不变的情况下提高了回忆阶段的性能：存储模式的数量不会因噪声而减少（直至达到一个阈值）。计算实验为我们的理论分析提供了额外支持。这项工作表明生物神经网络中噪声神经元具有功能优势。
