Department of Mathematics, University of Leicester, University Road, Leicester, LE1 7RH, UK.
Saint-Petersburg State Electrotechnical University, Prof. Popova Str. 5, Saint Petersburg, Russia.
Bull Math Biol. 2019 Nov;81(11):4856-4888. doi: 10.1007/s11538-018-0415-5. Epub 2018 Mar 19.
Codifying memories is one of the fundamental problems of modern Neuroscience. The functional mechanisms behind this phenomenon remain largely unknown. Experimental evidence suggests that some of the memory functions are performed by stratified brain structures such as the hippocampus. In this particular case, single neurons in the CA1 region receive a highly multidimensional input from the CA3 area, which is a hub for information processing. We thus assess the implication of the abundance of neuronal signalling routes converging onto single cells on the information processing. We show that single neurons can selectively detect and learn arbitrary information items, given that they operate in high dimensions. The argument is based on stochastic separation theorems and the concentration of measure phenomena. We demonstrate that a simple enough functional neuronal model is capable of explaining: (i) the extreme selectivity of single neurons to the information content, (ii) simultaneous separation of several uncorrelated stimuli or informational items from a large set, and (iii) dynamic learning of new items by associating them with already "known" ones. These results constitute a basis for organization of complex memories in ensembles of single neurons. Moreover, they show that no a priori assumptions on the structural organization of neuronal ensembles are necessary for explaining basic concepts of static and dynamic memories.
将记忆编码是现代神经科学的基本问题之一。这一现象背后的功能机制在很大程度上仍是未知的。实验证据表明，一些记忆功能是由分层的大脑结构（如海马体）来执行的。在这种特殊情况下，CA1 区域的单个神经元从 CA3 区域接收高度多维的输入，CA3 区域是信息处理的枢纽。因此，我们评估了大量神经元信号通路汇聚到单个细胞对信息处理的影响。我们表明，只要单个神经元在高维空间中工作，它们就可以选择性地检测和学习任意信息项。该论点基于随机分离定理和测度集中现象。我们证明，一个足够简单的功能性神经元模型能够解释：（i）单个神经元对信息内容的极端选择性，（ii）从大量集合中同时分离几个不相关的刺激或信息项，以及（iii）通过将新项与已经“已知”的项相关联来动态学习新项。这些结果为在单个神经元集合中组织复杂记忆提供了基础。此外，它们表明，在解释静态和动态记忆的基本概念时，不需要对神经元集合的结构组织做出任何先验假设。
