Encoding Binary Neural Codes in Networks of Threshold-Linear Neurons
Encoding Binary Neural Codes in Networks of Threshold-Linear Neurons
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DOI：
10.1162/neco_a_00504
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发表时间：
2013-11-01
影响因子：
2.9
通讯作者：
Itskov, Vladimir
中科院分区：
文献类型：
--
作者：
Curto, Carina;Degeratu, Anda;Itskov, Vladimir
大脑中的神经元网络通过它们的突触连接编码优选的神经活动模式。尽管受到相当大的关注，网络连接和编码模式之间的精确关系仍然知之甚少。在这里，我们考虑阈值线性神经元网络的这个问题，其计算功能是学习和存储一组二进制模式（例如，神经代码）作为网络的允许集合。我们引入一个简单的编码规则，选择性地打开共同出现在一个或多个模式的神经元之间的突触。该规则使用二进制的突触，在只有两个状态（开或关）的意义上，但也是异质的，具有从底层突触强度矩阵S中提取的权重。我们的主要结果精确地描述了存储的模式，从编码规则，包括无意的虚假状态，并给出了一个明确的特征依赖于S。特别是，我们发现，当神经元之间的兴奋性连接是几何平衡的时，二进制模式被成功地存储在这些网络中。它们满足一组几何约束。此外，我们发现某些类型的神经代码在这些网络中是自然的，这意味着可以从高度欠采样的模式集中准确地学习完整的代码。有趣的是，从这个意义上说，许多在皮质和海马区常见的神经代码都是自然的。作为一个应用程序，我们构建的网络，编码海马位置字段代码几乎完全，以下介绍只有一小部分的模式。为了获得我们的结果，我们使用凸几何和距离几何的经典思想证明了新的定理，例如Cayley-Menger行列式，揭示了这些数学领域与神经网络编码特性之间的新联系。
Networks of neurons in the brain encode preferred patterns of neural activity via their synaptic connections. Despite receiving considerable attention, the precise relationship between network connectivity and encoded patterns is still poorly understood. Here we consider this problem for networks of threshold-linear neurons whose computational function is to learn and store a set of binary patterns (e.g., a neural code) as permitted sets of the network. We introduce a simple encoding rule that selectively turns on synapses between neurons that coappear in one or more patterns. The rule uses synapses that are binary, in the sense of having only two states (on or off), but also heterogeneous, with weights drawn from an underlying synaptic strength matrix S. Our main results precisely describe the stored patterns that result from the encoding rule, including unintended spurious states, and give an explicit characterization of the dependence on S. In particular, we find that binary patterns are successfully stored in these networks when the excitatory connections between neurons are geometrically balancedi.e., they satisfy a set of geometric constraints. Furthermore, we find that certain types of neural codes are natural in the context of these networks, meaning that the full code can be accurately learned from a highly undersampled set of patterns. Interestingly, many commonly observed neural codes in cortical and hippocampal areas are natural in this sense. As an application, we construct networks that encode hippocampal place field codes nearly exactly, following presentation of only a small fraction of patterns. To obtain our results, we prove new theorems using classical ideas from convex and distance geometry, such as Cayley-Menger determinants, revealing a novel connection between these areas of mathematics and coding properties of neural networks.