An argument for hyperbolic geometry in neural circuits
An argument for hyperbolic geometry in neural circuits
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DOI：
10.1016/j.conb.2019.07.008
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发表时间：
2019-10-01
影响因子：
5.7
通讯作者：
Sharpee, Tatyana O.
中科院分区：
文献类型：
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作者：
Sharpee, Tatyana O.
这篇评论连接了几条研究路线，认为双曲几何应该广泛适用于神经电路以及其他生物电路。其原因是，符合双曲几何的网络对外部和内部扰动的响应最大。这些网络还允许在添加或移除节点的条件下进行有效通信。我们将讨论双曲几何的特征之一是著名的齐普夫定律（有时也被称为帕累托分布），它指出观察到给定模式的概率与其秩成反比。齐普夫定律在各种生物系统中都可以观察到-从蛋白质序列，神经网络到经济学。这些观测结果进一步证明了具有双曲度量结构的网络的普遍性。最近的神经科学研究特别指出了神经信号的三维双曲空间的相关性。与其他维度相比，三维双曲空间可以赋予额外的鲁棒性。我们说明了如何使用双曲线坐标揭示了一种新的拓扑组织内的嗅觉系统。使用这样的坐标可以促进大脑中其他地方的相关信号的表示。
This review connects several lines of research to argue that hyperbolic geometry should be broadly applicable to neural circuits as well as other biological circuits. The reason for this is that networks that conform to hyperbolic geometry are maximally responsive to external and internal perturbations. These networks also allow for efficient communication under conditions where nodes are added or removed. We will argue that one of the signatures of hyperbolic geometry is the celebrated Zipf's law (also sometimes known as the Pareto distribution) that states that the probability to observe a given pattern is inversely related to its rank. Zipf's law is observed in a variety of biological systems - from protein sequences, neural networks to economics. These observations provide further evidence for the ubiquity of networks with an underlying hyperbolic metric structure. Recent studies in neuroscience specifically point to the relevance of a three-dimensional hyperbolic space for neural signaling. The three-dimensional hyperbolic space may confer additional robustness compared to other dimensions. We illustrate how the use of hyperbolic coordinates revealed a novel topographic organization within the olfactory system. The use of such coordinates may facilitate representation of relevant signals elsewhere in the brain.