The cerebellum resembles a feedforward, three-layer network of neurons in which the "hidden layer" consists of Purkinje cells (P-cells), and the output layer consists of deep cerebellar nucleus (DCN) neurons. In this analogy, the output of each DCN neuron is a prediction that is compared to the actual observation, resulting in an error signal that originates in the inferior olive. Efficient learning requires that the error signal reach the DCN neurons, as well as the P-cells that project onto them. However, this basic rule of learning is violated in the cerebellum: the olivary projections to the DCN are weak, particularly in adulthood. Instead, an extraordinarily strong signal is sent from the olive to the P-cells, producing complex spikes. Curiously, P-cells are grouped into small populations that converge onto single DCN neurons. Why are the P-cells organized in this way, and what is the membership criterion of each population? Here, I apply elementary mathematics from machine learning and consider the fact that P-cells that form a population exhibit a special property: they can synchronize their complex spikes, which in turn suppress activity of DCN neuron they project to. Thus, complex spikes can not only act as a teaching signal for a P-cell, but through complex spike synchrony a P-cell population may act as a surrogate teacher for the DCN neuron that produced the erroneous output. It appears that grouping of P-cells into small populations that share a preference for error satisfies a critical requirement of efficient learning: providing error information to the output layer neuron (DCN) that was responsible for the error, as well as the hidden layer neurons (P-cells) that contributed to it. This population coding may account for several remarkable features of behavior during learning, including multiple timescales, protection from erasure, and spontaneous recovery of memory.

中文翻译：

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小脑中的人口编码：机器学习的观点

小脑类似于神经元的前馈三层网络，其中“隐藏层”由浦肯野细胞（P 细胞）组成，输出层由深小脑核 (DCN) 神经元组成。在这个类比中，每个 DCN 神经元的输出都是与实际观察结果进行比较的预测，从而产生源自劣橄榄的错误信号。有效的学习要求误差信号到达 DCN 神经元，以及投射到它们上的 P 细胞。然而，小脑违反了这一基本学习规则：橄榄球对 DCN 的投射很弱，尤其是在成年期。取而代之的是，一个非常强的信号从橄榄发送到 P 细胞，产生复杂的尖峰信号。奇怪的是，P 细胞被分成小群，这些小群会聚到单个 DCN 神经元上。为什么 P 细胞以这种方式组织，每个群体的成员标准是什么？在这里，我应用机器学习中的基础数学，并考虑这样一个事实，即形成群体的 P 细胞表现出一种特殊性质：它们可以同步复杂的尖峰信号，从而抑制它们投射到的 DCN 神经元的活动。因此，复杂尖峰不仅可以作为 P 细胞的教学信号，而且通过复杂尖峰同步，P 细胞群可以充当产生错误输出的 DCN 神经元的替代教师。似乎将 P 细胞分组为对错误有偏好的小群体满足了有效学习的关键要求：向负责错误的输出层神经元 (DCN) 提供错误信息，以及对它做出贡献的隐藏层神经元（P-cells）。这种群体编码可能解释了学习过程中行为的几个显着特征，包括多个时间尺度、防止擦除和记忆的自发恢复。