Cortical pyramidal neurons receive inputs from multiple distinct neural populations and integrate these inputs in separate dendritic compartments. We explore the possibility that cortical microcircuits implement canonical correlation analysis (CCA), an unsupervised learning method that projects the inputs onto a common subspace so as to maximize the correlations between the projections. To this end, we seek a multichannel CCA algorithm that can be implemented in a biologically plausible neural network. For biological plausibility, we require that the network operates in the online setting and its synaptic update rules are local. Starting from a novel CCA objective function, we derive an online optimization algorithm whose optimization steps can be implemented in a single-layer neural network with multicompartmental neurons and local non-Hebbian learning rules. We also derive an extension of our online CCA algorithm with adaptive output rank and output whitening. Interestingly, the extension maps onto a neural network whose neural architecture and synaptic updates resemble neural circuitry and non-Hebbian plasticity observed in the cortex.

皮质锥体神经元接收来自多个不同神经群的输入，并将这些输入整合到不同的树突隔室中。我们探索了皮层微电路实施典型相关分析 (CCA) 的可能性，CCA 是一种无监督学习方法，可将输入投影到公共子空间上，以最大化投影之间的相关性。为此，我们寻求一种可以在生物学上合理的神经网络中实现的多通道 CCA 算法。对于生物学上的合理性，我们要求网络在在线环境中运行，并且其突触更新规则是本地的。从一个新的 CCA 目标函数开始，我们推导出一种在线优化算法，其优化步骤可以在具有多室神经元和局部非赫布学习规则的单层神经网络中实现。我们还导出了我们的在线 CCA 算法的扩展，具有自适应输出等级和输出白化。有趣的是，扩展映射到一个神经网络，其神经结构和突触更新类似于在皮层中观察到的神经回路和非赫布可塑性。