Empirical estimates of the dimensionality of neural population activity are often much lower than the population size. Similar phenomena are also observed in trained and designed neural network models. These experimental and computational results suggest that mapping low-dimensional dynamics to high-dimensional neural space is a common feature of cortical computation. Despite the ubiquity of this observation, the constraints arising from such mapping are poorly understood. Here we consider a specific example of mapping low-dimensional dynamics to high-dimensional neural activity—the neural engineering framework. We analytically solve the framework for the classic ring model—a neural network encoding a static or dynamic angular variable. Our results provide a complete characterization of the success and failure modes for this model. Based on similarities between this and other frameworks, we speculate that these results could apply to more general scenarios.

神经种群活动维度的经验估计通常远低于种群规模。在经过训练和设计的神经网络模型中也观察到了类似的现象。这些实验和计算结果表明，将低维动态映射到高维神经空间是皮层计算的一个共同特征。尽管这种观察无处不在，但人们对这种映射所产生的限制知之甚少。在这里，我们考虑一个将低维动态映射到高维神经活动的具体示例——神经工程框架。我们分析解决了经典环模型的框架——一个编码静态或动态角度变量的神经网络。我们的结果提供了该模型成功和失败模式的完整特征。