Mapping Low-Dimensional Dynamics to High-Dimensional Neural Activity: A Derivation of the Ring Model From the Neural Engineering Framework

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.

Automated summary

Empirical estimates show that the dimensionality of neural population activity is often lower than the population size, leading to the common feature of mapping low-dimensional dynamics to high-dimensional neural space in cortical computation. By considering a specific example of this mapping, the study provides insights into the success and failure modes of such neural engineering frameworks, which may have implications for more general scenarios.