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

摘要

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