TY - JOUR
T1 - Mapping low-dimensional dynamics to high-dimensional neural activity
T2 - A derivation of the ring model from the neural engineering framework
AU - Barak, Omri
AU - Romani, Sandro
N1 - Publisher Copyright:
© 2021 Massachusetts Institute of Technology.
PY - 2021/3
Y1 - 2021/3
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85101755897&partnerID=8YFLogxK
U2 - 10.1162/neco_a_01361
DO - 10.1162/neco_a_01361
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AN - SCOPUS:85101755897
SN - 0899-7667
VL - 33
SP - 827
EP - 852
JO - Neural Computation
JF - Neural Computation
IS - 3
M1 - 3
ER -