Tensor Analysis Reveals Distinct Population Structure that Parallels the Different Computational Roles of Areas M1 and V1.
Cortical firing rates frequently display elaborate and heterogeneous temporal structure. One often wishes to compute quantitative summaries of such structure-a basic example is the frequency spectrum-and compare with model-based predictions. The advent of large-scale population recordings affords the opportunity to do so in new ways, with the hope of distinguishing between potential explanations for why responses vary with time. We introduce a method that assesses a basic but previously unexplored form of population-level structure: when data contain responses across multiple neurons, conditions, and times, they are naturally expressed as a third-order tensor. We examined tensor structure for multiple datasets from primary visual cortex (V1) and primary motor cortex (M1). All V1 datasets were 'simplest' (there were relatively few degrees of freedom) along the neuron mode, while all M1 datasets were simplest along the condition mode. These differences could not be inferred from surface-level response features. Formal considerations suggest why tensor structure might differ across modes. For idealized linear models, structure is simplest across the neuron mode when responses reflect external variables, and simplest across the condition mode when responses reflect population dynamics. This same pattern was present for existing models that seek to explain motor cortex responses. Critically, only dynamical models displayed tensor structure that agreed with the empirical M1 data. These results illustrate that tensor structure is a basic feature of the data. For M1 the tensor structure was compatible with only a subset of existing models.
Department of Neuroscience, Columbia University Medical Center, New York, NY, United States of America.
Jeffrey S
http://orcid.org/0000-0002-4242-8422
JS
Seely
Neurosciences Program,Stanford University, Stanford, CA, United States of America.|Cold Spring Harbor Laboratory, Cold Spring Harbor, NY, United States of America.
Matthew T
http://orcid.org/0000-0002-8072-023X
MT
Kaufman
Department of Electrical Engineering, Stanford University, Stanford, CA, United States of America.|Department of Neurosurgery, Palo Alto Medical Foundation, Palo Alto, CA, United States of America.
Stephen I
SI
Ryu
Neurosciences Program,Stanford University, Stanford, CA, United States of America.|Department of Electrical Engineering, Stanford University, Stanford, CA, United States of America.|Department of Bioengineering, Stanford University, Stanford, CA, United States of America.|Department of Neurobiology, Stanford University, Stanford, CA, United States of America.|Stanford Neurosciences Institute, Stanford University, Stanford, CA, United States of America.|Howard Hughes Medical Institute Stanford University, Stanford, CA, United States of America.
Krishna V
KV
Shenoy
Grossman Center for the Statistics of Mind, Columbia University Medical Center, New York, NY, United States of America.|Department of Statistics, Columbia University, New York, NY, United States of America.
John P
JP
Cunningham
Department of Neuroscience, Columbia University Medical Center, New York, NY, United States of America.|Grossman Center for the Statistics of Mind, Columbia University Medical Center, New York, NY, United States of America.|David Mahoney Center for Brain and Behavior Research, Columbia University Medical Center, New York, NY, United States of America.|Kavli Institute for Brain Science, Columbia University Medical Center, New York, NY, United States of America.
Mark M
MM
Churchland
D000818:Animals; D001931:Brain Mapping / Q000379:methods*; D003198:Computer Simulation; D056324:Diffusion Tensor Imaging / Q000379:methods; D000882:Haplorhini; D008959:Models, Neurological; D009044:Motor Cortex / Q000502:physiology*; D009068:Movement / Q000502:physiology*; D009415:Nerve Net / Q000502:physiology; D011597:Psychomotor Performance / Q000502:physiology; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D014793:Visual Cortex / Q000502:physiology*; D014796:Visual Perception / Q000502:physiology*