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Explore how information is represented and processed in populations of neurons, encoding quantities through rate codes or precise spiking patterns. Investigate mean, covariance responses, orientation tuning, and stimulus-triggered covariance matrices in neural populations.
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Cracking the Population Code Dario Ringach University of California, Los Angeles
The Questions Two basic questions in cortical computation: How is information represented? How is information processed?
Representation by Neuronal Populations How is information encoded in populations of neurons?
Representation by Neuronal Populations • How is information encoded in populations of neurons? • Quantities are encoded as rate codes in ensembles of 50-100 neurons (eg, Shadlen and Newsome, 1998).
Representation by Neuronal Populations • How is information encoded in populations of neurons? • Quantities are encoded as rate codes in ensembles of 50-100 neurons (eg, Shadlen and Newsome, 1998). • Quantities are encoded as precise temporal patterns of spiking across a population of cells (e.g, Abeles, 1991).
Representation by Neuronal Populations • How is information encoded in populations of neurons? • Quantities are encoded as rate codes in ensembles of 50-100 neurons (eg, Shadlen and Newsome, 1998). • Quantities are encoded as precise temporal patterns of spiking across a population of cells (e.g, Abeles, 1991). • Quantities might be encoded as the variance of responses across ensembles of neurons (Shamir & Sompolinsky, 2001; Abbott & Dayan, 1999)
Coding by Mean and Covariance Responses of two neurons to the repeated presentation of two stimuli: Mean only B Neuron #2 A Neuron #1 Averbeck et al, Nat Rev Neurosci, 2006
Coding by Mean and Covariance Responses of two neurons to the repeated presentation of two stimuli: Mean only Covariance only B B Neuron #2 A A Neuron #1 Neuron #1 Averbeck et al, Nat Rev Neurosci, 2006
Coding by Mean and Covariance Responses of two neurons to the repeated presentation of two stimuli: Mean only Covariance only Both A B B B Neuron #2 A A Neuron #1 Neuron #1 Neuron #1 Averbeck et al, Nat Rev Neurosci, 2006
Orientation Tuning Receptive field
Primary Visual Cortex V1 surface and vasculature under green illumination 4mm
Orientation Columns and Array Recordings Optical imaging of intrinsic signals under 700nm light 1mm
Alignment of Orientation Map and Array 0.4 0.0 Find the optimal translation and rotation of the array on the cortex that maximizes the agreement between the electrical and optical measurements of preferred orientation. (3 parameters and 96 data points!) Error surfaces:
Array Insertion Sequence 1 2 3 4
Basic Experiment Input Output We record single unit activity (12-50 cells), multi-unit activity (50-80 sites) and local field potentials (96 sites). What can we say about:
Dynamics of Mean Responses Multidimensional scaling to d=3 (for visualization only)
Dynamics of Mean Responses Multidimensional scaling to d=3 (for visualization only)
Covariance matrices are low-dimensional Average spectrum for co-variance matrices in two experiments
Covariance matrices are low-dimensional (!) Two Examples
Bhattacharyya Distance and Error Bounds Bhattacharyya distance: Differences in mean Differences in co-variance
Bayes’ Decision Boundaries – N-category classification Hyperquadratic decision surfaces Where:
Stimulus-Triggered Responses n=41 channels ordered according their preferred orientation 2.0 Channel # (orientation) 0.0 150ms
Stimulus-Triggered Responses n=32 channels ordered according their preferred orientation 2.0 Channel # (orientation) 0.0 150ms
Estimates of Mean and Variance in Single Trials Population of independent Poisson spiking cells:
Estimating Mean and Variances Trial-to-Trial Noise correlation = 0.0 mean variance
Estimating Mean and Variances Trial-to-Trial Noise correlation = 0.1 variance mean
Estimating Mean and Variances Trial-to-Trial Noise correlation = 0.2 variance mean
Tiling the Stimulus Space and Response Heterogeneity Dimension #2 Dimension #1 Orientation
Tiling the Stimulus Space and Response Heterogeneity Population response to the same stimulus Dimension #2 Dimension #1 Orientation
Tiling the Stimulus Space and Response Heterogeneity Population response to the same stimulus Dimension #2 Dimension #1 Orientation
Tiling the Stimulus Space and Response Heterogeneity Population response from independentsingle cell measurements Dimension #2 Dimension #1 Orientation
Tiling the Stimulus Space and Response Heterogeneity Population response from independentsingle cell measurements Dimension #2 Dimension #1 Orientation
Can single cells respond to input variance? Silberberg et al, J Neurophysiol., 2004