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Cracking the Population Code

This research explores how information is represented and processed in populations of neurons. It investigates the encoding of quantities as rate codes, temporal patterns of spiking, and variance of responses across ensembles of neurons. Additionally, it examines the role of mean and covariance responses in information coding and explores the dynamics of mean states and responses. The study also investigates stimulus-triggered responses, population tuning, and response heterogeneity.

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Cracking the Population Code

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  1. Cracking the Population Code Dario Ringach University of California, Los Angeles

  2. The Questions Two basic questions in cortical computation: How is information represented? How is information processed?

  3. Representation by Neuronal Populations How is information encoded in populations of neurons?

  4. 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).

  5. 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).

  6. 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)

  7. 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

  8. 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

  9. 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

  10. Macaque Primary Visual Cortex

  11. Orientation Tuning Receptive field

  12. Orientation Columns

  13. Primary Visual Cortex V1 surface and vasculature under green illumination 4mm

  14. Orientation Columns and Array Recordings Optical imaging of intrinsic signals under 700nm light 1mm

  15. 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:

  16. Micro-machined Electrode Arrays

  17. Array Insertion Sequence 1 2 3 4

  18. 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:

  19. Dynamics of Mean States

  20. Dynamics of Mean Responses Multidimensional scaling to d=3 (for visualization only)

  21. Dynamics of Mean Responses Multidimensional scaling to d=3 (for visualization only)

  22. Stimulus Triggered Covariance

  23. Covariance matrices are low-dimensional Average spectrum for co-variance matrices in two experiments

  24. Covariance matrices are low-dimensional (!) Two Examples

  25. Bhattacharyya Distance and Error Bounds Bhattacharyya distance: Differences in mean Differences in co-variance

  26. Information in Covariance Information in Mean

  27. Bayes’ Decision Boundaries – N-category classification Hyperquadratic decision surfaces Where:

  28. Confusion Matrix and Probability of Classification

  29. Confusion Matrix and Probability of Classification

  30. Stimulus-Triggered Responses n=41 channels ordered according their preferred orientation 2.0 Channel # (orientation) 0.0 150ms

  31. Stimulus-Triggered Responses n=32 channels ordered according their preferred orientation 2.0 Channel # (orientation) 0.0 150ms

  32. Mean Population Responses

  33. Mean Population Responses

  34. Population Mean and Variance Tuning

  35. Population Mean and Variance Tuning

  36. Population Mean and Variance Tuning

  37. Population Mean and Variance Tuning

  38. Population Mean and Variance Tuning

  39. Population Mean and Variance Tuning

  40. Bandwidth of Mean and Variance Signals

  41. Estimates of Mean and Variance in Single Trials Population of independent Poisson spiking cells:

  42. Estimating Mean and Variances Trial-to-Trial Noise correlation = 0.0 mean variance

  43. Estimating Mean and Variances Trial-to-Trial Noise correlation = 0.1 variance mean

  44. Estimating Mean and Variances Trial-to-Trial Noise correlation = 0.2 variance mean

  45. Tiling the Stimulus Space and Response Heterogeneity Dimension #2 Dimension #1 Orientation

  46. Tiling the Stimulus Space and Response Heterogeneity Population response to the same stimulus Dimension #2 Dimension #1 Orientation

  47. Tiling the Stimulus Space and Response Heterogeneity Population response to the same stimulus Dimension #2 Dimension #1 Orientation

  48. Tiling the Stimulus Space and Response Heterogeneity Population response from independentsingle cell measurements Dimension #2 Dimension #1 Orientation

  49. Tiling the Stimulus Space and Response Heterogeneity Population response from independentsingle cell measurements Dimension #2 Dimension #1 Orientation

  50. Can single cells respond to input variance? Silberberg et al, J Neurophysiol., 2004

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