Cracking the Population Code

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