Redundancy in the Population Code of the Retina

1. Redundancy in the Population Code of the Retina Puchalla, Schneidman, Harris, and Berry (2005)

2. They did simultaneous recordings from salamander retina using natural video stimuli. Examples of video frame Example of simultaneous recordings

3. There are strong similarities in some pairs of responses.

4. Quantifying the redundancy in the representation between two cells Fractional Redundancy: Numerator: overlapped information in bits (or bits/sec, bits/spike) Normalized by the maximum overlap. \Gamma = 1: maximum overlap \Gamma = 0: no overlap \Gamma < 0: synergy

5. Information is evaluated by spike words, consisting of 2-4 bins of spike count w/ 10ms bin size. • It captures precise spike patterns in time (but limited to 2-4 bins); it is not limited to the co-occurrence of spikes between two neurons.

6. There are pairs of cells showing significant redundancies. Color indicates types of the movie: red: object motion, blue: saccade, green: optic flow , black: smooth pursuit, orange: combination

7. There are pairs of cells showing significant redundancies. • Difference among five categories of movie motion are not clear. • Redundancy can be high if two cells are located close to each other. • But even if two cells are close, redundancy can be low.

8. One cell has one hundred of partners that show significant redundancy. • 40% of nearby cells are significantly redundant. • The shorter the distance is, the larger the fraction is. Fraction of cells showing (Fractional Redundancy)>.05 Average fractional redundancy for the above redundant cells • Redundancy is on average “moderate”. • Again, the shorter the distance is, the larger the average redundancy is.

9. Interim Summary: • A single retinal ganglion cell has about one hundred of cells that share the same sensory information. • The degree of redundancy is “moderate”. Q: As a whole, how many times the information conveyed by a single cell is represented?

10. “Over-representation Factor” measures how many times the information conveyed by a single cell is represented by the other cells. [white board]

11. Over-representation Factor = 11.0±1.0 10 times over-representation

12. Interim Discussion 1 • Tested natural video could not be the kind that Salamander adapted to. • Hard to answer. • They used various kind of natural stimuli. • Wide-field motion could cause overestimate of the redundancy. => Examine the redundancy for least-redundant visual stimuli. (their settings so far was totally fine)

13. Minimally redundant visual stimuli (checker): • Random flickering checkerboards • 55µm checker size (cf. 100µm center size) • 33ms frame time

14. There are significant redundancy even if they used checker stimuli. Color indicates pair types: blue: the same functional type red: different functional type (other than the next) green: ON and OFF pair However, ON and OFF pair does not show redundancy.

15. Redundancy is restricted to close-pairs for checker stimuli, but there is a significant amount of redundancy. • Over-representation factor is roughly the same as that of natural movies. • Number of redundant cells is smaller for checkers. • Implying that average redundancy for close-pairs are higher for checkers (no corresponding data shown as in Fig.2 A and B). • Still stimulus-driven?

16. Interim discussion 2 • Minimally redundant stimuli still yields redundant representation. • Regarding “independent” or less redundant pairs, what is their underlying mechanism? • Spatial-RF-overlap but different temporal characteristics. In general, “functional” diversity could cause such independence. • Alternatively, intrinsic “noise” could. => Stimulating cells identically by full-field flickering stimuli.

17. Functional similarity underlies the redundancy, but it does not yield a perfect redundancy (probably due to intrinsic noise). same functional type different functional type ON and OFF pair

18. Just a comparison for completion...

19. Fractional redundancy is an appropriate measure of over-representation: cf. Receptive field (RF) overlap. • Theoretically, fractional redundancy is the right measure. • RF could be appropriate if Neural transfer function is fully characterized by RF. • In addition, we need to consider the redundancy in the stimulus.

20. RF overlap is not a good predictor of Fractional Redundancy, as expected. Small RF overlap for ON and OFF pairs. The closer the distance is, the larger the overlap can be. same functional type different functional type ON and OFF pair There is a positive trend between overlap and fractional redundancy. However, there are significant variability. e.g., some pairs with zero RF overlap show significant fractional redundancy.

21. Summary • Representation in the RGCs are redundant. • Information conveyed by a single RGC is 10-fold overrepresented in the RGC population. • Assumption of neural coding: • A spike word with length of 2-4, w/ 10ms bin size. • Measure of redundancy: • Fractional redundancy (pair-wise overlap of mutual info normalized s/t the maximum is 1). • Over-representation factor (how many times the information conveyed by a single cell is represented by the others).