1. Population Codes in the Retina Michael Berry Department of Molecular Biology Princeton University

2. Population Neural Codes Many ganglion cells look at each point in an image Experimental & Conceptual Challenges Key Concepts: Correlation Independence

3. Recording from all of the Ganglion Cells Ganglion cells labeled with rhodamine dextran Segev et al., Nat. Neurosci. 2004

4. Spike Trains from Many Cells Responding to Natural Movie Clips

5. Correlations among Cells

6. Role of Correlations? Discretize spike train:  t = 20 ms; r i = {0,1} Cross-correlation coefficient: 90% of values between [-0.02, 0.1]

7. Correlations are Strong in Larger Populations N=10 cells: Excess synchrony by factor of ~100,000!

8. Combinations of Spiking and Silence Building Binary Spike Words Testing for Independence Errors up to ~1,000,000-fold!

9. Including All Pairwise Correlations Between Cells general form: setting parameters: limits: Maximum entropy formalism: Schneidman et al. Phys. Rev.Lett. 2003

10. Role of Pairwise Correlations P (2) (R) is an excellent approximation! Schneidman et al., Nature 2006

11. Rigorous Test Multi-information: Compare: Groups of N=10 cells

12. Implications for Larger Networks Connection to the Ising model Model of phase transitions At large N, correlations can dominate network states Analog of “freezing”?

13. Extrapolating to Large N Critical population size ~ 200 neurons Redundancy range ~250 µm Correlated patch ~275 neurons

14. Error Correction in Large Networks Information that population conveys about 1 cell

15. CONCLUSIONS Weak pairwise correlations lead to strong network correlations Can describe effect of all pairs on network with the maximum entropy formalism Robust, error-correcting codes

16. Final Thoughts Everyday vision: very low error rates “Seeing is believing” Problems: many cells, many objects, detection can occur anytime, anywhere – assume 1 error / ganglion cell / year – 10 6 ganglion cells => error every 2 seconds! Single neurons: noisy, ambiguous Perception: deterministic, certain Connection to large population, redundancy

17. Including Correlations in Decoder Use maximum entropy formalism: Simple circuit for log-likelihood: Problem: difficult to find {h i, J ij } for large populations

18. Acknowledgments Recording All Cells Natural Movies & Redundancy Ronen Segev Jason Puchalla Pairwise Correlations Population Decoding Elad Schneidman Greg Schwartz Bill Bialek Julien Dubuis Large N Limit Rava da Silveira (ENS) Gasper Tkachik