Population Codes in the Retina

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Population Codes in the Retina

• Michael Berry
• Department of Molecular Biology
• Princeton University

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Population Neural Codes
Many ganglion cells look at each point in an image
Experimental Conceptual Challenges
Key Concepts Correlation
Independence
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Recording from all of the Ganglion Cells
Ganglion cells labeled with rhodamine dextran
Segev et al., Nat. Neurosci. 2004
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Spike Trains from Many CellsResponding to
Natural Movie Clips
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Correlations among Cells
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Role of Correlations?
Discretize spike train ?t 20 ms ri
0,1 Cross-correlation coefficient
90 of values between -0.02 , 0.1
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Correlations are Strong in Larger Populations
N10 cellsExcess synchrony byfactor of
100,000!
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Combinations of Spiking and Silence
Building Binary Spike Words Testing for
Independence
Errors up to 1,000,000-fold!
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Including All Pairwise CorrelationsBetween Cells
Maximum entropy formalism Schneidman et al.
Phys. Rev.Lett. 2003
general form setting parameters
limits
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Role of Pairwise Correlations
Schneidman et al., Nature 2006
P(2)(R) is an excellent approximation!
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Rigorous Test
Multi-information Compare
Groups of N10 cells
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Implications for Larger Networks
Connection to the Ising model
Model of phase transitions At large N,
correlations can dominate network states
Analog of freezing?
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Extrapolating to Large N
Critical population size 200 neurons
Redundancy range 250 µm Correlated patch
275 neurons
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Error Correction in Large Networks
Information that population conveys about 1
cell
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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
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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 106 ganglion cells gt error every 2
seconds! Single neurons noisy, ambiguous
Perception deterministic, certain Connection
to large population, redundancy
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Including Correlations in Decoder

• Use maximum entropy formalism
• Simple circuit for log-likelihood
• Problem difficult to find hi, Jij for large
  populations

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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