Redundancy in the Population Code of the Retina

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Redundancy in the Population Code of the Retina

• Puchalla, Schneidman, Harris, and Berry (2005)

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They did simultaneous recordings from salamander
retina using natural video stimuli.
Examples of video frame
Example of simultaneous recordings
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There are strong similarities in some pairs of
responses.
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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 lt 0 synergy
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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.

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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
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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.

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One cell has one hundred of partners that show
significant redundancy.
Fraction of cells showing (Fractional
Redundancy)gt.05

• 40 of nearby cells are significantly redundant.
• The shorter the distance is, the larger the
  fraction is.

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.

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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?

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Over-representation Factor measures how many
times the information conveyed by a single cell
is represented by the other cells.

• white board

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Over-representation Factor 11.01.0
10 times over-representation
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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.
• gt Examine the redundancy for least-redundant
  visual stimuli.
• (their settings so far was totally fine)

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Minimally redundant visual stimuli (checker)

• Random flickering checkerboards
• 55µm checker size (cf. 100µm center size)
• 33ms frame time

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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.
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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?

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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.
• gt Stimulating cells identically by full-field
  flickering stimuli.

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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
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Just a comparison for completion...
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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.

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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.
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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).