Cracking the Population Code

1
Cracking the Population Code
Dario Ringach University of California, Los
Angeles
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The Questions
Two basic questions in cortical computation
How is information represented? How is
information processed?
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Representation by Neuronal Populations
How is information encoded in populations of
neurons?
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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).

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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).

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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)

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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
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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
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Macaque Primary Visual Cortex
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Orientation Tuning
Receptive field
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Orientation Columns
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Primary Visual Cortex
V1 surface and vasculature under green
illumination
4mm
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Orientation Columns and Array Recordings
Optical imaging of intrinsic signals under 700nm
light
1mm
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Alignment of Orientation Map and Array
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
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Micro-machined Electrode Arrays
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Array Insertion Sequence
1
2
3
4
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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
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Dynamics of Mean States
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Dynamics of Mean Responses
Multidimensional scaling to d3 (for
visualization only)
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Dynamics of Mean Responses
Multidimensional scaling to d3 (for
visualization only)
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Stimulus Triggered Covariance
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Covariance matrices are low-dimensional
Average spectrum for co-variance matrices in two
experiments
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Covariance matrices are low-dimensional (!)
Two Examples
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Bhattacharyya Distance and Error Bounds
Bhattacharyya distance
Differences in mean
Differences in co-variance
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Information in Covariance Information
in Mean
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Bayes Decision Boundaries N-category
classification
Hyperquadratic decision surfaces
Where
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Confusion Matrix and Probability of
Classification
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Confusion Matrix and Probability of
Classification
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Stimulus-Triggered Responses
n41 channels ordered according their preferred
orientation
2.0
Channel (orientation)
0.0
150ms
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Stimulus-Triggered Responses
n32 channels ordered according their preferred
orientation
2.0
Channel (orientation)
0.0
150ms
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Mean Population Responses
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Mean Population Responses
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Population Mean and Variance Tuning
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Population Mean and Variance Tuning
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Population Mean and Variance Tuning
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Population Mean and Variance Tuning
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Population Mean and Variance Tuning
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Population Mean and Variance Tuning
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Bandwidth of Mean and Variance Signals
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Estimates of Mean and Variance in Single Trials
Population of independent Poisson spiking cells
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Estimating Mean and Variances Trial-to-Trial
Noise correlation 0.0
mean
variance
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Estimating Mean and Variances Trial-to-Trial
Noise correlation 0.1
variance
mean
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Estimating Mean and Variances Trial-to-Trial
Noise correlation 0.2
variance
mean
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Tiling the Stimulus Space and Response
Heterogeneity
Dimension 2
Dimension 1
Orientation
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Tiling the Stimulus Space and Response
Heterogeneity
Population response to the same stimulus
Dimension 2
Dimension 1
Orientation
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Tiling the Stimulus Space and Response
Heterogeneity
Population response to the same stimulus
Dimension 2
Dimension 1
Orientation
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Tiling the Stimulus Space and Response
Heterogeneity
Population response from independentsingle cell
measurements
Dimension 2
Dimension 1
Orientation
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Tiling the Stimulus Space and Response
Heterogeneity
Population response from independentsingle cell
measurements
Dimension 2
Dimension 1
Orientation
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Can single cells respond to input variance?
Silberberg et al, J Neurophysiol., 2004
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Can single cells respond to input variance?
Silberberg et al, J Neurophysiol., 2004
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Summary

• Heterogeneity leads to population variance as a
  natural coding signal in the cortex.
• Response variance has as smaller bandwidth than
  the mean response.
• For small values of noise correlation variance
  is already a more reliable signal than the mean.

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Summary

• In a two-category classification problem the
  variance signal carries about 95 of the total
  information (carried by mean and variance
  together.)
• The covariance of the class-conditional
  population responses is low dimensional, with the
  first eigenvector most likely indicating
  fluctuations in cortical excitability (or gain).
• Cells may be perfectly capable of decoding the
  variance across their inputs (Silberberg et al,
  2004)
• In prostheses, the use of linear decoding based
  on population rates may be sub-optimal.
  Quadratic models may work better.

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Acknowledgements
V1 imaging/electrophysiology (NIH/NEI) Brian
Malone Andy Henrie Ian Nauhaus Topological Data
Analysis (DARPA) Gunnar Carlsson
(Stanford) Guillermo Sapiro (UMN) Tigran Ishakov
(Stanford) Facundo Memoli (Stanford) Bayesian
Analysis of Motion in MT (NSF/ONR) Alan Yuille
(UCLA) HongJing Lu (Hong Kong)
Neovision phase 2 (DARPA) Frank Werblin
(Berkeley) Volkan Ozguz (Irvine Sensors) Suresh
Subramanian (Irvine Sensors) James DiCarlo
(MIT) Bob Desimone (MIT) Tommy Poggio (MIT) Dean
Scribner (Naval Research Labs)