Cracking the Population Code Dario Ringach University of California, Los Angeles.

Cracking the Population Code

Dario Ringach

University of California, Los Angeles

Two basic questions in cortical computation:

The Questions

How is information represented?

How is information processed?

How is information encoded in populations of neurons?

Representation by Neuronal Populations

How is information encoded in populations of neurons?

1. Quantities are encoded as rate codes in ensembles of 50-100 neurons (eg, Shadlen and Newsome, 1998).

Representation by Neuronal Populations

How is information encoded in populations of neurons?

1. Quantities are encoded as rate codes in ensembles of 50-100 neurons (eg, Shadlen and Newsome, 1998).

2. Quantities are encoded as precise temporal patterns of spiking across a population of cells (e.g, Abeles, 1991).

Representation by Neuronal Populations

How is information encoded in populations of neurons?

1. Quantities are encoded as rate codes in ensembles of 50-100 neurons (eg, Shadlen and Newsome, 1998).

2. Quantities are encoded as precise temporal patterns of spiking across a population of cells (e.g, Abeles, 1991).

3. Quantities might be encoded as the variance of responses across ensembles of neurons (Shamir & Sompolinsky, 2001; Abbott & Dayan, 1999)

Representation by Neuronal Populations

Coding by Mean and Covariance

Neuron #1

Neuro

n #

2

Averbeck et al, Nat Rev Neurosci, 2006

Mean only

B

A

Responses of two neurons to the repeated presentation of two stimuli:

Coding by Mean and Covariance

Neuron #1

Neuro

n #

2

Averbeck et al, Nat Rev Neurosci, 2006

Neuron #1

Mean only Covariance only

B

A A

B

Responses of two neurons to the repeated presentation of two stimuli:

Coding by Mean and Covariance

Neuron #1

Neuro

n #

2

Averbeck et al, Nat Rev Neurosci, 2006

Neuron #1

Mean only Covariance only

Neuron #1

Both

B

A A

B BA

Responses of two neurons to the repeated presentation of two stimuli:

Macaque Primary Visual Cortex

Orientation Tuning

Receptive field

Orientation Columns

Primary Visual Cortex

4mm

V1 surface and vasculature under green illumination

Orientation Columns and Array Recordings

1mm

Optical imaging of intrinsic signals under 700nm light

Alignment of Orientation Map and Array

0.0

0.4

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:

xt xt

yt ytf

f

opticalq

elecq

Micro-machined Electrode Arrays

Array Insertion Sequence

1 2

3 4

( ) dt Rt+ Îr

Input

Output

Basic Experiment

( ) 1t Sq Î

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:

/

0, , 1k k N

k N

q p=

= -L

( ) ( )( )|P t tr t q+

Dynamics of Mean States

( ) ( ) ( ){ }| 1i iE t trm t t q= + =

18m

1m

( )( )1

0i

i

if tt

otherwise

q qq

ì =ïïº íïïî

2m

3m

Dynamics of Mean Responses

Multidimensional scaling to d=3 (for visualization only)

Dynamics of Mean Responses

Multidimensional scaling to d=3 (for visualization only)

Stimulus Triggered Covariance

( ) ( ) ( ) ( ){ }| 1Ti iE t t tr rt t t qS = D + D + =

18m

1m

2m

3m

2S

3S

Covariance matrices are low-dimensional

il

Average spectrum for co-variance matrices in two experiments

Covariance matrices are low-dimensional (!)

Two Examples

18m

1m

im

jm

iS

jS

Bhattacharyya Distance and Error Bounds

( ) ( )| ,i i iP Nr :q m S

( ) 1 1 21 2

1 2

1 1log

4 2 2

TBD m m- S +S

= D S +S D +S S

Differences in mean Differences in co-variance

( ) ( )exp / 2P error BD< -

Bhattacharyya distance:

Information in Covariance Information in Mean?

Bayes’ Decision Boundaries – N-category classification

( ) ( )| ,i i iP Nr :q m S iS

jmjS

imHyperquadratic decision surfaces

( ) 0t t

i i i ig x xW x w x w= + +

Where:

11

2i iW -=- S

1i i iw m-=S

( )1 10

1 1log log

2 2i

ti i i i iw Pm m q- -=- S - S +

Confusion Matrix and Probability of Classification

Confusion Matrix and Probability of Classification

Stimulus-Triggered Responses

150ms

n=41 channels ordered according their preferred orientationC

hannel #

(ori

enta

tion)

0.0

2.0

/r rD

Stimulus-Triggered Responses

150ms

n=32 channels ordered according their preferred orientationC

hannel #

(ori

enta

tion)

0.0

2.0

/r rD

Mean Population Responses

Mean Population Responses

Population Mean and Variance Tuning

( )2,l s

( )2,l s

Population Mean and Variance Tuning

( )2,l s

Population Mean and Variance Tuning

Population Mean and Variance Tuning

Population Mean and Variance Tuning

Population Mean and Variance Tuning

Bandwidth of Mean and Variance Signals

Estimates of Mean and Variance in Single Trials

1i

inl l= å ( )

22 1i

ins l l l= - +å

Population of independent Poisson spiking cells:

{ }il

Estimating Mean and Variances Trial-to-Trial

mean

variance

Noise correlation = 0.0

Estimating Mean and Variances Trial-to-Trial

mean

variance

Noise correlation = 0.1

Estimating Mean and Variances Trial-to-Trial

mean

variance

Noise correlation = 0.2

Tiling the Stimulus Space and Response Heterogeneity

Dimension #1

Dim

en

sion #

2

Orientation

Tiling the Stimulus Space and Response Heterogeneity

Dimension #1

Dim

en

sion #

2

Orientation

Population response to the same stimulus

Tiling the Stimulus Space and Response Heterogeneity

Dimension #1

Dim

en

sion #

2

Orientation

Population response to the same stimulus

Tiling the Stimulus Space and Response Heterogeneity

Dimension #1

Dim

en

sion #

2

Orientation

Population response from independentsingle cell measurements

Tiling the Stimulus Space and Response Heterogeneity

Dimension #1

Dim

en

sion #

2

Orientation

Population response from independentsingle cell measurements

Silberberg et al, J Neurophysiol., 2004

Can single cells respond to input variance?

Can single cells respond to input variance?

Silberberg et al, J Neurophysiol., 2004

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.

• 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.

Summary

ty x Hx=

Acknowledgements

V1 imaging/electrophysiology (NIH/NEI)

Brian MaloneAndy HenrieIan 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)