cracking the population code dario ringach university of california, los angeles
Post on 22-Dec-2015
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Two basic questions in cortical computation:
The Questions
How is information represented?
How is information processed?
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:
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
( ) 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
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
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:
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 +
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
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
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
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)