Download Tsodyks-Banbury-2006

Information encoding and
processing via spatio-temporal
spike patterns in cortical
networks
Misha Tsodyks,
Dept of Neurobiology, Weizmann Institute, Rehovot, Israel
Thanks to:
Alex Loebel, Omri Barak, Asher Uziel,
Henry Markram
Rate coding (V1)
Y. Prut, …, M. Abeles 1998
W. Bair & C. Koch 1996
DeWeese, …, Zador 2003
Open questions:
How do precise spike patterns emerge in the cortex?
How can they be robust in the presence of random
firing of surrounding neurons?
What is the relation between the spike patterns and the
stimuli that they are coding for?
How can the information carried by spike patterns be
processed?
Open questions:
How do precise spike patterns emerge in the cortex?
How can they be robust in the presence of random
firing of surrounding neurons?
(Synfire chains? – I don’t like it!)
What is the relation between the spike patterns and the
stimuli that they are coding for?
How can the information carried by spike patterns be
processed?
Recurrent networks with dynamic synapses
(unstructured)
Tsodyks et al 2000
Wang Yun et al 1998
Modeling Time-Dependent Release
4 Synaptic Parameters
Absolute strength
Probability of release
Depression time constant
Facilitation time constant
R




1 R
 UR (t  t sp )
tr
En1 
En (1  U ) exp(t / tr )  E1 (1  exp(t / tr ))
EPSP  A *U * Rn
Population spikes
Population spikes
Origin of Population Bursts
Temporal Correlations
Network response to stimulation
Simplified model (no inhibition, uniform
connections, rate equations)
e1
eN
i
J
J
The rate equations
Two sets of equations representing the
excitatory units firing rate, E, and their
depression factor, R :

N
dEi
J

  Ei  [  E j R j  ei ]
dt
N j 1
dRi
1  Ri

 UEi Ri
dt
tr
Loebel & Tsodyks 2002
Population spikes in the simplified
model
Adiabatic approximation
tr

 Ri  Ri*
(except during the population spike)
Adiabatic approximation
tr

 Ri  Ri*
Population spike:
(except during the population spike)
J

iactive
R*i (t )  1
Adiabatic approximation
tr

Population spike:
J

R*i (t )  1
iactive
Higher spontaneous activity – lower propensity for population spikes.
Response to excitatory pulses
Inputs:
Ei  Ei  Ei
Response:
1
H   Ei
T 
*
1  UtrEi
i
T 
Population spike
No population spike
E
Inputs:
Ei  Ei  Ei
Ji
E  sign ( eiJi  T )
i
ei
Response:
1
H   Ei
T 
*
1  UtrEi
i
T 
Population spike
No population spike
E
Inputs:
Ei  Ei  Ei
Ji
E  sign ( eiJi  T )
i
ei
Response:
1
H   Ei
T 
*
1  UtrEi
i
T 
Population spike
No population spike
Response to tonic stimuli
The tonic stimuli is
represented by a
constant shift of the
{e}’s, that, when large
enough, causes the
network to burst and
reach a new steady
state
Interaction between stimuli
Open questions:
How do precise spike patterns emerge in the cortex?
(Synfire chains?)
How can they be robust in the presence of random
spontaneous and evoked firing of surrounding neurons?
What is the relation between the spike patterns and the
stimuli that they are coding for?
How can the information carried by spike patterns be
processed?
Extended model
Loebel & Tsodyks 2006
The model response to a ‘pure tone’
Constraining the propagation of the PS along the map
Forward suppression
Rotman et al, 2001
Network response to complex stimuli
Network response to complex stimuli
Open questions:
How do precise spike patterns emerge in the cortex?
(Synfire chains?)
How can they be robust in the presence of random
spontaneous and evoked firing of surrounding neurons?
What is the relation between the spike patterns and the
stimuli that they are coding for?
How can the information carried by spike patterns be
processed?
Processing spike patterns: Tempotron (Guetig and
Sompolinsky, 2006)
N
I  (t )   Wi I i  (t )
i 1
ni 
 I i(t )   I i  (t )    (t  ti ,k  )
k 1
Learned patterns   1: P
vs background patterns
Barak & Tsodyks, 2006
Variance-based learning

I 

N
Wn

T
i 1



i i
n
T
N
W
i 1
i

Var ( I )  W C W
T
where

Cij 

2T
n
e
ki , k j

|t  i ,ki t  j ,k j |

 n 
 
T 
2
Cost function for learning
P
E  Var ( I )  W CW
 1
P
C  C
 1
N
2
W
 i 1
i 1

T
Learning rules for spatio-temporal
patterns
Gradient descent:

N
Correlation-based:

W   (t )  I  (t ) I i  (t )  Wi (t ) I  (t ) 
Wi  k  Cij
j 1
Convergence of learning
Performance of the tempotron
Measuring the tempotron performance
Robustness to time warps
Conclusions
1. Networks with synaptic depression
can
encode spatio-temporal inputs by precise
spike patterns.
2. Random spontaneous activity could play a
crucial role in setting the sensitivity of the
network to sensory inputs (top-down
control, attention, expectations, …?)
3. Coding by spike patterns is highly nonlinear.
4. Effective learning rules for recognition of
spike patterns in tempotron-like networks
can be derived.