Transcript Babadi08 - School of Cognitive Sciences

Impact of Correlated inputs
on Spiking Neural Models
Baktash Babadi
School of Cognitive Sciences
PM, Tehran, Iran
Background
The neuroscientists are mostly concerned
with how the world is represented in the
nervous system.
But equally important is how the neurons
communicate with each other.
Rate Coding vs. Temporal Coding
Given that the neurons transmit spike
trains between each other,
Is there the rate of the spike train that
matters,
Or the timing between the individual
spikes carries the information?
In The Single Cell Level
Is a single neuron and integrator (rate
coder)?
Or a coincidence detector (temporal
coding)?

(Sofkey & Koch 1993, Abeles 1988,…)
Population Level(1)
Balanced excitation/inhibition in cortical
network is inconsistent with temporal
coding (Shadlen, Newsome 1998)
In vivo irregular ISI in cortical neurons
cannot be due to integration of input spike
trains  Rate coding
Population Level (2)
Stable synchronous spike patterns in
cortical models (Synfire Chaines) (Abeles
1991, Diesman et al 1999,…)
Loss of temporal information in long feedforward networks (Litvak et al 2002)
System Level
Visual system: Object detection by rank
order coding in ventral visual pathway
(Van Rullen, Thorpe 1998-2201)
Motor System: Precise Firing Sequences
in the motor cortex (Prut et al 1998,
Vaadia et al 1997)
Auditory System: Stimulus locked neural
activity in auditory cortex
Invertebrates: Desynchronization of bee’s
chemical sensitive neurons
Neural Models
Rate coder neural models (Somplinsky,
Poggio, Treves,…)
Spiking neural models (Koch, Segev,
Gerstner,…)
However, it is generally
accepted that about 90% of
information is carried by firing
rates (Rieke et al 1997)
The temporal structure in the
nervous system
Two kinds of temporal structures are
ubiquitous in nervous system:

Oscillations

Synchrony (correlation)
Neural Oscillations
Engel et al (1991).
Singer et al (1991-2003).
Correlations
Temporal Correlations in the Visual
System (1)
Usrey & Reid (1999)
Temporal Correlations in the Visual
System (2)
Sources of synchrony in Visual system
(Usrey & Reid 1999)

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
Due to anatomical divergence/convergence
(shared input)
Stimulus locked synchrony
Emergent synchrony (and oscillation)
The Role of temporal structures
Given that the temporal structures are
evident in nervous system, what role do
they play in information processing?
Oscillations
The phase locked oscillations in different
areas of the nervous system are capable
of solving the binding problem (Gray &
Singer 1996…)
Highly controversial!
Correlations
Sejnowsky, Salinas (2001):


Although the firing rates carry the information
content of the neural signals, the correlations
modulate the flow of information.
A modest position in the controversy!
The effect of correlations on firing
rate of a single neuron
Given that the firing rate is the carrier of
the information of the neural activity, how
does the temporal correlation modulate
the firing rate?
Salinas & sejnowski 2000,
Feng 2002
Kuhn et al 2002,2003
How to Generate Correlated Spike
Trains?
Mother spike train:

Poissonian, rate=α
Daughter spike trains:


Copies of mother train
Trimmed with the
probability of (1-c)
Every two daughter spike trains are pair wise
correlated with rate r=c*α and correlation
coefficient c.
The Neuron Model
Conductance-based Integrate-and-fire
model:


The input spikes cause the synaptic channels
to open which intern initiate the synaptic
current
The synaptic current will be integrated and
when the membrane potential reaches a
threshold, the neuron fires.
What does the neuron receive?
The correlated spike
trains (100-200)
Balance inhibitory spike
trains (similar to
correlated but without
correlation)
Balanced non-specific
uncorrelated spike
trains (typical of cortical
neurons)
?
The effect of correlations on the
firing rate
?
What causes the non monotonous
dependence of firing rate to the
correlations?
The correlated spike train +






The background non-specific inputs
The balanced condition
The synaptic gating mechanism
The membrane leakage
The threshold crossing mechanism
Nothing more!
The Model without Background
Noise
?
The Model without Balance
Inhibition
?
What causes the non monotonous
dependence of firing rate to the
correlations?
The correlated spike train +






The background non-specific inputs
The balanced condition
The synaptic gating mechanism
The membrane leakage
The threshold crossing mechanism
Nothing more!
The Current-Based Integrate-and-Fire
neuron
The synaptic gating mechanism is
replaced by a simple current injection
upon receipt of every spike.
The Current-Based Integrate-andFire neuron
?
The Non-leaky Integrate-and-fire
Neuron
No membrane leakage
Simple summation of synaptic currents
Threshold crossing
The simplest possible spiking neural
model
The Non-leaky Integrate-and-fire
Neuron
?
What causes the non monotonous
dependence of firing rate to the
correlations?
The correlated spike train +




The synaptic gating mechanism
The membrane leakage
The threshold crossing mechanism
Nothing more!
Analytical Results
For the non-leaky
Integrate-and-Fire
neuron:
Th  j.N .c
f (c)  r [c  c Erf (
)]1
2. j.N .c.(1  c)
j 0

Where:



r = Input firing rate
c = Correlation coefficient
Th = Threshold
Capable of producing multiple peaks
Why non-monotonicity?
In the moderate correlation
regime, many moderately
synchronous spike volleys
are present, so the firing rate
is higher.
In the high correlation regime,
strong synchronous spike
volleys are present, but their
incidence is low, and many
spikes will be wasted.
Conclusions
The pair wise correlation in the spike trains
has a fundamental effect on the firing rate
of the recipient neuron
The effect is qualitatively independent of
the neural model
The neurons have specific preferences to
certain levels of correlations in input trains
The temporal correlation can dramatically
modulate the neural responsiveness