The Neural Code
Baktash Babadi
baktash@ipm.ir
SCS, IPM
Fall 2004
References
Rieke et al, Spikes: Exploring the Neural
Code MIT Press(1997)
Koch, Biophysics of computation MIT
Press (1998)
Dayan & Abbott, Theoretical
Neuroscience, Chapters 1-3, MIT Press
(2001)
Which feature conveys
information?
Posing the Problem
Which feature of neural spike train
contains information?

Rate?

Or single spikes?
Rate Coding/ Temporal Coding
Debate
Temporal Coding
Rate Coding


The physiologic data shows
that information is carried
by firing rates only.
Each neuron receives input
from thousands of neurons,
so a few milliseconds is
enough for a reliable
population rate estimation.




We have already
neurons!
1012


But the physiologic data
shows that information is
carried by firing rates only.
Rate coding is impossible,
since each neuron should
wait at least 100 ms for a
estimate of the received
firing rate.
This would cause a waste of
neural resources.
There are effective temporal
coding algorithms.
… (Maybe your physiologic
methods are biased)
Independent Spikes/ Correlated
Spikes (1)
Independent Spikes:



There is now correlation between the
successive spikes of a neuron (Poisson)
No meaning-full pattern appears in the spike
trains
Thus only rate matters.
Independent Neurons/ Correlated
Neurons (1)
Independent neurons:


In a population of neurons which respond to
the same stimulus, the spikes of each neuron
occurs independent of the others.
The average firing rate of the population
conveys the information only.
Independent Spikes/ Correlated
Spikes (2)
Correlated Spikes:


Although the spike trains look random and
independent, some temporal structures may
be hidden in the spike trains.
Thus the spike train contains something more
than merely its rate.
Independent Neurons/
Correlated Neurons (2)
Correlated neurons:


Although each individual spike train looks
random, correlations are possible between
the spike trains of a population.
These correlations may have some meaning
for the system.
In defense of Rate Coding (1)!
Shadlen & Newsome (1998):


Cortical neurons receive roughly equal
amount of excitation and inhibition.
The cortical neurons are in balanced state.
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In defense of Rate Coding (2)!
What causes the neuron to fire is the
random fluctuations of the membrane
potential


The spiking is a random process
No temporal order is possible between the
spikes
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In defense of Rate Coding (4)!
Correlations are not likely to arise between
the neurons in a population


The probabilistic nature of spiking and random
connectivity restrains correlations
If the neurons are correlated the sampling by
upstream units will be biased and non reliable.
In defense of Rate Coding (5)!
Conclusion:



The spikes generated by a cortical neuron are
independent
Different neurons spike in an almost
independent manner from each other.
The information is carried by the firing rates
only.
In defense of Rate Coding (3)!
Downstream neurons receive the input
from hundred of similar neurons.

A very short sampling time is sufficient for a
reliable rate estimation
X
An example of correlated spikes:
Precise Firing Patterns
Prut et al, 1998:
Synfire Chains
The reproducibility of PFSs implies that
there are synchronous pools of neurons in
the cortex (Abeles 1991).
An example of correlated neurons:
Spike Based Strategies in Neural
Coding (1)
Thorpe et al 1995-2004

Spike based strategies for rapid processing.
10 neurons, 10 milliseconds,
single or no spike:
Count code:
10+1 states,
H=log2(N+1)=3.46 bits
Binary code:
210 states,
H=log2(2N)=10 bits
Latency code:
1010 states,
H=N.log2(t)=33 bits
Rank order code: N! states,
H=log2(N!)=20 bits
Question
Synchrony Code:

How much is the amount of information in this
case?
Rank Order Coding
Thorpe et al :

Rank Order Coding in the Retina
Sampling the image by different scales of
Retinal ganglion cells
Image reconstruction as a function
of percentage of neurons that fired
An example of correlated neurons:
Oscillations in Cat’s Visual Cortex
Engel, Gray Singer 1989-2004
Is synchronous oscillation a
Solution for binding problem?
Correlations in Visual Stream
Usrey and Ried 2000
The effect of correlations on firing
rate (1)
Sejnowski & Salinas 2000:


The information is coded by firing rate
The flow of information is controlled by
temporal correlations
The effect of correlations on
firing rate (2)
Without uncorrelated
background
Without inhibitory
balance
The effect of correlations on
firing rate (3)
For the non-leaky
Integrate-and-Fire
neuron:
Where:



r = Input firing rate
c = Correlation coefficient
Th = Threshold
Th  j.N .c
f (c)  r [c  c Erf (
)]1
2. j.N .c.(1  c)
j 0

Another definition for temporal
code?
sd
If spikes are independent:


Rate code: If r(t) changes
slowly
Temporal Code: if r(t)
changes rapidly.
Defining Temporal code:


1) The peaks in r(t) occur in
roughly the same rate as
the single spikes
2) The dominant Fourier
components of r(t) are
higher frequencies than
that of the stimulus
An example of a temporal Code?
Phase precession in the hippocampal
place cells (Harris et al 2002, O’Keefe &
Reece 1993).
Neural Decoding in single neuron
level (1)
What does a single neuron do?


Integration?
Or coincidence detection?
dV
 g l (Vl  V )  I Syn
dt
 C  dV  V  V   I Syn 


 g 
l
g
l  dt
l


C

dV
I

 V  Vl   Syn 
gl 
dt

Neural Decoding in single neuron
level (2)
Rate coding



The time constant of cortical neurons are 15-50 msec.
The temporal orders will be washed out during
integration
Firing rate modfels.
Temporal coding





The cortical neurons are under bombardment of
thousands of other neurons
This causes the membrane to shunt dramatically (gl)
and the time constant will decrease severely.
Tolerance to noise
Speed of processing
Integrate-and-fire models.