The Neural Code

1
The Neural Code

• Baktash Babadi
• baktash_at_ipm.ir
• SCS, IPM
• Fall 2004

2
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)

3
Which feature conveys information?
4
Posing the Problem

• Which feature of neural spike train contains
  information?
• Rate?
• Or single spikes?

5
Rate Coding/ Temporal Coding Debate

• Temporal Coding
• 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)

• 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 1012 neurons!
• But the physiologic data shows that information
  is carried by firing rates only.

6
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.

7
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.

8
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.

9
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.

10
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

12
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.

13
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.

14
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
15
An example of correlated spikes Precise Firing
Patterns

• Prut et al, 1998

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Synfire Chains

• The reproducibility of PFSs implies that there
  are synchronous pools of neurons in the cortex
  (Abeles 1991).

17
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
101 states, Hlog2(N1)3.46 bits
Binary code
210 states, Hlog2(2N)10 bits
Latency code
1010 states, HN.log2(t)33 bits
Rank order code
N! states, Hlog2(N!)20 bits
18
Question

• Synchrony Code
• How much is the amount of information in this
  case?

19
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
20
An example of correlated neurons Oscillations in
Cats Visual Cortex

• Engel, Gray Singer 1989-2004

Is synchronous oscillation a Solution for
binding problem?
21
Correlations in Visual Stream

• Usrey and Ried 2000

22
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

23
The effect of correlations on firing rate (2)

• Without uncorrelated background
• Without inhibitory balance

24
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

25
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

26
An example of a temporal Code?

• Phase precession in the hippocampal place cells
  (Harris et al 2002, OKeefe Reece 1993).

27
Neural Decoding in single neuron level (1)

• What does a single neuron do?
• Integration?
• Or coincidence detection?

28
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.