1. The Neural Code Baktash Babadi baktash@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? Rate? Or single spikes? Or single spikes?

5. Rate Coding/ Temporal Coding Debate Rate Coding The physiologic data shows that information is carried by firing rates only. 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. Each neuron receives input from thousands of neurons, so a few milliseconds is enough for a reliable population rate estimation. We have already 10 12 neurons! We have already 10 12 neurons! But the physiologic data shows that information is carried by firing rates only. But the physiologic data shows that information is carried by firing rates only. 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)

6. Independent Spikes/ Correlated Spikes (1) Independent Spikes: There is now correlation between the successive spikes of a neuron (Poisson) There is now correlation between the successive spikes of a neuron (Poisson) No meaning-full pattern appears in the spike trains No meaning-full pattern appears in the spike trains Thus only rate matters. 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. 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. The average firing rate of the population conveys the information only.

8. Correlated Spikes: Although the spike trains look random and independent, some temporal structures may be hidden in the spike trains. 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. Thus the spike train contains something more than merely its rate. Independent Spikes/ Correlated Spikes (2)

9. Correlated neurons: Although each individual spike train looks random, correlations are possible between the spike trains of a population. 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. These correlations may have some meaning for the system. Independent Neurons/ Correlated Neurons (2)

10. In defense of Rate Coding (1)! Shadlen & Newsome (1998): Cortical neurons receive roughly equal amount of excitation and inhibition. Cortical neurons receive roughly equal amount of excitation and inhibition. The cortical neurons are in balanced state. The cortical neurons are in balanced state.

11. What causes the neuron to fire is the random fluctuations of the membrane potential The spiking is a random process The spiking is a random process No temporal order is possible between the spikes No temporal order is possible between the spikes In defense of Rate Coding (2)!

12. Correlations are not likely to arise between the neurons in a population The probabilistic nature of spiking and random connectivity restrains correlations 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. If the neurons are correlated the sampling by upstream units will be biased and non reliable. In defense of Rate Coding (4)!

13. Conclusion: The spikes generated by a cortical neuron are independent The spikes generated by a cortical neuron are independent Different neurons spike in an almost independent manner from each other. Different neurons spike in an almost independent manner from each other. The information is carried by the firing rates only. The information is carried by the firing rates only. In defense of Rate Coding (5)!

14. Downstream neurons receive the input from hundred of similar neurons. A very short sampling time is sufficient for a reliable rate estimation A very short sampling time is sufficient for a reliable rate estimation In defense of Rate Coding (3)! X

15. An example of correlated spikes: Precise Firing Patterns Prut et al, 1998: Prut et al, 1998:

16. 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. Spike based strategies for rapid processing. 10 neurons, 10 milliseconds, single or no spike: Count code: Latency code: Rank order code: 10+1 states, H=log 2 (N+1)=3.46 bits Binary code: 2 10 states, H=log 2 (2 N )=10 bits 10 10 states, H=N.log 2 (t)=33 bits N! states, H=log 2 (N!)=20 bits

18. Synchrony Code: How much is the amount of information in this case? How much is the amount of information in this case? Question

19. Rank Order Coding Thorpe et al : Rank Order Coding in the Retina Rank Order Coding in the Retina Image reconstruction as a function of percentage of neurons that fired Sampling the image by different scales of Retinal ganglion cells

20. An example of correlated neurons: Oscillations in Cat’s 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 information is coded by firing rate The flow of information is controlled by temporal correlations 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 r = Input firing rate c = Correlation coefficient c = Correlation coefficient Th = Threshold 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, O’Keefe & Reece 1993).

27. Neural Decoding in single neuron level (1) What does a single neuron do? Integration? Integration? Or coincidence detection? Or coincidence detection?

28. Neural Decoding in single neuron level (2) Rate coding The time constant of cortical neurons are 15-50 msec. The time constant of cortical neurons are 15-50 msec. The temporal orders will be washed out during integration The temporal orders will be washed out during integration Firing rate modfels. Firing rate modfels. Temporal coding The cortical neurons are under bombardment of thousands of other neurons The cortical neurons are under bombardment of thousands of other neurons This causes the membrane to shunt dramatically (g l ) and the time constant will decrease severely. This causes the membrane to shunt dramatically (g l ) and the time constant will decrease severely. Tolerance to noise Tolerance to noise Speed of processing Speed of processing Integrate-and-fire models. Integrate-and-fire models.