Impact of Correlated inputs on Spiking Neural Models

1. Impact of Correlated inputs on Spiking Neural Models Baktash Babadi School of Cognitive Sciences PM, Tehran, Iran

2. 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.

3. 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?

4. In The Single Cell Level • Is a single neuron and integrator (rate coder)? • Or a coincidence detector (temporal coding)? • (Sofkey & Koch 1993, Abeles 1988,…)

5. 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

6. Population Level (2) • Stable synchronous spike patterns in cortical models (Synfire Chaines) (Abeles 1991, Diesman et al 1999,…) • Loss of temporal information in long feed-forward networks (Litvak et al 2002)

7. 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

8. Neural Models • Rate coder neural models (Somplinsky, Poggio, Treves,…) • Spiking neural models (Koch, Segev, Gerstner,…)

9. However, it is generally accepted that about 90% of information is carried by firing rates (Rieke et al 1997)

10. The temporal structure in the nervous system • Two kinds of temporal structures are ubiquitous in nervous system: • Oscillations • Synchrony (correlation)

11. Neural Oscillations • Engel et al (1991). • Singer et al (1991-2003).

12. Correlations

13. Temporal Correlations in the Visual System (1) • Usrey & Reid (1999)

14. Temporal Correlations in the Visual System (2) • Sources of synchrony in Visual system (Usrey & Reid 1999) • Due to anatomical divergence/convergence (shared input) • Stimulus locked synchrony • Emergent synchrony (and oscillation)

15. The Role of temporal structures • Given that the temporal structures are evident in nervous system, what role do they play in information processing?

16. Oscillations • The phase locked oscillations in different areas of the nervous system are capable of solving the binding problem (Gray & Singer 1996…) • Highly controversial!

17. 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!

18. 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

19. 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*αand correlation coefficient c.

20. 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.

21. 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(

22. The effect of correlations on the firing rate ?

23. 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!

24. The Model without Background Noise ?

25. The Model without Balance Inhibition ?

26. 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!

27. The Current-Based Integrate-and-Fire neuron • The synaptic gating mechanism is replaced by a simple current injection upon receipt of every spike.

28. The Current-Based Integrate-and-Fire neuron ?

29. The Non-leaky Integrate-and-fire Neuron • No membrane leakage • Simple summation of synaptic currents • Threshold crossing • The simplest possible spiking neural model

30. The Non-leaky Integrate-and-fire Neuron ?

31. 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!

32. Analytical Results • For the non-leaky Integrate-and-Fire neuron: • Where: • r = Input firing rate • c = Correlation coefficient • Th = Threshold Capable of producing multiple peaks

33. 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.

34. 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