Impact of Correlated inputs on Spiking Neural Models Baktash Babadi Baktash Babadi School of Cognitive Sciences PM, Tehran, Iran 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,…) (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 feed- forward networks (Litvak et al 2002)

System Level Visual system: Object detection by rank order coding in ventral visual pathway (Van Rullen, Thorpe ) 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 Oscillations Synchrony (correlation) Synchrony (correlation)

Neural Oscillations Engel et al (1991). Singer et al ( ).

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) Due to anatomical divergence/convergence (shared input) Due to anatomical divergence/convergence (shared input) Stimulus locked synchrony Stimulus locked synchrony Emergent synchrony (and oscillation) 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. 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! 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 Poissonian, rate=α Daughter spike trains: Copies of mother train Copies of mother train Trimmed with the probability of (1-c) Trimmed with the probability of (1-c) Every two daughter spike trains are pair wise α 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 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. 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 ( ) 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 background non-specific inputs The balanced condition The balanced condition The synaptic gating mechanism The synaptic gating mechanism The membrane leakage The membrane leakage The threshold crossing mechanism The threshold crossing mechanism Nothing more! 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 background non-specific inputs The balanced condition The balanced condition The synaptic gating mechanism The synaptic gating mechanism The membrane leakage The membrane leakage The threshold crossing mechanism The threshold crossing mechanism Nothing more! 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-and- Fire 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 synaptic gating mechanism The membrane leakage The membrane leakage The threshold crossing mechanism The threshold crossing mechanism Nothing more! Nothing more!

Analytical Results 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 Capable of producing multiple peaks

Why non-monotonicity? In the high correlation regime, strong synchronous spike volleys are present, but their incidence is low, and many spikes will be wasted. In the moderate correlation regime, many moderately synchronous spike volleys are present, so the firing rate is higher.

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