Integrate-and-Fire Neurons

Investigation into the computational properties of spiking neurons: e.g. summation, multiplication, motion detection. Conditions under which irregular firing occurs



Participants:
Guido Bugmann
Chris Christodoulou, John G. Taylor (King's College London).

Background:
We are interested in replicating high-level functions of the brain in intelligent machines. It is therefore tempting to analyse and copy the computational principles of the brain. However, while the architecture of the brain reflects the computational principles used, it reflects also the constraints of having to compute with biological neurons. In order to disentangle these two effects, we need to understand the computational capabilities and limitations of biological neurons.


Results:
1. Using a simple Leaky Integrate-and-Fire neuron (LIF) we have defined theoretically the parameter ranges in which the neuron can operate as a multiplier or adder of n inputs frequencies (Bugmann, 1991).

2. A problem with multiplication mode is the poor operation with irregular input spike trains, due to the uncontrolled background potential due to past input spikes. A solution to that problem has been found in form of time-dependent synaptic weights, where the weight drops to zero after each input spike, and recovers with a time constant equal to the soma RC constant (Bugmann, 1992).

3. Another problem with multiplication is the small output firing frequency, compared to the input firing rates. One solution to that is to provide the neuron with external feedback, for instance by embedding it in a self-excitatory cluster of neurons. This solution underlies a number of investigations described on the page on "Networks of Spiking Neurons".

4. Another solution to the problem of low frequency is to provide the neuron with an internal feedback. This can be produced by using partial reset of the somatic potential after each output spike. Partial reset increases the gain of the neuron by reducing temporarily the actual firing threshold (Bugmann and Taylor, 1997).

5. An old problem with LIF neurons was the impossibility to reproduce the highly irregular firing of biological neurons. We have found that partial reset allows to produce such an irregular firing (Bugmann, 1995). Partial reset results in a time dependent actual firing threshold with increases at a rate similar to the somatic potential due to the integration of synaptic input currents. This allows current fluctuations to cause firing at any time, resulting in irregular, Poisson-type firing (Bugmann, Christodoulou and Taylor, 1996).

6. By providing the LIF neurons with a more detailed model of the effects of the dendritic propagation, namely the widening of the synaptic current pulse, motion detection can be performed (Christodoulou et al, 1992, Bugmann 1996).

7. By providing the LIF neuron with probabilistic synapses, decaying memory effects can be generated in recurrent clusters of neurons (see page Networks of Spiking Neurons).

8. Probabilistic synapses also enable to design recurrent networks with pattern recognition capabilities ("The transfer function of a Hopfield Network") (see page Networks of Spiking Neurons).


Open questions:
1. Learning algorithm to determine the dendritic delays for motion detection.

Reference:

"Summation and multiplication: two distinct operation domains of leaky integrate- and-fire neurons"
Bugmann, G. (1991),
Network, 2, 489-509.

"Multiplying with neurons: Compensation for irregular input spike trains by using time dependent synaptic efficiencies"
Bugmann, G. (1992)
Biological Cybernetics, 68, 87-92.

"An extension to the temporal noisy-leaky integrator neuron and its potential applications"
Christodoulou, C., Bugmann, G., Taylor, J.G. and Clarkson, T. (1992)
Proc. IJCNN'92 (Beijing), Vol III, 165-170.

"Control of the irregularity of spike trains"
Bugmann G. (1995)
Research Report NRG-95-04, School of Computing, University of Plymouth, Plymouth PL4 8AA, UK.
nrg9504.zip (ps file)(114995)

"A stochastic short-term memory using a pRAM neuron and its potential applications"
Bugmann, G. and Taylor J.G. (1997)
in Beale R. and Plumbley M.D. (eds) "Recent advances in neural networks", to be published by Prentice Hall.
stm1_ps.zip (126089)

 "Role of Temporal Integration and Fluctuation Detection in the highly irregular firing of a Leaky Integrator Neuron Model with Partial Reset" (PDF 193K).
Bugmann G., Christodoulou C. and Taylor J.G. (1997)
Neural Computation, 9, pp. 985-1000. (see also paper #57 above). 

 "Biologically Plausible Neural Computation" (PDF 150K)
Bugmann G. (1997)
Biosystems, 40, pp. 11-19.

 "Is Working Memory Stochastic ?" (PDF Abstract,   PDF Poster)
Bugmann G.
Abstract book of FENS'2000, Brighton, UK, European J of Neuroscience 12, Suppl. S,  p. 168..

 Analysis of Fluctuation-Induced Firing in the Presence of Inhibition (PDF 237.775)
Chris Christodoulou, Trevor G Clarkson , Guido Bugmann and John G Taylor
Proc. of the Int Joint Conf on Neural Networks 2000 (IJCNN'2000), Como, Italy,
IEEE Computer Society Press, Vol. III, pp. 115-120. (ISBN 0-7695-0619-4)

Near-Poisson firing induced by concurrent excitation and inhibition
Chris Christodoulou, Guido Bugmann (2000)
Biosystems, 58, pp. 41-48.(ISSN 0303-2647)

Coefficient of Variation (CV) vs Mean Interspike Interval (ISI) curves: what do they tell us about the brain?
Chris Christodoulou, Guido Bugmann (2001).
Neurocomputing,  Vol 38-40, pp 1141-1149 (ISSN: 0925-2312)

"A Spiking Neuron Model: Applications and Learning" (PDF 396K)
Chris Christodoulou , Guido Bugmann and Trevor G. Clarkson (2002)
Neural Networks, 15, 891-908 (ISSN 0893-6080)

 "Synaptic depression increases the selectivity of a neuron to its preferred pattern and binarizes the neural code" (PDF 172K)
Bugmann G. (2002)
Biosystems: Special Issue on Neural Coding, 67, 17-26.

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