UA Dr. Robert Legenstein, WiMAus Prashant Joshi, M.S.
Institute for Theoretical Computer Science
Technische Universität Graz
A-8010 Graz, Austria
In this exercise you are going to simulate the output of a sigmoidal neuron using a feedforward circuit of intergrate-and-fire neurons. You are going to use the CSIM simulator for the purpose of this simulation.
Figure 1 shows a neuron that receives R inputs. The individual inputs are each weighted by corresponding elements of the weight matrix W.
The neuron has a bias , which is summed with the weighted inputs to form the net input :
This expression can be written in matrix form:
Now the output of this neuron can be written as
For this exercise, let: , , and the transfer function of the neurons be the hyperbolic tangent sigmoid function that is defined as 2:
which is called in MATLAB as the function.
In this problem, you have to simulate the output of the sigmoidal neuron with above mentioned properties using a feed-forward citcuit of integrate-and-fire neurons. An integrate-and-fire neuron is one of the simplest mathematical model of a spiking neuron whose membrane potential is given by:
where is the membrane time constant, is the membrane resistance, is the current supplied by the synapses, is a non-specific background current and is a Gaussian random variable with a zero mean and a given variance noise.
At time is set to . If exceeds the threshold voltage it is reset to and held there for the length , which is the absolute refractory period of this neuron.
In principle, you can simulate the output of a sigmoidal neuron using a feedforward circuit of integrate-and-fire neurons. In this exercise we are going to test this. The setup that acheives this is shown in figure 2. For this, each of the integrate-and-fire neurons of the feedforward circuit receive the input , and the output of this circuit at any time point is defined as:
For this you will have to simulate the circuit once per input pattern followed by a reset.
NOTE: You are also required to submit the source code that you used to do this exercise.
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