Simulation with Concurrent Inputs in a Dynamic Network :: Neuron Model and Network Architectures (Neural Network Toolbox)

Neural Network Toolbox

Simulation with Concurrent Inputs in a Dynamic Network

If we were to apply the same inputs from the previous example as a set of concurrent inputs instead of a sequence of inputs, we would obtain a completely different response. (Although it is not clear why we would want to do this with a dynamic network.) It would be as if each input were applied concurrently to a separate parallel network. For the previous example, if we use a concurrent set of inputs we have

which can be created with the following code:

```
P = [1 2 3 4];
```

When we simulate with concurrent inputs we obtain

A = sim(net,P)
A =
     1     2     3     4

The result is the same as if we had concurrently applied each one of the inputs to a separate network and computed one output. Note that since we did not assign any initial conditions to the network delays, they were assumed to be zero. For this case the output will simply be 1 times the input, since the weight that multiplies the current input is 1.

In certain special cases, we might want to simulate the network response to several different sequences at the same time. In this case, we would want to present the network with a concurrent set of sequences. For example, let's say we wanted to present the following two sequences to the network:

The input P should be a cell array, where each element of the array contains the two elements of the two sequences that occur at the same time:

```
P = {[1 4] [2 3] [3 2] [4 1]};
```

We can now simulate the network:

```
A = sim(net,P);
```

The resulting network output would be

```
A = {[ 1 4] [4 11] [7 8] [10 5]}
```

As you can see, the first column of each matrix makes up the output sequence produced by the first input sequence, which was the one we used in an earlier example. The second column of each matrix makes up the output sequence produced by the second input sequence. There is no interaction between the two concurrent sequences. It is as if they were each applied to separate networks running in parallel.

The following diagram shows the general format for the input P to the sim function when we have Q concurrent sequences of TS time steps. It covers all cases where there is a single input vector. Each element of the cell array is a matrix of concurrent vectors that correspond to the same point in time for each sequence. If there are multiple input vectors, there will be multiple rows of matrices in the cell array.

In this section, we have applied sequential and concurrent inputs to dynamic networks. In the previous section, we applied concurrent inputs to static networks. It is also possible to apply sequential inputs to static networks. It will not change the simulated response of the network, but it can affect the way in which the network is trained. This will become clear in the next section.

Simulation with Sequential Inputs in a Dynamic Network Training Styles