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By Howard Demuth

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If the inputs are passed as a sequence, then the network is trained in incremental mode. If the inputs are passed as concurrent vectors, then batch mode training is used. With dynamic networks, batch mode training is typically done with train only, especially if only one training sequence exists. To illustrate this, let’s consider again the linear network with a delay. 02 for the training. epochs = 1; Pi = {1}; P = {2 3 4}; T = {3 5 6}; We want to train the network with the same sequence we used for the incremental training earlier, but this time we want to update the weights only after all of the inputs are applied (batch mode).

The same three-layer network discussed previously also can be drawn using our abbreviated notation. Layer 1 Input Layer 2 p Rx1 a1 IW1,1 S1xR n1 S1x1 1 R Layer 3 S1x1 S2xS1 f1 b1 S1 a1 = f1 (IW1,1p +b1) n2 S2x1 1 S1x1 a3 = y a2 LW2,1 S2x1 S 3x S 2 f2 b2 S2x1 LW 3,2 n3 S3 x1 b3 1 S2 S3x1 a2 = f2 (LW2,1 a1 +b2) a3 =f3 (LW3,2 f2 (LW2,1f1 (IW1,1p +b1)+ b2)+ b3 S3 x1 f3 S3 a3 =f3 (LW3,2a2 +b3) = y Multiple-layer networks are quite powerful. For instance, a network of two layers, where the first layer is sigmoid and the second layer is linear, can be trained to approximate any function (with a finite number of discontinuities) arbitrarily well.

A constant input 1 is fed to the biases for each neuron. Note that the outputs of each intermediate layer are the inputs to the following layer. Thus layer 2 can be analyzed as a one-layer network with S1 inputs, S2 neurons, and an S2xS1 weight matrix W2. The input to layer 2 is a1; the output is a2. Now that we have identified all the vectors and matrices of layer 2, we can treat it as a single-layer network on its own. This approach can be taken with any layer of the network. The layers of a multilayer network play different roles.

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