Back Propagation


Learning Rate

The learning rate is parameter that represents how fast an ANN is being trained. The learning rate range is from 0 to 1. When the learning rate is closed to 1, the ANN may learn quickly, however, the quality of the training may be compromised.

Back Propagation

The method of back propagation is used to train ANN. The method begins by computing the ANN output with the current weights values. At each iteration, the weights are updated in a way that the actual network output is closer and closer to the target. The method has five steps:
  1. Find the output value for each output neuron.
  2. Compute the mse.
  3. Compute the delta for each output neuron using the formula shown below.
  4. Compute the beta for each hidden neuron using the formula shown below.
  5. Update the weights using the formula shown below.
Note that the formulas apply only when the activation function is the z=logsig(z).

Backpropagation

Problem 1
Create a Neural Lab project called FindOutput. Find the values of: x1, x2, y1 and z1, suppose the activation function is logsig(x).

FindOutput

FindOutput.lab
Vector u;
u.Create(...

Matrix H;
H.Create(...

Vector v = ...
Vector x = ...

Matrix W;
W.Create(...

Vector y = ...
Vector z = ...

Output

Problem 2
Compute the mse when the target of the ANN is 1.05.

mse

Problem 3
Compute the delta of the output neuron.

delta

Problem 4
Compute the beta for each neuron in the hidden layer. In this specific case, there is only one delta, thus, you must use i = 1 to compute beta.

beta

Problem 5
Compute the new weights: H and W. Suppose that the learning rate is 0.2.

WeightsH

WeightsW

Problem 6
For the new weights, compute the values of: x1, x2, y1 and z1.

NewOutput

Problem 7
For the new weights, compute the mse when the target of the ANN is 1.05. The new mse must be smaller than the previous one.

NewMse

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