Weight derivatives of the neurons in the output layer


Weight Derivatives

There are several methods to compute the weights of an ANN, however, some of these methods require the partial derivative of the mse (mean squared error) with respect each of the weights in the network. The formulas presented below illustrates how to compute the partial derivatives for the mse for a single training case; to compute the partial derivates for the whole training set the average of the partial derivatives for each case is used.

Output Layer Weights

In order to compute the derivative of the mse for each weight in the output layer, we need to perform two steps:
  1. For each neuron in the hidden compute the real part of δ and the imaginary part of δ
  2. For each weight in the output layer compute the partial derivative of the mse with respect to real part of the weight, and the partial derivative of the mse with respect to imaginary part the weight
The figure below illustrates how to compute these deltas and partial derivatives.

delta

weightsDerivatives

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