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I am having a hard time understanding the Gradient Descent Rule for learning in a feedforward ANN. In particular, how do we determine the initial weight vector, and how is this weight vector adjusted after each epoch?

From what I've read, I know that we first define some error function depending on the weights, and I think that we choose the initial weight to be the minimizer of this error function. Is this right?

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Typically neural network weights are initialized at random (for example: Xavier Initialization - Formula Clarification) while the biases are initialized at 0.

Gradient descent applies updates of the form $$x^{(k+1)} = x^{(k)} - \eta \nabla f(x^{(k)})$$ where ${}^{(k)}$ indicates that this is the $k$th iteration of the procedure and $\eta$ is the learning rate. Stochastic gradient descent only uses a fraction of the data to estimate $\nabla f(x^{(k)})$.

Gradient descent is an imperfect tool. Some discussion:

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