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Gradient descent is a first-order iterative optimization algorithm. To find a local minimum of a function using gradient descent, one takes steps proportional to the negative of the gradient (or of the approximate gradient) of the function at the current point. For stochastic gradient descent there is also the [sgd] tag.
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Higher Order of Vectorization in Backpropagation in Neural Network
$\frac{\partial \mathcal{L}}{\partial W^{[2]}}$ must be 2x3 as just like dimensions of $ W^{[2]}$.
I suggest you to use the backprop formulas (and notation) given in Nielsen's book. When the networks …