How a network computes, why gradients vanish, and what makes depth trainable
A network is a list of matrices and vectors. Before any training happens you should be able to say how many numbers that list contains, where they sit, and what shape the data has at each step. Those are questions of arithmetic, and getting them wrong is the most common way a first network fails to run at all.
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▶ Shapes, Widths and Parameter Counts