Demo note. This note demonstrates what the SciDraft Hugo theme can do for academic and scientific publishing — for research institutions, researchers and students. Its content is demonstration material only: readers should ignore whether the demo content is correct. Backpropagation computes, for one layer, three gradients: one for each parameter of the layer and one to hand to the layer before it. The third is what makes deep networks trainable — without it, error could not travel past the last layer. The procedure below is the backward pass of a single dense layer. ...