Scalar backpropagation and vector backpropagation only differ in their arithmetic notation and the

implementation of their underlying arithmetic

Both scalar backpropagation and vector backpropagation are optimization algorithms that are used to

find parameters that minimize a loss function

Scalar backpropagation rules explicitly loop over the neurons in a layer to compute derivatives, while

vector backpropagation computes derivative terms for all of them in a single matrix operation

Scalar backpropagation is required for scalar activation functions, while vector backpropagation is

essential for vector activation functions