  The backpropagation algorithm for neural networks is widely felt hard to
understand, despite the existence of some well-written explanations and/or
derivations. This paper provides a new derivation of this algorithm based on
the concept of derivative amplification coefficients. First proposed by this
author for fully connected cascade networks, this concept is found to well
carry over to conventional feedforward neural networks and it paves the way for
the use of mathematical induction in establishing a key result that enables
backpropagation for derivative amplification coefficients. Then we establish
the connection between derivative amplification coefficients and error
coefficients (commonly referred to as errors in the literature), and show that
the same backpropagation procedure can be used for error coefficients. The
entire derivation is thus rigorous, simple, and elegant.
