On the relative time complexities of standard and conjugate gradient backpropagation

It is well known that conjugate gradient backpropagation is much faster than standard backpropagation on many given problem instances. However, it has not been established that the conjugate gradient form has a lower time complexity than the standard algorithm. We describe an empirical estimation of the algorithms´ respective time complexities, on N2N encoder problems. The algorithms were found to have near equal median time complexities, approximately O(N⁴)