A Fixed Size Storage O(n³) Time Complexity Learning Algorithm for Fully Recurrent Continually Running Networks

The real-time recurrent learning (RTRL) algorithm (Robinson and Fallside 1987; Williams and Zipser 1989) requires O(n⁴) computations per time step, where n is the number of noninput units. I describe a method suited for on-line learning that computes exactly the same gradient and requires fixed-size storage of the same order but has an average time complexity per time step of O(n³).