A modified BPTT algorithm for trajectory learning in block-diagonal recurrent neural networks

This paper deals with a discrete time recurrent neural network (DTRNN) with a block-diagonal feedback weight matrix, called the block-diagonal recurrent neural network (BDRNN), that allows a simplified approach to online trajectory learning. The BDRNN is a sparse but structured architecture in which the feedback connections are restricted to between pairs of state variables. The block-diagonal structure of the BDRNN is exploited to modify the backpropagation-through-time (BPTT) algorithm to reduce the storage requirements while still maintaining exactness and locality of gradient computation. To achieve this, a numerically stable method for recomputing the state variables in the backward pass of the BPTT algorithm is presented.