Current methods for training recurrent neural networks are based on
backpropagation through time, which requires storing a complete history of
network states, and prohibits updating the weights `online' (after every
timestep). Real Time Recurrent Learning (RTRL) eliminates the need for history
storage and allows for online weight updates, but does so at the expense of
computational costs that are quartic in the state size. This renders RTRL
training intractable for all but the smallest networks, even ones that are made
highly sparse.
We introduce the Sparse n-step Approximation (SnAp) to the RTRL influence
matrix, which only keeps entries that are nonzero within n steps of the
recurrent core. SnAp with n=1 is no more expensive than backpropagation, and we
find that it substantially outperforms other RTRL approximations with
comparable costs such as Unbiased Online Recurrent Optimization. For highly
sparse networks, SnAp with n=2 remains tractable and can outperform
backpropagation through time in terms of learning speed when updates are done
online. SnAp becomes equivalent to RTRL when n is large.

介绍了 Sparse n-step Approximation (SnAp) 来优化 Real Time Recurrent Learning (RTRL) 的影响矩阵，在保持计算成本低的同时提高了网络的学习速度，特别是在稀疏网络时，n=2 时的 SnAp 能够优于 backpropagation in terms of learning speed when updates are done online。