  Structural credit assignment for recurrent learning is challenging. An
algorithm called RTRL can compute gradients for recurrent networks online but
is computationally intractable for large networks. Alternatives, such as BPTT,
are not online. In this work, we propose a credit-assignment algorithm --
\algoname{} -- that approximates the gradients for recurrent learning in
real-time using $O(n)$ operations and memory per-step. Our method builds on the
idea that for modular recurrent networks, composed of columns with scalar
states, it is sufficient for a parameter to only track its influence on the
state of its column. We empirically show that as long as connections between
columns are sparse, our method approximates the true gradient well. In the
special case when there are no connections between columns, the $O(n)$ gradient
estimate is exact. We demonstrate the utility of the approach for both
recurrent state learning and meta-learning by comparing the estimated gradient
to the true gradient on a synthetic test-bed.
