  Spiking recurrent neural networks (RNNs) are a promising tool for solving a
wide variety of complex cognitive and motor tasks, due to their rich temporal
dynamics and sparse processing. However training spiking RNNs on dedicated
neuromorphic hardware is still an open challenge. This is due mainly to the
lack of local, hardware-friendly learning mechanisms that can solve the
temporal credit assignment problem and ensure stable network dynamics, even
when the weight resolution is limited. These challenges are further
accentuated, if one resorts to using memristive devices for in-memory computing
to resolve the von-Neumann bottleneck problem, at the expense of a substantial
increase in variability in both the computation and the working memory of the
spiking RNNs. To address these challenges and enable online learning in
memristive neuromorphic RNNs, we present a simulation framework of
differential-architecture crossbar arrays based on an accurate and
comprehensive Phase-Change Memory (PCM) device model. We train a spiking RNN
whose weights are emulated in the presented simulation framework, using a
recently proposed e-prop learning rule. Although e-prop locally approximates
the ideal synaptic updates, it is difficult to implement the updates on the
memristive substrate due to substantial PCM non-idealities. We compare several
widely adapted weight update schemes that primarily aim to cope with these
device non-idealities and demonstrate that accumulating gradients can enable
online and efficient training of spiking RNN on memristive substrates.
