  Recurrent neural networks (RNNs) hold immense potential for computations due
to their Turing completeness and sequential processing capabilities, yet
existing methods for their training encounter efficiency challenges.
Backpropagation through time (BPTT), the prevailing method, extends the
backpropagation (BP) algorithm by unrolling the RNN over time. However, this
approach suffers from significant drawbacks, including the need to interleave
forward and backward phases and store exact gradient information. Furthermore,
BPTT has been shown to struggle with propagating gradient information for long
sequences, leading to vanishing gradients. An alternative strategy to using
gradient-based methods like BPTT involves stochastically approximating
gradients through perturbation-based methods. This learning approach is
exceptionally simple, necessitating only forward passes in the network and a
global reinforcement signal as feedback. Despite its simplicity, the random
nature of its updates typically leads to inefficient optimization, limiting its
effectiveness in training neural networks. In this study, we present a new
approach to perturbation-based learning in RNNs whose performance is
competitive with BPTT, while maintaining the inherent advantages over
gradient-based learning. To this end, we extend the recently introduced
activity-based node perturbation (ANP) method to operate in the time domain,
leading to more efficient learning and generalization. Subsequently, we conduct
a range of experiments to validate our approach. Our results show similar
performance, convergence time and scalability when compared to BPTT, strongly
outperforming standard node perturbation and weight perturbation methods. These
findings suggest that perturbation-based learning methods offer a versatile
alternative to gradient-based methods for training RNNs which can be ideally
suited for neuromorphic applications
