  The ability to process time-series at low energy cost is critical for many
applications. Recurrent neural network, which can perform such tasks, are
computationally expensive when implementing in software on conventional
computers. Here we propose to implement a recurrent neural network in hardware
using spintronic oscillators as dynamical neurons. Using numerical simulations,
we build a multi-layer network and demonstrate that we can use backpropagation
through time (BPTT) and standard machine learning tools to train this network.
Leveraging the transient dynamics of the spintronic oscillators, we solve the
sequential digits classification task with $89.83\pm2.91~\%$ accuracy, as good
as the equivalent software network. We devise guidelines on how to choose the
time constant of the oscillators as well as hyper-parameters of the network to
adapt to different input time scales.
