  A recurrent neural network (RNN) is a universal approximator of dynamical
systems, whose performance often depends on sensitive hyperparameters. Tuning
of such hyperparameters may be difficult and, typically, based on a
trial-and-error approach. In this work, we adopt a graph-based framework to
interpret and characterize the internal RNN dynamics. Through this insight, we
are able to design a principled unsupervised method to derive configurations
with maximized performances, in terms of prediction error and memory capacity.
In particular, we propose to model time series of neurons activations with the
recently introduced horizontal visibility graphs, whose topological properties
reflect important dynamical features of the underlying dynamic system.
Successively, each graph becomes a layer of a larger structure, called
multiplex. We show that topological properties of such a multiplex reflect
important features of RNN dynamics and are used to guide the tuning procedure.
To validate the proposed method, we consider a class of RNNs called echo state
networks. We perform experiments and discuss results on several benchmarks and
real-world dataset of call data records.
