Multiplex visibility graphs to investigate recurrent neural networks dynamics

Abstract

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.

References in corpus (4)

• Deep Learning in Neural Networks: An Overview
• The structure and dynamics of multilayer networks
• Data for Development: the D4D Challenge on Mobile Phone Data
• Approximating the largest eigenvalue of network adjacency matrices

Cited by in corpus (4)

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• Analytic degree distributions of horizontal visibility graphs mapped from unrelated random series and multifractal binomial measures