Multiplex visibility graphs to investigate recurrent neural networks dynamics

TL;DR

This paper introduces a graph-based framework using multiplex visibility graphs to interpret, characterize, and optimize recurrent neural network dynamics, improving hyperparameter tuning and performance.

Contribution

It proposes a novel multiplex visibility graph approach to analyze RNN dynamics, enabling principled hyperparameter tuning without trial-and-error.

Findings

Topological properties of multiplex graphs reflect RNN dynamical features.

The method improves hyperparameter tuning for echo state networks.

Experimental validation on benchmarks and real-world data shows effectiveness.

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.