# Multiplex visibility graphs to investigate recurrent neural networks dynamics

arXiv: https://arxiv.org/abs/1609.03068 · HTML: https://mlsanity.com/paper/1609.03068/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Sep 2016.

## Built on by (most cited first, 3 of 3)

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- [Novel Features for Time Series Analysis: A Complex Networks Approach](https://mlsanity.com/paper/2110.09888/) (2021)
- [Probabilistic load forecasting with Reservoir Computing](https://mlsanity.com/paper/2308.12844/) (2023)

## Abstract (arXiv)

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.