# Seeing double with a multifunctional reservoir computer

arXiv: https://arxiv.org/abs/2305.05799 · HTML: https://mlsanity.com/paper/2305.05799/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 34 references that are in the map.
- First posted on arXiv 9 May 2023.

## Builds on (most cited first, 5 of 5)

- [Multifunctionality in a Reservoir Computer](https://mlsanity.com/paper/2008.06348/) (2020)
- [Do Reservoir Computers Work Best at the Edge of Chaos?](https://mlsanity.com/paper/2012.01409/) (2020)
- [Interpreting recurrent neural networks behaviour via excitable network attractors](https://mlsanity.com/paper/1807.10478/) (2018)
- [Designing spontaneous behavioral switching via chaotic itinerancy](https://mlsanity.com/paper/2002.08332/) (2020)
- [The Global Structure of Codimension-2 Local Bifurcations in Continuous-Time Recurrent Neural Networks](https://mlsanity.com/paper/2111.04547/) (2021)

## Built on by (most cited first, 12 of 12)

- [Attractor reconstruction with reservoir computers: The effect of the reservoir's conditional Lyapunov exponents on faithful attractor reconstruction](https://mlsanity.com/paper/2401.00885/) (2023)
- [Exploring the origins of switching dynamics in a multifunctional reservoir computer](https://mlsanity.com/paper/2408.15400/) (2024)
- [Unsupervised learning for anticipating critical transitions](https://mlsanity.com/paper/2501.01579/) (2025)
- [Confabulation dynamics in a reservoir computer: Filling in the gaps with untrained attractors](https://mlsanity.com/paper/2505.04792/) (2025)
- [Multifunctionality in a Connectome-Based Reservoir Computer](https://mlsanity.com/paper/2306.01885/) (2023)
- [Multifunctional physical reservoir computing in soft tensegrity robots](https://mlsanity.com/paper/2507.21496/) (2025)
- [Thermodynamic limit in learning period three](https://mlsanity.com/paper/2405.08825/) (2024)
- [Reconstruction of neuromorphic dynamics from a single scalar time series using variational autoencoder and neural network map](https://mlsanity.com/paper/2411.07055/) (2024)
- [Attractor-merging Crises and Intermittency in Reservoir Computing](https://mlsanity.com/paper/2504.12695/) (2025)
- [Deficiency of equation-finding approach to data-driven modeling of dynamical systems](https://mlsanity.com/paper/2509.03769/) (2025)
- [Storage and selection of multiple chaotic attractors in minimal reservoir computers](https://mlsanity.com/paper/2603.15155/) (2026)
- [Context-dependent time-series prediction via HyperReservoirs](https://mlsanity.com/paper/2609.34847/) (2026)

## Abstract (arXiv)

Multifunctional biological neural networks exploit multistability in order to perform multiple tasks without changing any network properties. Enabling artificial neural networks (ANNs) to obtain certain multistabilities in order to perform several tasks, where each task is related to a particular attractor in the network's state space, naturally has many benefits from a machine learning perspective. Given the association to multistability, in this paper we explore how the relationship between different attractors influences the ability of a reservoir computer (RC), which is a dynamical system in the form of an ANN, to achieve multifunctionality. We construct the `seeing double' problem to systematically study how a RC reconstructs a coexistence of attractors when there is an overlap between them. As the amount of overlap increases, we discover that for multifunctionality to occur, there is a critical dependence on a suitable choice of the spectral radius for the RC's internal network connections. A bifurcation analysis reveals how multifunctionality emerges and is destroyed as the RC enters a chaotic regime that can lead to chaotic itinerancy.