Random Unicycle Network (RUN!): supercharging harmonic oscillator networks via non-holonomic constraints

Mariano Ramirez Montero, Andrea Ceni, Andrea Cossu, Davide Bacciu, Claudio Gallicchio, and Cosimo Della Santina, "Random Unicycle Network (RUN!): supercharging harmonic oscillator networks via non-holonomic constraints", in proceedings of the European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning, 2026.

Abstract: Motivated by advances in physical reservoir computing, we seek models that retain the modularity of echo state networks while enriching their internal dynamics. Recent studies have demonstrated that oscillator networks can achieve this balance, although their simple harmonic nature may limit their expressiveness. Here, we investigate the idea of augmenting harmonic oscillators with non-holonomic (velocity-level) constraints, known to induce rich, nonlocal behaviors. We implement these constraints intrinsically within each dynamical unit, yielding a model equivalent to the unicycle — the canonical representation of the simplest vehicle. We test the model on three time-series classification benchmarks, achieving competitive or superior accuracy compared to the state of the art, with reservoirs as small as 20 unicycles.