Between Amnesia and Chaos: A Memory Stability Expressivity Trilemma for Trainable Dissipative Oscillator Networks

The paper presents a study on trainable dissipative oscillator networks in physical reservoir computing, demonstrating that the memory horizon, gradient stability, and dynamical expressivity are interdependent and cannot be maximized simultaneously due to damping effects. The authors employ a symplectic integrator to learn the mass, damping, and stiffness of a twenty-oscillator network, revealing that while learned substrates outperform frozen ones at shorter horizons, this advantage diminishes beyond eleven steps, aligning with their theoretical predictions about stability limits. This work is significant for practitioners as it provides insights into optimizing the training of physical substrates, highlighting the trade-offs involved in maximizing performance in reservoir computing systems.