Perturbative Gradient Training for Embedded Physical Magnonic Reservoir Computers

Physical reservoir computing offers a promising path toward energy-efficient neuromorphic systems [1] but remains constrained by the inability to backpropagate through hardware-dependent dynamics. We extend perturbation-based gradient estimation [2] to embedded physical reservoirs, introducing Perturbative Gradient Training (PGT) as a framework for hybrid physical–digital networks. By applying controlled perturbations in parameter space, PGT approximates gradient updates using only forward evaluations, enabling training where backpropagation is impractical. We demonstrate this on simulated architectures and on hardware using a magnonic auto-oscillation ring as the physical reservoir [3]. Our results [4] show that PGT effectively optimizes hybrid systems without backpropagation, achieving performance comparable to standard gradient methods while preserving experimental integrity. This work highlights a viable route for integrating physical reservoirs into deep networks and advancing scalable, energy-efficient AI training.

This material is based upon work supported by the National Science Foundation under Award No. ECCS-2138236

[1] Chumak et al., J. Phys. D: Appl. Phys. 50, 244001 (2017)

[2] Fernández et al., Front. Neurosci. 18, 1439155 (2024)

[3] Ustinov et al., Appl. Phys. Lett. 124, 042401 (2024)

[4] C. Abbott et al., ArXiv:2506.04523 (2025)