LoRA-RC Adapts Reservoir Computing to System Drift with Stable Low-Rank Updates

Summary

Reservoir computing (RC) is efficient for online prediction because it trains only a linear readout over a fixed recurrent reservoir. That fixed structure can become ineffective when the underlying system drifts, while changing the reservoir without constraints may undermine the echo-state and incremental-stability properties that support reliable operation. The paper introduces LoRA-RC, which updates the recurrent matrix through a low-rank correction driven by streaming prediction errors. The base reservoir and adaptation bases are fixed offline, leaving only a small core matrix to adapt online. Each update is projected onto a spectral-norm ball and low-pass filtered before being applied. The projection keeps every resulting recurrent matrix inside a certified contraction set, and the authors establish an incremental input-to-state stability bound along each online adaptation path with a path-independent rate and gain. On a Lorenz system with abrupt parameter drift, LoRA-RC reduced post-drift prediction error by 56% compared with fixed RC and by 51% compared with readout-only adaptation. In ablations across 20 seeds, removing the projection increased post-drift error by more than 40 times.