LoRA-RC: Reservoir Computing with Low-Rank Adaptation

Abstract:Reservoir computing (RC) trains only a linear readout over a fixed recurrent layer, making it fast and data-efficient for online prediction. However, a static reservoir degrades under system drift, readout-only adaptation is then insufficient, and unconstrained reservoir adaptation can destroy the echo-state and incremental stability properties that make RC reliable. This paper proposes LoRA-RC, which adapts the recurrent matrix through a low-rank correction driven by streaming prediction errors. The base reservoir and adaptation bases are fixed offline; a small core matrix is adapted online, projected onto a spectral-norm ball, and low-pass filtered at each step. The projection guarantees that every applied recurrent matrix remains within a certified contraction set, and an incremental input-to-state stability bound is established for the reservoir along each online adaptation path, with path-independent rate and gain. On a Lorenz system with an abrupt parameter drift, LoRA-RC cuts post-drift prediction error by 56% versus a fixed RC and 51% versus readout-only adaptation; ablations over 20 seeds show that removing the projection inflates this error by more than a factor of 40.

Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Systems and Control (eess.SY); Dynamical Systems (math.DS)

arXiv:2609.12327 [cs.AI]

(or arXiv:2609.12327v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2609.12327 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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