# LoRA-RC: Reservoir Computing with Low-Rank Adaptation

arXiv: https://arxiv.org/abs/2609.12327 · HTML: https://mlsanity.com/paper/2609.12327/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 31 references that are in the map.
- First posted on arXiv 11 Sep 2026.

## Builds on (most cited first, 11 of 11)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [AdaLoRA: Adaptive Budget Allocation for Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2303.10512/) (2023)
- [Universal discrete-time reservoir computers with stochastic inputs and linear readouts using non-homogeneous state-affine systems](https://mlsanity.com/paper/1712.00754/) (2017)
- [FlyLoRA: Boosting Task Decoupling and Parameter Efficiency via Implicit Rank-Wise Mixture-of-Experts](https://mlsanity.com/paper/2510.08396/) (2025)
- [KeepLoRA: Continual Learning with Residual Gradient Adaptation](https://mlsanity.com/paper/2601.19659/) (2026)
- [On the stability properties of Gated Recurrent Units neural networks](https://mlsanity.com/paper/2011.06806/) (2020)
- [Nonlinear MPC design for incrementally ISS systems with application to GRU networks](https://mlsanity.com/paper/2309.16428/) (2023)
- [Asymptotic Stability in Reservoir Computing](https://mlsanity.com/paper/2206.03854/) (2022)
- [Regional stability conditions for recurrent neural network-based control systems](https://mlsanity.com/paper/2409.15792/) (2024)
- [Reservoir Predictive Path Integral Control for Unknown Nonlinear Dynamics](https://mlsanity.com/paper/2509.03839/) (2025)
- [Computing with Living Neurons: Chaos-Controlled Reservoir Computing with Knowledge Transplant](https://mlsanity.com/paper/2604.02552/) (2026)

## Abstract (arXiv)

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.