发表机构
University of New Mexico（新墨西哥大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
LoRA-RC通过低秩校正在线适应储层循环矩阵，在保证稳定性的同时，将漂移后预测误差降低56%，优于固定RC和仅读出适应。
AI 中文摘要
储层计算（RC）仅训练固定循环层之上的线性读出，使其在在线预测中快速且数据高效。然而，静态储层在系统漂移下性能退化，仅调整读出不足以应对，而无约束的储层适应可能破坏使RC可靠的回声状态和增量稳定性属性。本文提出LoRA-RC，通过由流式预测误差驱动的低秩校正来适应循环矩阵。基础储层和适应基离线固定；一个小型核心矩阵在线适应，投影到谱范数球上，并在每一步进行低通滤波。该投影保证每个应用的循环矩阵保持在认证的收缩集内，并为沿每条在线适应路径的储层建立了增量输入到状态稳定性界，其速率和增益与路径无关。在具有突然参数漂移的Lorenz系统上，LoRA-RC将漂移后预测误差相对于固定RC降低了56%，相对于仅读出适应降低了51%；在20个种子上的消融实验表明，移除投影会使该误差膨胀超过40倍。
英文摘要
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.
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