发表机构
Heritage Institute of Technology（遗产技术学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对地表预测中状态空间模型吸收非平稳混杂偏差的问题，提出SSU-LSF框架，利用影响函数和正则化梯度上升实现高效遗忘，在三个基准上显著降低混杂，且GPU成本远低于重训练。
AI 中文摘要
基于Mamba族结构化状态空间模型（SSM）的业务化地表预测系统，会将非平稳混杂事件（未记录的灌溉激增、大坝运行变化、传感器重新校准）吸收进其状态转移矩阵，从而在物理原因结束后长期静默地偏置NDVI、LST和作物物候预测。本文提出SSU-LSF（面向地表预测的状态空间遗忘学习），这是首个专为地球科学领域基于Mamba的SSM设计的机器遗忘框架。我们开发了专门针对Mamba状态矩阵的EKFac影响函数，通过闭式矩阵指数梯度实现；使用谱半径加权肘部阈值法来定位时间混杂足迹$\boldsymbol{\rho}$；并在由空间总变差（TV）正则化增强的KL散度信任域内，应用无Hessian的投影梯度上升。命题1建立了残余混杂的上界为$\boldsymbol{\rho}$，其随窗口长度$T_c$增长。在三个异构基准和十一个基线中，SSU-LSF在CropHarvest、NDVI-LST和ERA5上分别实现了0.773、0.821和0.859的混杂降低率，在ERA5上最坏情况下的干净域RMSE退化仅为4.2%，并且每次遗忘请求的GPU成本比完全重训练低8.4倍，收敛仅需3-5个epoch。代码：见链接。
英文摘要
Operational land surface forecasting systems built on Mamba-family Structured State Space Models absorb non-stationary confounding events (unrecorded irrigation booms, dam-operation shifts, sensor recalibrations) into their state-transition matrices, silently biasing NDVI, LST, and crop phenology predictions long after the physical cause ends. This paper introduces SSU-LSF (State-Space Unlearning for Land Surface Forecasting), the first machine-unlearning framework purpose-built for geoscientific Mamba-based SSMs. We develop EKFac influence functions specialized to the Mamba state matrices via a closed-form matrix-exponential gradient, use spectral-radius-weighted elbow thresholding to localize a temporal confounding footprint $Φ$, and apply Hessian-free projected gradient ascent within a KL-divergence trust region augmented by spatial total-variation (TV) regularization. Proposition 1 establishes that residual confounding is bounded by $\mathcal{O}\big((1-ρ(\bar{A})^{T_c})/((1-ρ(\bar{A}))μ)\big)$, which grows with the window length $T_c$. Across three heterogeneous benchmarks and eleven baselines, SSU-LSF achieves confounding reduction rates of $0.773$ (CropHarvest), $0.821$ (NDVI-LST), and $0.859$ (ERA5), with worst-case clean-domain RMSE degradation of $4.2\%$ on ERA5, converging in 3--5 epochs at $8.4\times$ lower GPU-cost per unlearning request than full retraining. Code: https://github.com/Anidipta/SSU-LSF
