# State-Space Unlearning for Non-Stationary Bias in Land Surface Forecasting

arXiv: https://arxiv.org/abs/2610.02248 · HTML: https://mlsanity.com/paper/2610.02248/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Time series forecasting with SSMs, one of 10 directions in State-space sequence models (S4, Mamba).
- Builds on 18 of its 38 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Placed in

- State-space sequence models (S4, Mamba) / [Time series forecasting with SSMs](https://mlsanity.com/ssm/time-series-forecasting-with-ssms/)

## Builds on (most cited first, 18 of 18)

- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [Machine Unlearning](https://mlsanity.com/paper/1912.03817/) (2019)
- [VMamba: Visual State Space Model](https://mlsanity.com/paper/2401.10166/) (2024)
- [Membership Inference Attacks From First Principles](https://mlsanity.com/paper/2112.03570/) (2021)
- [Eternal Sunshine of the Spotless Net: Selective Forgetting in Deep Networks](https://mlsanity.com/paper/1911.04933/) (2019)
- [Certified Data Removal from Machine Learning Models](https://mlsanity.com/paper/1911.03030/) (2019)
- [Learning under Concept Drift: A Review](https://mlsanity.com/paper/2004.05785/) (2020)
- [SalUn: Empowering Machine Unlearning via Gradient-based Weight Saliency in Both Image Classification and Generation](https://mlsanity.com/paper/2310.12508/) (2023)
- [Can Bad Teaching Induce Forgetting? Unlearning in Deep Networks using an Incompetent Teacher](https://mlsanity.com/paper/2205.08096/) (2022)
- [Earthformer: Exploring Space-Time Transformers for Earth System Forecasting](https://mlsanity.com/paper/2207.05833/) (2022)
- [A Kronecker-factored approximate Fisher matrix for convolution layers](https://mlsanity.com/paper/1602.01407/) (2016)
- [SiMBA: Simplified Mamba-Based Architecture for Vision and Multivariate Time series](https://mlsanity.com/paper/2403.15360/) (2024)
- [Rewind-to-Delete: Certified Machine Unlearning for Nonconvex Functions](https://mlsanity.com/paper/2409.09778/) (2024)
- [SEMU: Singular Value Decomposition for Efficient Machine Unlearning](https://mlsanity.com/paper/2502.07587/) (2025)

## Abstract (arXiv)

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 Phi, 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 Obig((1-ρ(barA)Tc)/((1-ρ(barA))μ)big), which grows with the window length Tc. 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× lower GPU-cost per unlearning request than full retraining. Code: https://github.com/Anidipta/SSU-LSF