A Control-Theoretic View of Mamba on Stability and Robustness

Liang Cao, Weide Liu, Zhuo Chen, Yan Qin
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:11350-11364, 2026.

Abstract

Selective State Space Models (SSMs) such as Mamba have emerged as efficient alternatives to Transformers, achieving linear complexity through input-dependent parameterization. However, this selectivity transforms the system from linear time-invariant (LTI) to linear parameter-varying (LPV), where individually stable matrices can produce unbounded trajectories under switching. Existing work focuses on empirical performance, leaving global stability, robustness bounds, and practical certification unresolved. This paper develops a control-theoretic framework providing a comprehensive stability and robustness analysis for selective SSMs. We prove BIBO stability by viewing selective scans as continuous-time LTI sampling and establish two-term robustness bounds with linear growth in sequence length. For general LPV systems, we provide common quadratic Lyapunov function conditions and develop algorithms to extract certificate constants directly from network weights. These results bridge control theory and SSM architectures, providing verifiable certificates for individual selective-SSM layers as a step toward formal guarantees for deployment.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-cao26l, title = {A Control-Theoretic View of Mamba on Stability and Robustness}, author = {Cao, Liang and Liu, Weide and Chen, Zhuo and Qin, Yan}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {11350--11364}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/cao26l/cao26l.pdf}, url = {https://proceedings.mlr.press/v306/cao26l.html}, abstract = {Selective State Space Models (SSMs) such as Mamba have emerged as efficient alternatives to Transformers, achieving linear complexity through input-dependent parameterization. However, this selectivity transforms the system from linear time-invariant (LTI) to linear parameter-varying (LPV), where individually stable matrices can produce unbounded trajectories under switching. Existing work focuses on empirical performance, leaving global stability, robustness bounds, and practical certification unresolved. This paper develops a control-theoretic framework providing a comprehensive stability and robustness analysis for selective SSMs. We prove BIBO stability by viewing selective scans as continuous-time LTI sampling and establish two-term robustness bounds with linear growth in sequence length. For general LPV systems, we provide common quadratic Lyapunov function conditions and develop algorithms to extract certificate constants directly from network weights. These results bridge control theory and SSM architectures, providing verifiable certificates for individual selective-SSM layers as a step toward formal guarantees for deployment.} }
Endnote
%0 Conference Paper %T A Control-Theoretic View of Mamba on Stability and Robustness %A Liang Cao %A Weide Liu %A Zhuo Chen %A Yan Qin %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-cao26l %I PMLR %P 11350--11364 %U https://proceedings.mlr.press/v306/cao26l.html %V 306 %X Selective State Space Models (SSMs) such as Mamba have emerged as efficient alternatives to Transformers, achieving linear complexity through input-dependent parameterization. However, this selectivity transforms the system from linear time-invariant (LTI) to linear parameter-varying (LPV), where individually stable matrices can produce unbounded trajectories under switching. Existing work focuses on empirical performance, leaving global stability, robustness bounds, and practical certification unresolved. This paper develops a control-theoretic framework providing a comprehensive stability and robustness analysis for selective SSMs. We prove BIBO stability by viewing selective scans as continuous-time LTI sampling and establish two-term robustness bounds with linear growth in sequence length. For general LPV systems, we provide common quadratic Lyapunov function conditions and develop algorithms to extract certificate constants directly from network weights. These results bridge control theory and SSM architectures, providing verifiable certificates for individual selective-SSM layers as a step toward formal guarantees for deployment.
APA
Cao, L., Liu, W., Chen, Z. & Qin, Y.. (2026). A Control-Theoretic View of Mamba on Stability and Robustness. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:11350-11364 Available from https://proceedings.mlr.press/v306/cao26l.html.

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