SparseSSM: Efficient Selective Structured State Space Models Can Be Pruned in One-Shot

Kaiwen Tuo, Huan Wang
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:122606-122627, 2026.

Abstract

State-space language models such as Mamba match Transformer quality while permitting linear complexity inference, yet still comprise billions of parameters that hinder deployment. While existing one-shot pruning methods are effective for generic linear and attention blocks, they are not designed with the overall Mamba architecture in mind and fail to account for the time-shared and discretized state-transition matrix at the heart of the selective state-space module (SSM). In this paper, we introduce SparseSSM, the first training-free pruning framework that extends the classic optimal brain surgeon (OBS) framework to state space architectures. Our layer-wise algorithm (i) derives an approximate second-order saliency score that aggregates Hessian-trace information across time steps, (ii) incorporates a component sensitivity analysis to guide feed-forward network (FFN) pruning, which also sheds light on where redundancy resides in mamba architecture, (iii) can be easily extended to semi-structured and structured sparsity, and generalized to other SSM-based architectures. Empirically, we prune 50% of SSM weights without fine-tuning and observe only limited performance degradation, achieving the current state-of-the-art one-shot pruning algorithm for Mamba-based LLMs.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-tuo26a, title = {{S}parse{SSM}: Efficient Selective Structured State Space Models Can Be Pruned in One-Shot}, author = {Tuo, Kaiwen and Wang, Huan}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {122606--122627}, 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/tuo26a/tuo26a.pdf}, url = {https://proceedings.mlr.press/v306/tuo26a.html}, abstract = {State-space language models such as Mamba match Transformer quality while permitting linear complexity inference, yet still comprise billions of parameters that hinder deployment. While existing one-shot pruning methods are effective for generic linear and attention blocks, they are not designed with the overall Mamba architecture in mind and fail to account for the time-shared and discretized state-transition matrix at the heart of the selective state-space module (SSM). In this paper, we introduce SparseSSM, the first training-free pruning framework that extends the classic optimal brain surgeon (OBS) framework to state space architectures. Our layer-wise algorithm (i) derives an approximate second-order saliency score that aggregates Hessian-trace information across time steps, (ii) incorporates a component sensitivity analysis to guide feed-forward network (FFN) pruning, which also sheds light on where redundancy resides in mamba architecture, (iii) can be easily extended to semi-structured and structured sparsity, and generalized to other SSM-based architectures. Empirically, we prune 50% of SSM weights without fine-tuning and observe only limited performance degradation, achieving the current state-of-the-art one-shot pruning algorithm for Mamba-based LLMs.} }
Endnote
%0 Conference Paper %T SparseSSM: Efficient Selective Structured State Space Models Can Be Pruned in One-Shot %A Kaiwen Tuo %A Huan Wang %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-tuo26a %I PMLR %P 122606--122627 %U https://proceedings.mlr.press/v306/tuo26a.html %V 306 %X State-space language models such as Mamba match Transformer quality while permitting linear complexity inference, yet still comprise billions of parameters that hinder deployment. While existing one-shot pruning methods are effective for generic linear and attention blocks, they are not designed with the overall Mamba architecture in mind and fail to account for the time-shared and discretized state-transition matrix at the heart of the selective state-space module (SSM). In this paper, we introduce SparseSSM, the first training-free pruning framework that extends the classic optimal brain surgeon (OBS) framework to state space architectures. Our layer-wise algorithm (i) derives an approximate second-order saliency score that aggregates Hessian-trace information across time steps, (ii) incorporates a component sensitivity analysis to guide feed-forward network (FFN) pruning, which also sheds light on where redundancy resides in mamba architecture, (iii) can be easily extended to semi-structured and structured sparsity, and generalized to other SSM-based architectures. Empirically, we prune 50% of SSM weights without fine-tuning and observe only limited performance degradation, achieving the current state-of-the-art one-shot pruning algorithm for Mamba-based LLMs.
APA
Tuo, K. & Wang, H.. (2026). SparseSSM: Efficient Selective Structured State Space Models Can Be Pruned in One-Shot. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:122606-122627 Available from https://proceedings.mlr.press/v306/tuo26a.html.

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