# AIRE-Prune: Asymptotic Impulse-Response Energy for State Pruning in State Space Models

arXiv: https://arxiv.org/abs/2602.00534 · HTML: https://mlsanity.com/paper/2602.00534/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 35 references that are in the map.
- First posted on arXiv 31 Jan 2026.

## Builds on (most cited first, 21 of 21)

- [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)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [Speech Commands: A Dataset for Limited-Vocabulary Speech Recognition](https://mlsanity.com/paper/1804.03209/) (2018)
- [Long Range Arena: A Benchmark for Efficient Transformers](https://mlsanity.com/paper/2011.04006/) (2020)
- [Combining Recurrent, Convolutional, and Continuous-time Models with Linear State-Space Layers](https://mlsanity.com/paper/2110.13985/) (2021)
- [HiPPO: Recurrent Memory with Optimal Polynomial Projections](https://mlsanity.com/paper/2008.07669/) (2020)
- [To prune, or not to prune: exploring the efficacy of pruning for model compression](https://mlsanity.com/paper/1710.01878/) (2017)
- [The State of Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1902.09574/) (2019)
- [On the Parameterization and Initialization of Diagonal State Space Models](https://mlsanity.com/paper/2206.11893/) (2022)
- [Diagonal State Spaces are as Effective as Structured State Spaces](https://mlsanity.com/paper/2203.14343/) (2022)
- [Scalable Training of Artificial Neural Networks with Adaptive Sparse Connectivity inspired by Network Science](https://mlsanity.com/paper/1707.04780/) (2017)
- [ListOps: A Diagnostic Dataset for Latent Tree Learning](https://mlsanity.com/paper/1804.06028/) (2018)
- [Layer-adaptive sparsity for the Magnitude-based Pruning](https://mlsanity.com/paper/2010.07611/) (2020)
- [One ticket to win them all: generalizing lottery ticket initializations across datasets and optimizers](https://mlsanity.com/paper/1906.02773/) (2019)
- [Learning long-range spatial dependencies with horizontal gated-recurrent units](https://mlsanity.com/paper/1805.08315/) (2018)
- [Effectively Modeling Time Series with Simple Discrete State Spaces](https://mlsanity.com/paper/2303.09489/) (2023)
- [State-Free Inference of State-Space Models: The Transfer Function Approach](https://mlsanity.com/paper/2405.06147/) (2024)
- [Efficient Joint Optimization of Layer-Adaptive Weight Pruning in Deep Neural Networks](https://mlsanity.com/paper/2308.10438/) (2023)
- [Layer-Adaptive State Pruning for Deep State Space Models](https://mlsanity.com/paper/2411.02824/) (2024)

## Built on by (most cited first, 1 of 1)

- [Continuity Laws for Sequential Models](https://mlsanity.com/paper/2605.08539/) (2026)

## Abstract (arXiv)

State space models (SSMs) often sacrifice capacity, search space, or stability to offset the memory and compute costs of large state dimensions. We introduce a structured post-training pruning method for SSMs -- AIRE-Prune (Asymptotic Impulse-Response Energy for State PRUN(E)) -- that reduces each layer's state dimension by directly minimizing long-run output-energy distortion. AIRE-Prune assigns every state a closed-form asymptotic impulse-response energy-based score, i.e., the total impulse-response energy it contributes over an infinite horizon (time), and normalizes these scores layer-wise to enable global cross-layer comparison and selection. This extends modal truncation from single systems to deep stacks and aligns pruning with asymptotic response energy rather than worst-case gain. Across diverse sequence benchmarks, AIRE-Prune reveals substantial redundancy in SISO and MIMO SSMs with average pruning of 60.8%, with average accuracy drop of 0.29% without retraining, while significantly lowering compute. Code: https://github.com/falcon-arrow/AIRE-Prune.