# The Curious Case of In-Training Compression of State Space Models

arXiv: https://arxiv.org/abs/2510.02823 · HTML: https://mlsanity.com/paper/2510.02823/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 46 references that are in the map.
- First posted on arXiv 3 Oct 2025.

## Builds on (most cited first, 30 of 34)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [Pruning Filters for Efficient ConvNets](https://mlsanity.com/paper/1608.08710/) (2016)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [Long Range Arena: A Benchmark for Efficient Transformers](https://mlsanity.com/paper/2011.04006/) (2020)
- [Gated Delta Networks: Improving Mamba2 with Delta Rule](https://mlsanity.com/paper/2412.06464/) (2024)
- [Sparsity in Deep Learning: Pruning and growth for efficient inference and training in neural networks](https://mlsanity.com/paper/2102.00554/) (2021)
- [Gated Linear Attention Transformers with Hardware-Efficient Training](https://mlsanity.com/paper/2312.06635/) (2023)
- [PACT: Parameterized Clipping Activation for Quantized Neural Networks](https://mlsanity.com/paper/1805.06085/) (2018)
- [Resurrecting Recurrent Neural Networks for Long Sequences](https://mlsanity.com/paper/2303.06349/) (2023)
- [Parallelizing Linear Transformers with the Delta Rule over Sequence Length](https://mlsanity.com/paper/2406.06484/) (2024)
- [LQ-Nets: Learned Quantization for Highly Accurate and Compact Deep Neural Networks](https://mlsanity.com/paper/1807.10029/) (2018)
- [A Survey on Model Compression for Large Language Models](https://mlsanity.com/paper/2308.07633/) (2023)
- [Griffin: Mixing Gated Linear Recurrences with Local Attention for Efficient Language Models](https://mlsanity.com/paper/2402.19427/) (2024)
- [It's Raw! Audio Generation with State-Space Models](https://mlsanity.com/paper/2202.09729/) (2022)
- [Liquid Structural State-Space Models](https://mlsanity.com/paper/2209.12951/) (2022)
- [Baby Llama: knowledge distillation from an ensemble of teachers trained on a small dataset with no performance penalty](https://mlsanity.com/paper/2308.02019/) (2023)
- [Oscillatory State-Space Models](https://mlsanity.com/paper/2410.03943/) (2024)
- [Quamba: A Post-Training Quantization Recipe for Selective State Space Models](https://mlsanity.com/paper/2410.13229/) (2024)
- [Structured Linear CDEs: Maximally Expressive and Parallel-in-Time Sequence Models](https://mlsanity.com/paper/2505.17761/) (2025)
- [Dimensionality Reduced Training by Pruning and Freezing Parts of a Deep Neural Network, a Survey](https://mlsanity.com/paper/2205.08099/) (2022)
- [HOPE for a Robust Parameterization of Long-memory State Space Models](https://mlsanity.com/paper/2405.13975/) (2024)
- [Model Compression Method for S4 with Diagonal State Space Layers using Balanced Truncation](https://mlsanity.com/paper/2402.15993/) (2024)

## Built on by (most cited first, 4 of 4)

- [On State Reduction in Linear Attention](https://mlsanity.com/paper/2602.04852/) (2026)
- [A Deep State-Space Model Compression Method using Upper Bound on Output Error](https://mlsanity.com/paper/2510.14542/) (2025)
- [Continuity Laws for Sequential Models](https://mlsanity.com/paper/2605.08539/) (2026)
- [MambAdapter: Lightweight Mamba-Based Adapters for Parameter-Efficient Transfer Learning in Speech and Audio](https://mlsanity.com/paper/2606.15638/) (2026)

## Abstract (arXiv)

State Space Models (SSMs), developed to tackle long sequence modeling tasks efficiently, offer both parallelizable training and fast inference. At their core are recurrent dynamical systems that maintain a hidden state, with update costs scaling with the state dimension. A key design challenge is striking the right balance between maximizing expressivity and limiting this computational burden. Control theory, and more specifically Hankel singular value analysis, provides a potent framework for the measure of energy for each state, as well as the balanced truncation of the original system down to a smaller representation with performance guarantees. Leveraging the eigenvalue stability properties of Hankel matrices, we apply this lens to SSMs during training, where only dimensions of high influence are identified and preserved. Our approach, textscCompreSSM, applies to Linear Time-Invariant SSMs such as Linear Recurrent Units, but is also extendable to selective models. Experiments show that in-training reduction significantly accelerates optimization while preserving expressivity, with compressed models retaining task-critical structure lost by models trained directly at smaller dimension. In other words, SSMs that begin large and shrink during training achieve computational efficiency while maintaining higher performance. Project code is available at github.com/camail-official/compressm.