# Parameter-Efficient Fine-Tuning of State Space Models

arXiv: https://arxiv.org/abs/2410.09016 · HTML: https://mlsanity.com/paper/2410.09016/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Placed in Core SSM architectures for language, one of 10 directions in State-space sequence models (S4, Mamba).
- Builds on 45 of its 52 references that are in the map.
- First posted on arXiv 11 Oct 2024.

## Placed in

- State-space sequence models (S4, Mamba) / [Core SSM architectures for language](https://mlsanity.com/ssm/core-ssm-architectures-for-language/)

## Builds on (most cited first, 30 of 45)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [BitFit: Simple Parameter-efficient Fine-tuning for Transformer-based Masked Language-models](https://mlsanity.com/paper/2106.10199/) (2021)
- [How transferable are features in deep neural networks?](https://mlsanity.com/paper/1411.1792/) (2014)
- [Spider: A Large-Scale Human-Labeled Dataset for Complex and Cross-Domain Semantic Parsing and Text-to-SQL Task](https://mlsanity.com/paper/1809.08887/) (2018)
- [Towards a Unified View of Parameter-Efficient Transfer Learning](https://mlsanity.com/paper/2110.04366/) (2021)
- [RWKV: Reinventing RNNs for the Transformer Era](https://mlsanity.com/paper/2305.13048/) (2023)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [GPT Understands, Too](https://mlsanity.com/paper/2103.10385/) (2021)
- [Retentive Network: A Successor to Transformer for Large Language Models](https://mlsanity.com/paper/2307.08621/) (2023)
- [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)
- [SAMSum Corpus: A Human-annotated Dialogue Dataset for Abstractive Summarization](https://mlsanity.com/paper/1911.12237/) (2019)
- [Hungry Hungry Hippos: Towards Language Modeling with State Space Models](https://mlsanity.com/paper/2212.14052/) (2022)
- [DeCAF: A Deep Convolutional Activation Feature for Generic Visual Recognition](https://mlsanity.com/paper/1310.1531/) (2013)
- [On the Parameterization and Initialization of Diagonal State Space Models](https://mlsanity.com/paper/2206.11893/) (2022)
- [PICARD: Parsing Incrementally for Constrained Auto-Regressive Decoding from Language Models](https://mlsanity.com/paper/2109.05093/) (2021)
- [Jamba: A Hybrid Transformer-Mamba Language Model](https://mlsanity.com/paper/2403.19887/) (2024)
- [LoRA+: Efficient Low Rank Adaptation of Large Models](https://mlsanity.com/paper/2402.12354/) (2024)

## Built on by (most cited first, 11 of 11)

- [MambaPEFT: Exploring Parameter-Efficient Fine-Tuning for Mamba](https://mlsanity.com/paper/2411.03855/) (2024)
- [Expansion Span: Combining Fading Memory and Retrieval in Hybrid State Space Models](https://mlsanity.com/paper/2412.13328/) (2024)
- [Augmenting Perceptual Super-Resolution via Image Quality Predictors](https://mlsanity.com/paper/2504.18524/) (2025)
- [SF-Mamba: Rethinking State Space Model for Vision](https://mlsanity.com/paper/2603.16423/) (2026)
- [EMRRG: Efficient Fine-Tuning Pre-trained X-ray Mamba Networks for Radiology Report Generation](https://mlsanity.com/paper/2510.16776/) (2025)
- [S0 Tuning: Zero-Overhead Adaptation of Hybrid Recurrent-Attention Models](https://mlsanity.com/paper/2604.01168/) (2026)
- [WriteSAE: Sparse Autoencoders for Recurrent State](https://mlsanity.com/paper/2605.12770/) (2026)
- [SAM: A Mamba-2 State-Space Audio-Language Model](https://mlsanity.com/paper/2509.15680/) (2025)
- [Where Should LoRA Go? Component-Type Placement in Hybrid Language Models](https://mlsanity.com/paper/2604.22127/) (2026)
- [A Reference-Free Framework for Evaluating Single-Frame ISP Pipelines](https://mlsanity.com/paper/2607.23321/) (2026)
- [Energy- and Memory-Efficient PEFT Methods for Personalized On-Device SLMs on Consumer GPUs](https://mlsanity.com/paper/2608.04488/) (2026)

## Abstract (arXiv)

Deep State Space Models (SSMs), such as Mamba (Gu & Dao, 2024), have become powerful tools for language modeling, offering high performance and linear scalability with sequence length. However, the application of parameter-efficient fine-tuning (PEFT) methods to SSM-based models remains largely underexplored. We start by investigating two fundamental questions on existing PEFT methods: (i) How do they perform on SSM-based models? (ii) Which parameters should they target for optimal results? Our analysis shows that LoRA and its variants consistently outperform all other PEFT methods. While LoRA is effective for linear projection matrices, it fails on SSM modules-yet still outperforms other methods applicable to SSMs, indicating their limitations. This underscores the need for a specialized SSM tuning approach. To address this, we propose Sparse Dimension Tuning (SDT), a PEFT method tailored for SSM modules. Combining SDT for SSMs with LoRA for linear projection matrices, we achieve state-of-the-art performance across extensive experiments.