# Technologies on Effectiveness and Efficiency: A Survey of State Spaces Models

arXiv: https://arxiv.org/abs/2503.11224 · HTML: https://mlsanity.com/paper/2503.11224/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 85 of its 127 references that are in the map.
- First posted on arXiv 14 Mar 2025.

## Builds on (most cited first, 30 of 85)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [Long Range Arena: A Benchmark for Efficient Transformers](https://mlsanity.com/paper/2011.04006/) (2020)
- [HiPPO: Recurrent Memory with Optimal Polynomial Projections](https://mlsanity.com/paper/2008.07669/) (2020)
- [On the Parameterization and Initialization of Diagonal State Space Models](https://mlsanity.com/paper/2206.11893/) (2022)
- [Jamba: A Hybrid Transformer-Mamba Language Model](https://mlsanity.com/paper/2403.19887/) (2024)
- [Learning to (Learn at Test Time): RNNs with Expressive Hidden States](https://mlsanity.com/paper/2407.04620/) (2024)
- [MambaIR: A Simple Baseline for Image Restoration with State-Space Model](https://mlsanity.com/paper/2402.15648/) (2024)
- [VideoMamba: State Space Model for Efficient Video Understanding](https://mlsanity.com/paper/2403.06977/) (2024)
- [SegMamba: Long-range Sequential Modeling Mamba For 3D Medical Image Segmentation](https://mlsanity.com/paper/2401.13560/) (2024)
- [Long Range Language Modeling via Gated State Spaces](https://mlsanity.com/paper/2206.13947/) (2022)
- [LocalMamba: Visual State Space Model with Windowed Selective Scan](https://mlsanity.com/paper/2403.09338/) (2024)
- [Repeat After Me: Transformers are Better than State Space Models at Copying](https://mlsanity.com/paper/2402.01032/) (2024)
- [HyenaDNA: Long-Range Genomic Sequence Modeling at Single Nucleotide Resolution](https://mlsanity.com/paper/2306.15794/) (2023)
- [Samba: Simple Hybrid State Space Models for Efficient Unlimited Context Language Modeling](https://mlsanity.com/paper/2406.07522/) (2024)
- [PointMamba: A Simple State Space Model for Point Cloud Analysis](https://mlsanity.com/paper/2402.10739/) (2024)
- [Liquid Structural State-Space Models](https://mlsanity.com/paper/2209.12951/) (2022)
- [Graph-Mamba: Towards Long-Range Graph Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2402.00789/) (2024)
- [The Mamba in the Llama: Distilling and Accelerating Hybrid Models](https://mlsanity.com/paper/2408.15237/) (2024)
- [Is Mamba Effective for Time Series Forecasting?](https://mlsanity.com/paper/2403.11144/) (2024)
- [Caduceus: Bi-Directional Equivariant Long-Range DNA Sequence Modeling](https://mlsanity.com/paper/2403.03234/) (2024)
- [Video Mamba Suite: State Space Model as a Versatile Alternative for Video Understanding](https://mlsanity.com/paper/2403.09626/) (2024)
- [Long Movie Clip Classification with State-Space Video Models](https://mlsanity.com/paper/2204.01692/) (2022)
- [Can Mamba Learn How to Learn? A Comparative Study on In-Context Learning Tasks](https://mlsanity.com/paper/2402.04248/) (2024)
- [DeMamba: AI-Generated Video Detection on Million-Scale GenVideo Benchmark](https://mlsanity.com/paper/2405.19707/) (2024)
- [Graph Mamba: Towards Learning on Graphs with State Space Models](https://mlsanity.com/paper/2402.08678/) (2024)
- [SiMBA: Simplified Mamba-Based Architecture for Vision and Multivariate Time series](https://mlsanity.com/paper/2403.15360/) (2024)
- [Theoretical Foundations of Deep Selective State-Space Models](https://mlsanity.com/paper/2402.19047/) (2024)

## Built on by (most cited first, 2 of 2)

- [Reasoning Beyond Limits: Advances and Open Problems for LLMs](https://mlsanity.com/paper/2503.22732/) (2025)
- [StateX: Enhancing RNN Recall via Post-training State Expansion](https://mlsanity.com/paper/2509.22630/) (2025)

## Abstract (arXiv)

State Space Models (SSMs) have emerged as a promising alternative to the popular transformer-based models and have been increasingly gaining attention. Compared to transformers, SSMs excel at tasks with sequential data or longer contexts, demonstrating comparable performances with significant efficiency gains. In this survey, we provide a coherent and systematic overview for SSMs, including their theoretical motivations, mathematical formulations, comparison with existing model classes, and various applications. We divide the SSM series into three main sections, providing a detailed introduction to the original SSM, the structured SSM represented by S4, and the selective SSM typified by Mamba. We put an emphasis on technicality, and highlight the various key techniques introduced to address the effectiveness and efficiency of SSMs. We hope this manuscript serves as an introduction for researchers to explore the theoretical foundations of SSMs.