# IMSSA: Deploying modern state-space models on memristive in-memory compute hardware

arXiv: https://arxiv.org/abs/2412.20215 · HTML: https://mlsanity.com/paper/2412.20215/

## Key facts

- Cited by 2 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 10 of its 32 references that are in the map.
- First posted on arXiv 28 Dec 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, 10 of 10)

- [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)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [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)
- [The Era of 1-bit LLMs: All Large Language Models are in 1.58 Bits](https://mlsanity.com/paper/2402.17764/) (2024)
- [Do RNN and LSTM have Long Memory?](https://mlsanity.com/paper/2006.03860/) (2020)
- [Factorization tricks for LSTM networks](https://mlsanity.com/paper/1703.10722/) (2017)
- [Q-S5: Towards Quantized State Space Models](https://mlsanity.com/paper/2406.09477/) (2024)

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

- [The Curious Case of In-Training Compression of State Space Models](https://mlsanity.com/paper/2510.02823/) (2025)
- [QS4D: Quantization-aware training for efficient hardware deployment of structured state-space sequential models](https://mlsanity.com/paper/2507.06079/) (2025)

## Abstract (arXiv)

Processing long temporal sequences is a key challenge in deep learning. In recent years, Transformers have become state-of-the-art for this task, but suffer from excessive memory requirements due to the need to explicitly store the sequences. To address this issue, structured state-space sequential (S4) models recently emerged, offering a fixed memory state while still enabling the processing of very long sequence contexts. The recurrent linear update of the state in these models makes them highly efficient on modern graphics processing units (GPU) by unrolling the recurrence into a convolution. However, this approach demands significant memory and massively parallel computation, which is only available on the latest GPUs. In this work, we aim to bring the power of S4 models to edge hardware by significantly reducing the size and computational demand of an S4D model through quantization-aware training, even achieving ternary weights for a simple real-world task. To this end, we extend conventional quantization-aware training to tailor it for analog in-memory compute hardware. We then demonstrate the deployment of recurrent S4D kernels on memrisitve crossbar arrays, enabling their computation in an in-memory compute fashion. To our knowledge, this is the first implementation of S4 kernels on in-memory compute hardware.