# Structured state-space models are deep Wiener models

arXiv: https://arxiv.org/abs/2312.06211 · HTML: https://mlsanity.com/paper/2312.06211/

## Key facts

- Cited by 4 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 16 of its 30 references that are in the map.
- First posted on arXiv 11 Dec 2023.

## 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, 16 of 16)

- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [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)
- [Resurrecting Recurrent Neural Networks for Long Sequences](https://mlsanity.com/paper/2303.06349/) (2023)
- [Diagonal State Spaces are as Effective as Structured State Spaces](https://mlsanity.com/paper/2203.14343/) (2022)
- [On weight initialization in deep neural networks](https://mlsanity.com/paper/1704.08863/) (2017)
- [Stable Recurrent Models](https://mlsanity.com/paper/1805.10369/) (2018)
- [Nonlinear System Identification: A User-Oriented Roadmap](https://mlsanity.com/paper/1902.00683/) (2019)
- [dynoNet: a neural network architecture for learning dynamical systems](https://mlsanity.com/paper/2006.02250/) (2020)
- [Deep Convolutional Networks in System Identification](https://mlsanity.com/paper/1909.01730/) (2019)
- [Identification of block-oriented nonlinear systems starting from linear approximations: A survey](https://mlsanity.com/paper/1607.01217/) (2016)
- [On Recurrent Neural Networks for learning-based control: recent results and ideas for future developments](https://mlsanity.com/paper/2111.13557/) (2021)
- [Nonlinear MPC design for incrementally ISS systems with application to GRU networks](https://mlsanity.com/paper/2309.16428/) (2023)
- [Improved Initialization for Nonlinear State-Space Modeling](https://mlsanity.com/paper/1804.08654/) (2018)
- [Wiener system identification with generalized orthonormal basis functions](https://mlsanity.com/paper/1612.04558/) (2016)

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

- [State Space Model for New-Generation Network Alternative to Transformers: A Survey](https://mlsanity.com/paper/2404.09516/) (2024)
- [L2RU: a Structured State Space Model with prescribed L2-bound](https://mlsanity.com/paper/2503.23818/) (2025)
- [Controller Design for Structured State-space Models via Contraction Theory](https://mlsanity.com/paper/2604.07069/) (2026)
- [Stability-Preserving Online Adaptation of Neural Closed-loop Maps](https://mlsanity.com/paper/2603.22469/) (2026)

## Abstract (arXiv)

The goal of this paper is to provide a system identification-friendly introduction to the Structured State-space Models (SSMs). These models have become recently popular in the machine learning community since, owing to their parallelizability, they can be efficiently and scalably trained to tackle extremely-long sequence classification and regression problems. Interestingly, SSMs appear as an effective way to learn deep Wiener models, which allows to reframe SSMs as an extension of a model class commonly used in system identification. In order to stimulate a fruitful exchange of ideas between the machine learning and system identification communities, we deem it useful to summarize the recent contributions on the topic in a structured and accessible form. At last, we highlight future research directions for which this community could provide impactful contributions.