# Recurrent switching linear dynamical systems

arXiv: https://arxiv.org/abs/1610.08466 · HTML: https://mlsanity.com/paper/1610.08466/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Oct 2016.

## Built on by (most cited first, 30 of 35)

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- [Almost-Linear RNNs Yield Highly Interpretable Symbolic Codes in Dynamical Systems Reconstruction](https://mlsanity.com/paper/2410.14240/) (2024)
- [Deep Explicit Duration Switching Models for Time Series](https://mlsanity.com/paper/2110.13878/) (2021)
- [Decomposed Linear Dynamical Systems (dLDS) for learning the latent components of neural dynamics](https://mlsanity.com/paper/2206.02972/) (2022)
- [Graph Switching Dynamical Systems](https://mlsanity.com/paper/2306.00370/) (2023)
- [On the Identifiability of Switching Dynamical Systems](https://mlsanity.com/paper/2305.15925/) (2023)
- [A scalable generative model for dynamical system reconstruction from neuroimaging data](https://mlsanity.com/paper/2411.02949/) (2024)
- [Continuous Locomotive Crowd Behavior Generation](https://mlsanity.com/paper/2504.04756/) (2025)
- [POCO: Scalable Neural Forecasting through Population Conditioning](https://mlsanity.com/paper/2506.14957/) (2025)
- [Probabilistic Decomposed Linear Dynamical Systems for Robust Discovery of Latent Neural Dynamics](https://mlsanity.com/paper/2408.16862/) (2024)
- [Inverse Reinforcement Learning with Switching Rewards and History Dependency for Characterizing Animal Behaviors](https://mlsanity.com/paper/2501.12633/) (2025)
- [Learning-to-Defer in Non-Stationary Time Series via Switching State-Space Models](https://mlsanity.com/paper/2601.22538/) (2026)
- [SiBBlInGS: Similarity-driven Building-Block Inference using Graphs across States](https://mlsanity.com/paper/2306.04817/) (2023)
- [Uncovering the Computational Roles of Nonlinearity in Sequence Modeling Using Almost-Linear RNNs](https://mlsanity.com/paper/2506.07919/) (2025)
- [Conformal Prediction for Time-series Forecasting with Change Points](https://mlsanity.com/paper/2509.02844/) (2025)
- [Navigation under uncertainty: Trajectory prediction and occlusion reasoning with switching dynamical systems](https://mlsanity.com/paper/2410.10653/) (2024)
- [Continuous-Time Piecewise-Linear Recurrent Neural Networks](https://mlsanity.com/paper/2602.15649/) (2026)
- [Position: A Dynamical Systems Perspective is Needed to Advance Time Series Modeling](https://mlsanity.com/paper/2602.16864/) (2026)
- [Segmenting Hybrid Trajectories using Latent ODEs](https://mlsanity.com/paper/2105.03835/) (2021)
- [AXIOM: Learning to Play Games in Minutes with Expanding Object-Centric Models](https://mlsanity.com/paper/2505.24784/) (2025)
- [Detecting Invariant Manifolds in ReLU-Based RNNs](https://mlsanity.com/paper/2510.03814/) (2025)
- [Learning Reactive and Predictive Differentiable Controllers for Switching Linear Dynamical Models](https://mlsanity.com/paper/2103.14256/) (2021)
- [LINOCS: Lookahead Inference of Networked Operators for Continuous Stability](https://mlsanity.com/paper/2404.18267/) (2024)
- [A study of animal action segmentation algorithms across supervised, unsupervised, and semi-supervised learning paradigms](https://mlsanity.com/paper/2407.16727/) (2024)
- [Parameter-varying neural ordinary differential equations with partition-of-unity networks](https://mlsanity.com/paper/2210.00368/) (2022)
- [Long Range Switching Time Series Prediction via State Space Model](https://mlsanity.com/paper/2407.19201/) (2024)
- [Hybrid Recurrent Models Support Emergent Descriptions for Hierarchical Planning and Control](https://mlsanity.com/paper/2408.10970/) (2024)

## Abstract (arXiv)

Many natural systems, such as neurons firing in the brain or basketball teams traversing a court, give rise to time series data with complex, nonlinear dynamics. We can gain insight into these systems by decomposing the data into segments that are each explained by simpler dynamic units. Building on switching linear dynamical systems (SLDS), we present a new model class that not only discovers these dynamical units, but also explains how their switching behavior depends on observations or continuous latent states. These "recurrent" switching linear dynamical systems provide further insight by discovering the conditions under which each unit is deployed, something that traditional SLDS models fail to do. We leverage recent algorithmic advances in approximate inference to make Bayesian inference in these models easy, fast, and scalable.