# Tree-Structured Recurrent Switching Linear Dynamical Systems for Multi-Scale Modeling

arXiv: https://arxiv.org/abs/1811.12386 · HTML: https://mlsanity.com/paper/1811.12386/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Nov 2018.

## Built on by (most cited first, 27 of 27)

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- [The Recurrent Sticky Hierarchical Dirichlet Process Hidden Markov Model](https://mlsanity.com/paper/2411.04278/) (2024)
- [Bayesian Inference in Recurrent Explicit Duration Switching Linear Dynamical Systems](https://mlsanity.com/paper/2411.04280/) (2024)
- [Decision Trees That Remember: Gradient-Based Learning of Recurrent Decision Trees with Memory](https://mlsanity.com/paper/2502.04052/) (2025)
- [Behavior-dLDS: A decomposed linear dynamical systems model for neural activity partially constrained by behavior](https://mlsanity.com/paper/2603.05612/) (2026)

## Abstract (arXiv)

Many real-world systems studied are governed by complex, nonlinear dynamics. By modeling these dynamics, we can gain insight into how these systems work, make predictions about how they will behave, and develop strategies for controlling them. While there are many methods for modeling nonlinear dynamical systems, existing techniques face a trade off between offering interpretable descriptions and making accurate predictions. Here, we develop a class of models that aims to achieve both simultaneously, smoothly interpolating between simple descriptions and more complex, yet also more accurate models. Our probabilistic model achieves this multi-scale property through a hierarchy of locally linear dynamics that jointly approximate global nonlinear dynamics. We call it the tree-structured recurrent switching linear dynamical system. To fit this model, we present a fully-Bayesian sampling procedure using Polya-Gamma data augmentation to allow for fast and conjugate Gibbs sampling. Through a variety of synthetic and real examples, we show how these models outperform existing methods in both interpretability and predictive capability.