# Modeling Latent Neural Dynamics with Gaussian Process Switching Linear Dynamical Systems

arXiv: https://arxiv.org/abs/2408.03330 · HTML: https://mlsanity.com/paper/2408.03330/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 69 references that are in the map.
- First posted on arXiv 19 Jul 2024.

## Builds on (most cited first, 20 of 20)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Variational Gaussian Process State-Space Models](https://mlsanity.com/paper/1406.4905/) (2014)
- [Black box variational inference for state space models](https://mlsanity.com/paper/1511.07367/) (2015)
- [Identification of Gaussian Process State Space Models](https://mlsanity.com/paper/1705.10888/) (2017)
- [Learning interpretable continuous-time models of latent stochastic dynamical systems](https://mlsanity.com/paper/1902.04420/) (2019)
- [Tree-Structured Recurrent Switching Linear Dynamical Systems for Multi-Scale Modeling](https://mlsanity.com/paper/1811.12386/) (2018)
- [Dual Parameterization of Sparse Variational Gaussian Processes](https://mlsanity.com/paper/2111.03412/) (2021)
- [Reverse engineering recurrent neural networks with Jacobian switching linear dynamical systems](https://mlsanity.com/paper/2111.01256/) (2021)
- [Amortized Reparametrization: Efficient and Scalable Variational Inference for Latent SDEs](https://mlsanity.com/paper/2312.10550/) (2023)
- [Decomposed Linear Dynamical Systems (dLDS) for learning the latent components of neural dynamics](https://mlsanity.com/paper/2206.02972/) (2022)
- [On Simplicity and Complexity in the Brave New World of Large-Scale Neuroscience](https://mlsanity.com/paper/1503.08779/) (2015)
- [Variational Gaussian Process Diffusion Processes](https://mlsanity.com/paper/2306.02066/) (2023)
- [Variational Inference for Continuous-Time Switching Dynamical Systems](https://mlsanity.com/paper/2109.14492/) (2021)
- [Expressive dynamics models with nonlinear injective readouts enable reliable recovery of latent features from neural activity](https://mlsanity.com/paper/2309.06402/) (2023)
- [Expectation propagation for continuous time stochastic processes](https://mlsanity.com/paper/1512.06098/) (2015)
- [Learning non-stationary Langevin dynamics from stochastic observations of latent trajectories](https://mlsanity.com/paper/2012.14944/) (2020)
- [Markov Chain Monte Carlo for Continuous-Time Switching Dynamical Systems](https://mlsanity.com/paper/2205.08803/) (2022)
- [Trainability, Expressivity and Interpretability in Gated Neural ODEs](https://mlsanity.com/paper/2307.06398/) (2023)
- [Empirical fixed point bifurcation analysis](https://mlsanity.com/paper/1807.01486/) (2018)

## Built on by (most cited first, 11 of 11)

- [Learning-to-Defer in Non-Stationary Time Series via Switching State-Space Models](https://mlsanity.com/paper/2601.22538/) (2026)
- [SING: SDE Inference via Natural Gradients](https://mlsanity.com/paper/2506.17796/) (2025)
- [Generative Modeling of Neural Dynamics via Latent Stochastic Differential Equations](https://mlsanity.com/paper/2412.12112/) (2024)
- [ODEBrain: Continuous-Time EEG Graph for Modeling Dynamic Brain Networks](https://mlsanity.com/paper/2602.23285/) (2026)
- [Modeling Neural Activity with Conditionally Linear Dynamical Systems](https://mlsanity.com/paper/2502.18347/) (2025)
- [Finding separatrices of dynamical flows with Deep Koopman Eigenfunctions](https://mlsanity.com/paper/2505.15231/) (2025)
- [Interpretable time series analysis with Gumbel dynamics](https://mlsanity.com/paper/2509.21578/) (2025)
- [Coupled Transformer Autoencoder for Disentangling Multi-Region Neural Latent Dynamics](https://mlsanity.com/paper/2510.20068/) (2025)
- [Nonlinear Dynamical Modeling of Human Intracranial Brain Activity with Flexible Inference](https://mlsanity.com/paper/2512.22785/) (2025)
- [Machine Learning Methods for Studying Latent Neural Activity Dynamics](https://mlsanity.com/paper/2606.10530/) (2026)
- [Simulation-Free Learning of GP-SDEs from Irregular Observations](https://mlsanity.com/paper/2609.33112/) (2026)

## Abstract (arXiv)

Understanding how the collective activity of neural populations relates to computation and ultimately behavior is a key goal in neuroscience. To this end, statistical methods which describe high-dimensional neural time series in terms of low-dimensional latent dynamics have played a fundamental role in characterizing neural systems. Yet, what constitutes a successful method involves two opposing criteria: (1) methods should be expressive enough to capture complex nonlinear dynamics, and (2) they should maintain a notion of interpretability often only warranted by simpler linear models. In this paper, we develop an approach that balances these two objectives: the Gaussian Process Switching Linear Dynamical System (gpSLDS). Our method builds on previous work modeling the latent state evolution via a stochastic differential equation whose nonlinear dynamics are described by a Gaussian process (GP-SDEs). We propose a novel kernel function which enforces smoothly interpolated locally linear dynamics, and therefore expresses flexible -- yet interpretable -- dynamics akin to those of recurrent switching linear dynamical systems (rSLDS). Our approach resolves key limitations of the rSLDS such as artifactual oscillations in dynamics near discrete state boundaries, while also providing posterior uncertainty estimates of the dynamics. To fit our models, we leverage a modified learning objective which improves the estimation accuracy of kernel hyperparameters compared to previous GP-SDE fitting approaches. We apply our method to synthetic data and data recorded in two neuroscience experiments and demonstrate favorable performance in comparison to the rSLDS.