# Modeling Neural Activity with Conditionally Linear Dynamical Systems

arXiv: https://arxiv.org/abs/2502.18347 · HTML: https://mlsanity.com/paper/2502.18347/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 62 references that are in the map.
- First posted on arXiv 25 Feb 2025.

## Builds on (most cited first, 19 of 19)

- [Variational Fourier features for Gaussian processes](https://mlsanity.com/paper/1611.06740/) (2016)
- [Mat'ern Gaussian processes on Riemannian manifolds](https://mlsanity.com/paper/2006.10160/) (2020)
- [A Unified, Scalable Framework for Neural Population Decoding](https://mlsanity.com/paper/2310.16046/) (2023)
- [Neural Latents Benchmark '21: Evaluating latent variable models of neural population activity](https://mlsanity.com/paper/2109.04463/) (2021)
- [Generalized Teacher Forcing for Learning Chaotic Dynamics](https://mlsanity.com/paper/2306.04406/) (2023)
- [Representation learning for neural population activity with Neural Data Transformers](https://mlsanity.com/paper/2108.01210/) (2021)
- [Tree-Structured Recurrent Switching Linear Dynamical Systems for Multi-Scale Modeling](https://mlsanity.com/paper/1811.12386/) (2018)
- [Beyond Geometry: Comparing the Temporal Structure of Computation in Neural Circuits with Dynamical Similarity Analysis](https://mlsanity.com/paper/2306.10168/) (2023)
- [Almost-Linear RNNs Yield Highly Interpretable Symbolic Codes in Dynamical Systems Reconstruction](https://mlsanity.com/paper/2410.14240/) (2024)
- [Reverse engineering recurrent neural networks with Jacobian switching linear dynamical systems](https://mlsanity.com/paper/2111.01256/) (2021)
- [Decomposed Linear Dynamical Systems (dLDS) for learning the latent components of neural dynamics](https://mlsanity.com/paper/2206.02972/) (2022)
- [Inferring stochastic low-rank recurrent neural networks from neural data](https://mlsanity.com/paper/2406.16749/) (2024)
- [Latent Diffusion for Neural Spiking Data](https://mlsanity.com/paper/2407.08751/) (2024)
- [Modeling Latent Neural Dynamics with Gaussian Process Switching Linear Dynamical Systems](https://mlsanity.com/paper/2408.03330/) (2024)
- [Hida-Mat'ern Kernel](https://mlsanity.com/paper/2107.07098/) (2021)
- [Linear Time GPs for Inferring Latent Trajectories from Neural Spike Trains](https://mlsanity.com/paper/2306.01802/) (2023)
- [Multi-Region Markovian Gaussian Process: An Efficient Method to Discover Directional Communications Across Multiple Brain Regions](https://mlsanity.com/paper/2402.02686/) (2024)
- [Statistical Neuroscience in the Single Trial Limit](https://mlsanity.com/paper/2103.05075/) (2021)
- [Comparing noisy neural population dynamics using optimal transport distances](https://mlsanity.com/paper/2412.14421/) (2024)

## Built on by (most cited first, 1 of 1)

- [Behavior-dLDS: A decomposed linear dynamical systems model for neural activity partially constrained by behavior](https://mlsanity.com/paper/2603.05612/) (2026)

## Abstract (arXiv)

Neural population activity exhibits complex, nonlinear dynamics, varying in time, over trials, and across experimental conditions. Here, we develop Conditionally Linear Dynamical System (CLDS) models as a general-purpose method to characterize these dynamics. These models use Gaussian Process (GP) priors to capture the nonlinear dependence of circuit dynamics on task and behavioral variables. Conditioned on these covariates, the data is modeled with linear dynamics. This allows for transparent interpretation and tractable Bayesian inference. We find that CLDS models can perform well even in severely data-limited regimes (e.g. one trial per condition) due to their Bayesian formulation and ability to share statistical power across nearby task conditions. In example applications, we apply CLDS to model thalamic neurons that nonlinearly encode heading direction and to model motor cortical neurons during a cued reaching task.