# Linear dynamical neural population models through nonlinear embeddings

arXiv: https://arxiv.org/abs/1605.08454 · HTML: https://mlsanity.com/paper/1605.08454/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 May 2016.

## Built on by (most cited first, 30 of 36)

- [Neural Latents Benchmark '21: Evaluating latent variable models of neural population activity](https://mlsanity.com/paper/2109.04463/) (2021)
- [Representation learning for neural population activity with Neural Data Transformers](https://mlsanity.com/paper/2108.01210/) (2021)
- [Diagnosing and Fixing Manifold Overfitting in Deep Generative Models](https://mlsanity.com/paper/2204.07172/) (2022)
- [STNDT: Modeling Neural Population Activity with a Spatiotemporal Transformer](https://mlsanity.com/paper/2206.04727/) (2022)
- [Drop, Swap, and Generate: A Self-Supervised Approach for Generating Neural Activity](https://mlsanity.com/paper/2111.02338/) (2021)
- [Entropic Issues in Likelihood-Based OOD Detection](https://mlsanity.com/paper/2109.10794/) (2021)
- [Beyond expectations: Residual Dynamic Mode Decomposition and Variance for Stochastic Dynamical Systems](https://mlsanity.com/paper/2308.10697/) (2023)
- [Building population models for large-scale neural recordings: opportunities and pitfalls](https://mlsanity.com/paper/2102.01807/) (2021)
- [Self-supervised contrastive learning performs non-linear system identification](https://mlsanity.com/paper/2410.14673/) (2024)
- [Learning Time-Invariant Representations for Individual Neurons from Population Dynamics](https://mlsanity.com/paper/2311.02258/) (2023)
- [BRAID: Input-Driven Nonlinear Dynamical Modeling of Neural-Behavioral Data](https://mlsanity.com/paper/2509.18627/) (2025)
- [BaRISTA: Brain Scale Informed Spatiotemporal Representation of Human Intracranial Neural Activity](https://mlsanity.com/paper/2512.12135/) (2025)
- [Deep inference of latent dynamics with spatio-temporal super-resolution using selective backpropagation through time](https://mlsanity.com/paper/2111.00070/) (2021)
- [Expressive architectures enhance interpretability of dynamics-based neural population models](https://mlsanity.com/paper/2212.03771/) (2022)
- [BACE: Behavior-Adaptive Connectivity Estimation for Interpretable Graphs of Neural Dynamics](https://mlsanity.com/paper/2510.20831/) (2025)
- [Provably Scalable Black-Box Variational Inference with Structured Variational Families](https://mlsanity.com/paper/2401.10989/) (2024)
- [BLEND: Behavior-guided Neural Population Dynamics Modeling via Privileged Knowledge Distillation](https://mlsanity.com/paper/2410.13872/) (2024)
- [Cross-Modal Representational Knowledge Distillation for Enhanced Spike-Informed LFP Modeling](https://mlsanity.com/paper/2512.12461/) (2025)
- [Mesoscopic modeling of hidden spiking neurons](https://mlsanity.com/paper/2205.13493/) (2022)
- [TR0N: Translator Networks for 0-Shot Plug-and-Play Conditional Generation](https://mlsanity.com/paper/2304.13742/) (2023)
- [DeepGraphDMD: Interpretable Spatio-Temporal Decomposition of Non-linear Functional Brain Network Dynamics](https://mlsanity.com/paper/2306.03088/) (2023)
- [Dynamical modeling of nonlinear latent factors in multiscale neural activity with real-time inference](https://mlsanity.com/paper/2512.12462/) (2025)
- [Bayesian Inference in High-Dimensional Time-Serieswith the Orthogonal Stochastic Linear Mixing Model](https://mlsanity.com/paper/2106.13379/) (2021)
- [Neuronal Learning Analysis using Cycle-Consistent Adversarial Networks](https://mlsanity.com/paper/2111.13073/) (2021)
- [Inferring Inference](https://mlsanity.com/paper/2310.03186/) (2023)
- [Diffusion-Based Generation of Neural Activity from Disentangled Latent Codes](https://mlsanity.com/paper/2407.21195/) (2024)
- [Active learning of neural population dynamics using two-photon holographic optogenetics](https://mlsanity.com/paper/2412.02529/) (2024)
- [Deep Probabilistic Graphical Modeling](https://mlsanity.com/paper/2104.12053/) (2021)
- [Bubblewrap: Online tiling and real-time flow prediction on neural manifolds](https://mlsanity.com/paper/2108.13941/) (2021)
- [Overcoming the Domain Gap in Contrastive Learning of Neural Action Representations](https://mlsanity.com/paper/2111.14595/) (2021)

## Abstract (arXiv)

A body of recent work in modeling neural activity focuses on recovering low-dimensional latent features that capture the statistical structure of large-scale neural populations. Most such approaches have focused on linear generative models, where inference is computationally tractable. Here, we propose fLDS, a general class of nonlinear generative models that permits the firing rate of each neuron to vary as an arbitrary smooth function of a latent, linear dynamical state. This extra flexibility allows the model to capture a richer set of neural variability than a purely linear model, but retains an easily visualizable low-dimensional latent space. To fit this class of non-conjugate models we propose a variational inference scheme, along with a novel approximate posterior capable of capturing rich temporal correlations across time. We show that our techniques permit inference in a wide class of generative models.We also show in application to two neural datasets that, compared to state-of-the-art neural population models, fLDS captures a much larger proportion of neural variability with a small number of latent dimensions, providing superior predictive performance and interpretability.