# Neural Dynamics Discovery via Gaussian Process Recurrent Neural Networks

arXiv: https://arxiv.org/abs/1907.00650 · HTML: https://mlsanity.com/paper/1907.00650/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jul 2019.

## Built on by (most cited first, 13 of 13)

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- [Bayesian Non-linear Latent Variable Modeling via Random Fourier Features](https://mlsanity.com/paper/2306.08352/) (2023)
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- [Compressed Predictive Information Coding](https://mlsanity.com/paper/2203.02051/) (2022)
- [Dynamical modeling of nonlinear latent factors in multiscale neural activity with real-time inference](https://mlsanity.com/paper/2512.12462/) (2025)
- [Deep Probabilistic Time Series Forecasting using Augmented Recurrent Input for Dynamic Systems](https://mlsanity.com/paper/2106.05848/) (2021)
- [Bayesian Inference in High-Dimensional Time-Serieswith the Orthogonal Stochastic Linear Mixing Model](https://mlsanity.com/paper/2106.13379/) (2021)
- [A Factorized Low-Rank RNN Framework for Uncovering Independent Neural Latent Dynamics and Connectivity](https://mlsanity.com/paper/2511.13899/) (2025)
- [When predict can also explain: few-shot prediction to select better neural latents](https://mlsanity.com/paper/2405.14425/) (2024)

## Abstract (arXiv)

Latent dynamics discovery is challenging in extracting complex dynamics from high-dimensional noisy neural data. Many dimensionality reduction methods have been widely adopted to extract low-dimensional, smooth and time-evolving latent trajectories. However, simple state transition structures, linear embedding assumptions, or inflexible inference networks impede the accurate recovery of dynamic portraits. In this paper, we propose a novel latent dynamic model that is capable of capturing nonlinear, non-Markovian, long short-term time-dependent dynamics via recurrent neural networks and tackling complex nonlinear embedding via non-parametric Gaussian process. Due to the complexity and intractability of the model and its inference, we also provide a powerful inference network with bi-directional long short-term memory networks that encode both past and future information into posterior distributions. In the experiment, we show that our model outperforms other state-of-the-art methods in reconstructing insightful latent dynamics from both simulated and experimental neural datasets with either Gaussian or Poisson observations, especially in the low-sample scenario. Our codes and additional materials are available at https://github.com/sheqi/GP-RNN_UAI2019.