# Deep learning with differential Gaussian process flows

arXiv: https://arxiv.org/abs/1810.04066 · HTML: https://mlsanity.com/paper/1810.04066/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Oct 2018.

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

- [Infinitely Deep Bayesian Neural Networks with Stochastic Differential Equations](https://mlsanity.com/paper/2102.06559/) (2021)
- [Constructing Neural Network-Based Models for Simulating Dynamical Systems](https://mlsanity.com/paper/2111.01495/) (2021)
- [Scalable Inference in SDEs by Direct Matching of the Fokker-Planck-Kolmogorov Equation](https://mlsanity.com/paper/2110.15739/) (2021)
- [Inferring the Structure of Ordinary Differential Equations](https://mlsanity.com/paper/2107.07345/) (2021)
- [Bayesian Gaussian Process ODEs via Double Normalizing Flows](https://mlsanity.com/paper/2309.09222/) (2023)
- [Fully Bayesian Differential Gaussian Processes through Stochastic Differential Equations](https://mlsanity.com/paper/2408.06069/) (2024)
- [A General Framework for Uncertainty Quantification via Neural SDE-RNN](https://mlsanity.com/paper/2306.01189/) (2023)
- [Approximate Latent Force Model Inference](https://mlsanity.com/paper/2109.11851/) (2021)
- [Aligned Multi-Task Gaussian Process](https://mlsanity.com/paper/2110.15761/) (2021)
- [Shallow and Deep Nonparametric Convolutions for Gaussian Processes](https://mlsanity.com/paper/2206.08972/) (2022)
- [Traversing Time with Multi-Resolution Gaussian Process State-Space Models](https://mlsanity.com/paper/2112.03230/) (2021)

## Abstract (arXiv)

We propose a novel deep learning paradigm of differential flows that learn a stochastic differential equation transformations of inputs prior to a standard classification or regression function. The key property of differential Gaussian processes is the warping of inputs through infinitely deep, but infinitesimal, differential fields, that generalise discrete layers into a dynamical system. We demonstrate state-of-the-art results that exceed the performance of deep Gaussian processes and neural networks