# Thin and Deep Gaussian Processes

arXiv: https://arxiv.org/abs/2310.11527 · HTML: https://mlsanity.com/paper/2310.11527/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 23 references that are in the map.
- First posted on arXiv 17 Oct 2023.

## Builds on (most cited first, 9 of 9)

- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Doubly Stochastic Variational Inference for Deep Gaussian Processes](https://mlsanity.com/paper/1705.08933/) (2017)
- [GPflow: A Gaussian process library using TensorFlow](https://mlsanity.com/paper/1610.08733/) (2016)
- [The Promises and Pitfalls of Deep Kernel Learning](https://mlsanity.com/paper/2102.12108/) (2021)
- [Manifold Gaussian Processes for Regression](https://mlsanity.com/paper/1402.5876/) (2014)
- [Avoiding pathologies in very deep networks](https://mlsanity.com/paper/1402.5836/) (2014)
- [Non-Stationary Gaussian Process Regression with Hamiltonian Monte Carlo](https://mlsanity.com/paper/1508.04319/) (2015)
- [Deep Compositional Spatial Models](https://mlsanity.com/paper/1906.02840/) (2019)
- [GPflux: A Library for Deep Gaussian Processes](https://mlsanity.com/paper/2104.05674/) (2021)

## Built on by (most cited first, 3 of 3)

- [Universal Functional Regression with Neural Operator Flows](https://mlsanity.com/paper/2404.02986/) (2024)
- [Sparse Techniques for Regression in Deep Gaussian Processes](https://mlsanity.com/paper/2505.11355/) (2025)
- [Covariance-Boosted Gaussian Processes for Spatiotemporal Irregularities](https://mlsanity.com/paper/2607.23018/) (2026)

## Abstract (arXiv)

Gaussian processes (GPs) can provide a principled approach to uncertainty quantification with easy-to-interpret kernel hyperparameters, such as the lengthscale, which controls the correlation distance of function values. However, selecting an appropriate kernel can be challenging. Deep GPs avoid manual kernel engineering by successively parameterizing kernels with GP layers, allowing them to learn low-dimensional embeddings of the inputs that explain the output data. Following the architecture of deep neural networks, the most common deep GPs warp the input space layer-by-layer but lose all the interpretability of shallow GPs. An alternative construction is to successively parameterize the lengthscale of a kernel, improving the interpretability but ultimately giving away the notion of learning lower-dimensional embeddings. Unfortunately, both methods are susceptible to particular pathologies which may hinder fitting and limit their interpretability. This work proposes a novel synthesis of both previous approaches: Thin and Deep GP (TDGP). Each TDGP layer defines locally linear transformations of the original input data maintaining the concept of latent embeddings while also retaining the interpretation of lengthscales of a kernel. Moreover, unlike the prior solutions, TDGP induces non-pathological manifolds that admit learning lower-dimensional representations. We show with theoretical and experimental results that i) TDGP is, unlike previous models, tailored to specifically discover lower-dimensional manifolds in the input data, ii) TDGP behaves well when increasing the number of layers, and iii) TDGP performs well in standard benchmark datasets.