# The Gaussian Neural Process

arXiv: https://arxiv.org/abs/2101.03606 · HTML: https://mlsanity.com/paper/2101.03606/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 23 references that are in the map.
- First posted on arXiv 10 Jan 2021.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [Conditional Neural Processes](https://mlsanity.com/paper/1807.01613/) (2018)
- [Neural Processes](https://mlsanity.com/paper/1807.01622/) (2018)
- [Attentive Neural Processes](https://mlsanity.com/paper/1901.05761/) (2019)
- [Convolutional Conditional Neural Processes](https://mlsanity.com/paper/1910.13556/) (2019)
- [Universal approximations of invariant maps by neural networks](https://mlsanity.com/paper/1804.10306/) (2018)
- [Functional Variational Bayesian Neural Networks](https://mlsanity.com/paper/1903.05779/) (2019)
- [Meta-Learning Stationary Stochastic Process Prediction with Convolutional Neural Processes](https://mlsanity.com/paper/2007.01332/) (2020)
- [On Sparse variational methods and the Kullback-Leibler divergence between stochastic processes](https://mlsanity.com/paper/1504.07027/) (2015)
- [Variational Implicit Processes](https://mlsanity.com/paper/1806.02390/) (2018)
- [Scalable Training of Inference Networks for Gaussian-Process Models](https://mlsanity.com/paper/1905.10969/) (2019)

## Built on by (most cited first, 30 of 34)

- [Transformer Neural Processes: Uncertainty-Aware Meta Learning Via Sequence Modeling](https://mlsanity.com/paper/2207.04179/) (2022)
- [Priors in Bayesian Deep Learning: A Review](https://mlsanity.com/paper/2105.06868/) (2021)
- [Score-based Diffusion Models in Function Space](https://mlsanity.com/paper/2302.07400/) (2023)
- [Neural Diffusion Processes](https://mlsanity.com/paper/2206.03992/) (2022)
- [Autoregressive Conditional Neural Processes](https://mlsanity.com/paper/2303.14468/) (2023)
- [Latent Bottlenecked Attentive Neural Processes](https://mlsanity.com/paper/2211.08458/) (2022)
- [NP-Match: When Neural Processes meet Semi-Supervised Learning](https://mlsanity.com/paper/2207.01066/) (2022)
- [How Tight Can PAC-Bayes be in the Small Data Regime?](https://mlsanity.com/paper/2106.03542/) (2021)
- [The Neural Process Family: Survey, Applications and Perspectives](https://mlsanity.com/paper/2209.00517/) (2022)
- [Environmental Sensor Placement with Convolutional Gaussian Neural Processes](https://mlsanity.com/paper/2211.10381/) (2022)
- [Practical Equivariances via Relational Conditional Neural Processes](https://mlsanity.com/paper/2306.10915/) (2023)
- [Translation Equivariant Transformer Neural Processes](https://mlsanity.com/paper/2406.12409/) (2024)
- [Evidential Conditional Neural Processes](https://mlsanity.com/paper/2212.00131/) (2022)
- [Compositional Modeling of Nonlinear Dynamical Systems with ODE-based Random Features](https://mlsanity.com/paper/2106.05960/) (2021)
- [ALINE: Joint Amortization for Bayesian Inference and Active Data Acquisition](https://mlsanity.com/paper/2506.07259/) (2025)
- [Deep Stochastic Processes via Functional Markov Transition Operators](https://mlsanity.com/paper/2305.15574/) (2023)
- [Flow Matching Neural Processes](https://mlsanity.com/paper/2512.23853/) (2025)
- [NP-SemiSeg: When Neural Processes meet Semi-Supervised Semantic Segmentation](https://mlsanity.com/paper/2308.02866/) (2023)
- [Convolutional Neural Processes for Inpainting Satellite Images](https://mlsanity.com/paper/2205.12407/) (2022)
- [Spectral Convolutional Conditional Neural Processes](https://mlsanity.com/paper/2404.13182/) (2024)
- [Gridded Transformer Neural Processes for Large Unstructured Spatio-Temporal Data](https://mlsanity.com/paper/2410.06731/) (2024)
- [Efficient Autoregressive Inference for Transformer Probabilistic Models](https://mlsanity.com/paper/2510.09477/) (2025)
- [Adaptive Conditional Quantile Neural Processes](https://mlsanity.com/paper/2305.18777/) (2023)
- [Incorporating Prior Knowledge into Neural Networks through an Implicit Composite Kernel](https://mlsanity.com/paper/2205.07384/) (2022)
- [Bayesian Convolutional Deep Sets with Task-Dependent Stationary Prior](https://mlsanity.com/paper/2210.12363/) (2022)
- [Sparse Gaussian Neural Processes](https://mlsanity.com/paper/2504.01650/) (2025)
- [LLM Flow Processes for Text-Conditioned Regression](https://mlsanity.com/paper/2601.06147/) (2026)
- [Multi-Task Bayesian In-Context Learning](https://mlsanity.com/paper/2606.20538/) (2026)
- [Function-Space Regularization for Deep Bayesian Classification](https://mlsanity.com/paper/2307.06055/) (2023)
- [Neural Bridge Processes](https://mlsanity.com/paper/2508.07220/) (2025)

## Abstract (arXiv)

Neural Processes (NPs; Garnelo et al., 2018a,b) are a rich class of models for meta-learning that map data sets directly to predictive stochastic processes. We provide a rigorous analysis of the standard maximum-likelihood objective used to train conditional NPs. Moreover, we propose a new member to the Neural Process family called the Gaussian Neural Process (GNP), which models predictive correlations, incorporates translation equivariance, provides universal approximation guarantees, and demonstrates encouraging performance.