# Efficient Gaussian Neural Processes for Regression

arXiv: https://arxiv.org/abs/2108.09676 · HTML: https://mlsanity.com/paper/2108.09676/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 10 references that are in the map.
- First posted on arXiv 22 Aug 2021.

## Builds on (most cited first, 7 of 7)

- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Conditional Neural Processes](https://mlsanity.com/paper/1807.01613/) (2018)
- [Neural Processes](https://mlsanity.com/paper/1807.01622/) (2018)
- [Convolutional Conditional Neural Processes](https://mlsanity.com/paper/1910.13556/) (2019)
- [Meta-Learning Stationary Stochastic Process Prediction with Convolutional Neural Processes](https://mlsanity.com/paper/2007.01332/) (2020)
- [Group Equivariant Conditional Neural Processes](https://mlsanity.com/paper/2102.08759/) (2021)

## Built on by (most cited first, 10 of 10)

- [Autoregressive Conditional Neural Processes](https://mlsanity.com/paper/2303.14468/) (2023)
- [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)
- [Evidential Conditional Neural Processes](https://mlsanity.com/paper/2212.00131/) (2022)
- [Convolutional Neural Processes for Inpainting Satellite Images](https://mlsanity.com/paper/2205.12407/) (2022)
- [Real-time Adaptation for Condition Monitoring Signal Prediction using Label-aware Neural Processes](https://mlsanity.com/paper/2403.16377/) (2024)
- [Incorporating Prior Knowledge into Neural Networks through an Implicit Composite Kernel](https://mlsanity.com/paper/2205.07384/) (2022)
- [Sparse Gaussian Neural Processes](https://mlsanity.com/paper/2504.01650/) (2025)
- [Beyond Intuition, a Framework for Applying GPs to Real-World Data](https://mlsanity.com/paper/2307.03093/) (2023)
- [LLM Flow Processes for Text-Conditioned Regression](https://mlsanity.com/paper/2601.06147/) (2026)

## Abstract (arXiv)

Conditional Neural Processes (CNP; Garnelo et al., 2018) are an attractive family of meta-learning models which produce well-calibrated predictions, enable fast inference at test time, and are trainable via a simple maximum likelihood procedure. A limitation of CNPs is their inability to model dependencies in the outputs. This significantly hurts predictive performance and renders it impossible to draw coherent function samples, which limits the applicability of CNPs in down-stream applications and decision making. Neural Processes (NPs; Garnelo et al., 2018) attempt to alleviate this issue by using latent variables, relying on these to model output dependencies, but introduces difficulties stemming from approximate inference. One recent alternative (Bruinsma et al., 2021), which we refer to as the FullConvGNP, models dependencies in the predictions while still being trainable via exact maximum-likelihood. Unfortunately, the FullConvGNP relies on expensive 2D-dimensional convolutions, which limit its applicability to only one-dimensional data. In this work, we present an alternative way to model output dependencies which also lends itself maximum likelihood training but, unlike the FullConvGNP, can be scaled to two- and three-dimensional data. The proposed models exhibit good performance in synthetic experiments.