# Global Convolutional Neural Processes

arXiv: https://arxiv.org/abs/2109.00691 · HTML: https://mlsanity.com/paper/2109.00691/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 20 references that are in the map.
- First posted on arXiv 2 Sep 2021.

## Builds on (most cited first, 16 of 16)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Interpreting the Latent Space of GANs for Semantic Face Editing](https://mlsanity.com/paper/1907.10786/) (2019)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [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)
- [Image Processing Using Multi-Code GAN Prior](https://mlsanity.com/paper/1912.07116/) (2019)
- [Convolutional Conditional Neural Processes](https://mlsanity.com/paper/1910.13556/) (2019)
- [Deep Convolutional Networks as shallow Gaussian Processes](https://mlsanity.com/paper/1808.05587/) (2018)
- [Meta-Learning Stationary Stochastic Process Prediction with Convolutional Neural Processes](https://mlsanity.com/paper/2007.01332/) (2020)
- [Sequential Neural Processes](https://mlsanity.com/paper/1906.10264/) (2019)
- [Joint Modeling of Local and Global Temporal Dynamics for Multivariate Time Series Forecasting with Missing Values](https://mlsanity.com/paper/1911.10273/) (2019)
- [Residual Attention U-Net for Automated Multi-Class Segmentation of COVID-19 Chest CT Images](https://mlsanity.com/paper/2004.05645/) (2020)
- [Task-Agnostic Online Reinforcement Learning with an Infinite Mixture of Gaussian Processes](https://mlsanity.com/paper/2006.11441/) (2020)
- [When and How to Lift the Lockdown? Global COVID-19 Scenario Analysis and Policy Assessment using Compartmental Gaussian Processes](https://mlsanity.com/paper/2005.08837/) (2020)

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

- [The Neural Process Family: Survey, Applications and Perspectives](https://mlsanity.com/paper/2209.00517/) (2022)
- [R'enyi Neural Processes](https://mlsanity.com/paper/2405.15991/) (2024)
- [Revisiting Neural Processes via Fourier Transform and Volterra Series](https://mlsanity.com/paper/2606.01172/) (2026)

## Abstract (arXiv)

The ability to deal with uncertainty in machine learning models has become equally, if not more, crucial to their predictive ability itself. For instance, during the pandemic, governmental policies and personal decisions are constantly made around uncertainties. Targeting this, Neural Process Families (NPFs) have recently shone a light on prediction with uncertainties by bridging Gaussian processes and neural networks. Latent neural process, a member of NPF, is believed to be capable of modelling the uncertainty on certain points (local uncertainty) as well as the general function priors (global uncertainties). Nonetheless, some critical questions remain unresolved, such as a formal definition of global uncertainties, the causality behind global uncertainties, and the manipulation of global uncertainties for generative models. Regarding this, we build a member GloBal Convolutional Neural Process(GBCoNP) that achieves the SOTA log-likelihood in latent NPFs. It designs a global uncertainty representation p(z), which is an aggregation on a discretized input space. The causal effect between the degree of global uncertainty and the intra-task diversity is discussed. The learnt prior is analyzed on a variety of scenarios, including 1D, 2D, and a newly proposed spatial-temporal COVID dataset. Our manipulation of the global uncertainty not only achieves generating the desired samples to tackle few-shot learning, but also enables the probability evaluation on the functional priors.