# Convolutional Conditional Neural Processes

arXiv: https://arxiv.org/abs/1910.13556 · HTML: https://mlsanity.com/paper/1910.13556/

## Key facts

- Cited by 142 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Oct 2019.

## Built on by (most cited first, 30 of 142)

- [PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers](https://mlsanity.com/paper/2308.05732/) (2023)
- [From data to functa: Your data point is a function and you can treat it like one](https://mlsanity.com/paper/2201.12204/) (2022)
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- [Priors in Bayesian Deep Learning: A Review](https://mlsanity.com/paper/2105.06868/) (2021)
- [Generative Models as Distributions of Functions](https://mlsanity.com/paper/2102.04776/) (2021)
- [Position: Bayesian Deep Learning is Needed in the Age of Large-Scale AI](https://mlsanity.com/paper/2402.00809/) (2024)
- [Neural ODE Processes](https://mlsanity.com/paper/2103.12413/) (2021)
- [Neural Diffusion Processes](https://mlsanity.com/paper/2206.03992/) (2022)
- [Few-Shot Diffusion Models](https://mlsanity.com/paper/2205.15463/) (2022)
- [Generative Pretraining for Black-Box Optimization](https://mlsanity.com/paper/2206.10786/) (2022)
- [The Gaussian Neural Process](https://mlsanity.com/paper/2101.03606/) (2021)
- [Context-Aware Safe Reinforcement Learning for Non-Stationary Environments](https://mlsanity.com/paper/2101.00531/) (2021)
- [Autoregressive Conditional Neural Processes](https://mlsanity.com/paper/2303.14468/) (2023)
- [End-to-End Meta-Bayesian Optimisation with Transformer Neural Processes](https://mlsanity.com/paper/2305.15930/) (2023)
- [Convolutional conditional neural processes for local climate downscaling](https://mlsanity.com/paper/2101.07950/) (2021)
- [Learning to Defer to a Population: A Meta-Learning Approach](https://mlsanity.com/paper/2403.02683/) (2024)
- [Latent Bottlenecked Attentive Neural Processes](https://mlsanity.com/paper/2211.08458/) (2022)
- [Practical Conditional Neural Processes Via Tractable Dependent Predictions](https://mlsanity.com/paper/2203.08775/) (2022)
- [NP-Match: When Neural Processes meet Semi-Supervised Learning](https://mlsanity.com/paper/2207.01066/) (2022)
- [Spectral Diffusion Processes](https://mlsanity.com/paper/2209.14125/) (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)
- [Amortized Probabilistic Conditioning for Optimization, Simulation and Inference](https://mlsanity.com/paper/2410.15320/) (2024)
- [ExPT: Synthetic Pretraining for Few-Shot Experimental Design](https://mlsanity.com/paper/2310.19961/) (2023)
- [Model Predictive Task Sampling for Efficient and Robust Adaptation](https://mlsanity.com/paper/2501.11039/) (2025)
- [Graph Neural Processes for Spatio-Temporal Extrapolation](https://mlsanity.com/paper/2305.18719/) (2023)
- [What Matters For Meta-Learning Vision Regression Tasks?](https://mlsanity.com/paper/2203.04905/) (2022)
- [Meta Temporal Point Processes](https://mlsanity.com/paper/2301.12023/) (2023)
- [Group Equivariant Conditional Neural Processes](https://mlsanity.com/paper/2102.08759/) (2021)

## Abstract (arXiv)

We introduce the Convolutional Conditional Neural Process (ConvCNP), a new member of the Neural Process family that models translation equivariance in the data. Translation equivariance is an important inductive bias for many learning problems including time series modelling, spatial data, and images. The model embeds data sets into an infinite-dimensional function space as opposed to a finite-dimensional vector space. To formalize this notion, we extend the theory of neural representations of sets to include functional representations, and demonstrate that any translation-equivariant embedding can be represented using a convolutional deep set. We evaluate ConvCNPs in several settings, demonstrating that they achieve state-of-the-art performance compared to existing NPs. We demonstrate that building in translation equivariance enables zero-shot generalization to challenging, out-of-domain tasks.