# Equivariant Learning of Stochastic Fields: Gaussian Processes and Steerable Conditional Neural Processes

arXiv: https://arxiv.org/abs/2011.12916 · HTML: https://mlsanity.com/paper/2011.12916/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Nov 2020.

## Built on by (most cited first, 29 of 29)

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- [Beyond Unimodal: Generalising Neural Processes for Multimodal Uncertainty Estimation](https://mlsanity.com/paper/2304.01518/) (2023)
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- [Memory Efficient Neural Processes via Constant Memory Attention Block](https://mlsanity.com/paper/2305.14567/) (2023)
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- [Bayesian Convolutional Deep Sets with Task-Dependent Stationary Prior](https://mlsanity.com/paper/2210.12363/) (2022)
- [Efficiently Computable Safety Bounds for Gaussian Processes in Active Learning](https://mlsanity.com/paper/2402.18260/) (2024)
- [Adversarially Contrastive Estimation of Conditional Neural Processes](https://mlsanity.com/paper/2303.13004/) (2023)
- [On the Laplace Approximation as Model Selection Criterion for Gaussian Processes](https://mlsanity.com/paper/2403.09215/) (2024)
- [Fine-Tuning Flow Matching via Maximum Likelihood Estimation of Reconstructions](https://mlsanity.com/paper/2510.02081/) (2025)
- [From Drops to Grid: Noise-Aware Spatio-Temporal Neural Process for Rainfall Estimation](https://mlsanity.com/paper/2605.05912/) (2026)
- [Revisiting Neural Processes via Fourier Transform and Volterra Series](https://mlsanity.com/paper/2606.01172/) (2026)
- [Triply-Scalable Equivariant Gaussian Process Modeling](https://mlsanity.com/paper/2609.21085/) (2026)

## Abstract (arXiv)

Motivated by objects such as electric fields or fluid streams, we study the problem of learning stochastic fields, i.e. stochastic processes whose samples are fields like those occurring in physics and engineering. Considering general transformations such as rotations and reflections, we show that spatial invariance of stochastic fields requires an inference model to be equivariant. Leveraging recent advances from the equivariance literature, we study equivariance in two classes of models. Firstly, we fully characterise equivariant Gaussian processes. Secondly, we introduce Steerable Conditional Neural Processes (SteerCNPs), a new, fully equivariant member of the Neural Process family. In experiments with Gaussian process vector fields, images, and real-world weather data, we observe that SteerCNPs significantly improve the performance of previous models and equivariance leads to improvements in transfer learning tasks.