# Group Equivariant Conditional Neural Processes

arXiv: https://arxiv.org/abs/2102.08759 · HTML: https://mlsanity.com/paper/2102.08759/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 35 references that are in the map.
- First posted on arXiv 17 Feb 2021.

## Builds on (most cited first, 29 of 29)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Xception: Deep Learning with Depthwise Separable Convolutions](https://mlsanity.com/paper/1610.02357/) (2016)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [PointConv: Deep Convolutional Networks on 3D Point Clouds](https://mlsanity.com/paper/1811.07246/) (2018)
- [Learning to learn by gradient descent by gradient descent](https://mlsanity.com/paper/1606.04474/) (2016)
- [Meta-Learning with Latent Embedding Optimization](https://mlsanity.com/paper/1807.05960/) (2018)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [Conditional Neural Processes](https://mlsanity.com/paper/1807.01613/) (2018)
- [On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groups](https://mlsanity.com/paper/1802.03690/) (2018)
- [Attentive Neural Processes](https://mlsanity.com/paper/1901.05761/) (2019)
- [Cormorant: Covariant Molecular Neural Networks](https://mlsanity.com/paper/1906.04015/) (2019)
- [Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data](https://mlsanity.com/paper/2002.12880/) (2020)
- [A General Theory of Equivariant CNNs on Homogeneous Spaces](https://mlsanity.com/paper/1811.02017/) (2018)
- [Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control](https://mlsanity.com/paper/1909.12077/) (2019)
- [Convolutional Conditional Neural Processes](https://mlsanity.com/paper/1910.13556/) (2019)
- [Hamiltonian Generative Networks](https://mlsanity.com/paper/1909.13789/) (2019)
- [Hamiltonian Graph Networks with ODE Integrators](https://mlsanity.com/paper/1909.12790/) (2019)
- [B-Spline CNNs on Lie Groups](https://mlsanity.com/paper/1909.12057/) (2019)
- [The Functional Neural Process](https://mlsanity.com/paper/1906.08324/) (2019)
- [Deep Learning on Lie Groups for Skeleton-based Action Recognition](https://mlsanity.com/paper/1612.05877/) (2016)
- [MetaFun: Meta-Learning with Iterative Functional Updates](https://mlsanity.com/paper/1912.02738/) (2019)
- [Depthwise Separable Convolutions for Neural Machine Translation](https://mlsanity.com/paper/1706.03059/) (2017)
- [Meta-Learning surrogate models for sequential decision making](https://mlsanity.com/paper/1903.11907/) (2019)
- [DeepSphere: towards an equivariant graph-based spherical CNN](https://mlsanity.com/paper/1904.05146/) (2019)
- [Learning Group Structure and Disentangled Representations of Dynamical Environments](https://mlsanity.com/paper/2002.06991/) (2020)

## Built on by (most cited first, 16 of 16)

- [Learning to Defer to a Population: A Meta-Learning Approach](https://mlsanity.com/paper/2403.02683/) (2024)
- [Practical Conditional Neural Processes Via Tractable Dependent Predictions](https://mlsanity.com/paper/2203.08775/) (2022)
- [The Neural Process Family: Survey, Applications and Perspectives](https://mlsanity.com/paper/2209.00517/) (2022)
- [Practical Equivariances via Relational Conditional Neural Processes](https://mlsanity.com/paper/2306.10915/) (2023)
- [Contrastive Conditional Neural Processes](https://mlsanity.com/paper/2203.03978/) (2022)
- [Beyond Unimodal: Generalising Neural Processes for Multimodal Uncertainty Estimation](https://mlsanity.com/paper/2304.01518/) (2023)
- [Efficient Gaussian Neural Processes for Regression](https://mlsanity.com/paper/2108.09676/) (2021)
- [Approximately Equivariant Neural Processes](https://mlsanity.com/paper/2406.13488/) (2024)
- [Bridge the Inference Gaps of Neural Processes via Expectation Maximization](https://mlsanity.com/paper/2501.03264/) (2025)
- [Deep Stochastic Processes via Functional Markov Transition Operators](https://mlsanity.com/paper/2305.15574/) (2023)
- [Spectral Convolutional Conditional Neural Processes](https://mlsanity.com/paper/2404.13182/) (2024)
- [Bayesian Convolutional Deep Sets with Task-Dependent Stationary Prior](https://mlsanity.com/paper/2210.12363/) (2022)
- [Exploiting Inferential Structure in Neural Processes](https://mlsanity.com/paper/2306.15169/) (2023)
- [CLIPSym: Delving into Symmetry Detection with CLIP](https://mlsanity.com/paper/2508.14197/) (2025)
- [Autoencoding Conditional Neural Processes for Representation Learning](https://mlsanity.com/paper/2305.18485/) (2023)
- [Revisiting Neural Processes via Fourier Transform and Volterra Series](https://mlsanity.com/paper/2606.01172/) (2026)

## Abstract (arXiv)

We present the group equivariant conditional neural process (EquivCNP), a meta-learning method with permutation invariance in a data set as in conventional conditional neural processes (CNPs), and it also has transformation equivariance in data space. Incorporating group equivariance, such as rotation and scaling equivariance, provides a way to consider the symmetry of real-world data. We give a decomposition theorem for permutation-invariant and group-equivariant maps, which leads us to construct EquivCNPs with an infinite-dimensional latent space to handle group symmetries. In this paper, we build architecture using Lie group convolutional layers for practical implementation. We show that EquivCNP with translation equivariance achieves comparable performance to conventional CNPs in a 1D regression task. Moreover, we demonstrate that incorporating an appropriate Lie group equivariance, EquivCNP is capable of zero-shot generalization for an image-completion task by selecting an appropriate Lie group equivariance.