# Practical Equivariances via Relational Conditional Neural Processes

arXiv: https://arxiv.org/abs/2306.10915 · HTML: https://mlsanity.com/paper/2306.10915/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 44 references that are in the map.
- First posted on arXiv 19 Jun 2023.

## Builds on (most cited first, 27 of 27)

- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Learning to Compare: Relation Network for Few-Shot Learning](https://mlsanity.com/paper/1711.06025/) (2017)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Conditional Neural Processes](https://mlsanity.com/paper/1807.01613/) (2018)
- [The Expressive Power of Neural Networks: A View from the Width](https://mlsanity.com/paper/1709.02540/) (2017)
- [Neural Processes](https://mlsanity.com/paper/1807.01622/) (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)
- [Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data](https://mlsanity.com/paper/2002.12880/) (2020)
- [Convolutional Conditional Neural Processes](https://mlsanity.com/paper/1910.13556/) (2019)
- [Transformer Neural Processes: Uncertainty-Aware Meta Learning Via Sequence Modeling](https://mlsanity.com/paper/2207.04179/) (2022)
- [Building powerful and equivariant graph neural networks with structural message-passing](https://mlsanity.com/paper/2006.15107/) (2020)
- [On the Limitations of Representing Functions on Sets](https://mlsanity.com/paper/1901.09006/) (2019)
- [Meta-Learning Stationary Stochastic Process Prediction with Convolutional Neural Processes](https://mlsanity.com/paper/2007.01332/) (2020)
- [Universal Approximation of Functions on Sets](https://mlsanity.com/paper/2107.01959/) (2021)
- [The Gaussian Neural Process](https://mlsanity.com/paper/2101.03606/) (2021)
- [Autoregressive Conditional Neural Processes](https://mlsanity.com/paper/2303.14468/) (2023)
- [Equivariant Learning of Stochastic Fields: Gaussian Processes and Steerable Conditional Neural Processes](https://mlsanity.com/paper/2011.12916/) (2020)
- [Practical Conditional Neural Processes Via Tractable Dependent Predictions](https://mlsanity.com/paper/2203.08775/) (2022)
- [Exact Reconstruction of Euclidean Distance Geometry Problem Using Low-rank Matrix Completion](https://mlsanity.com/paper/1804.04310/) (2018)
- [Model-based Meta Reinforcement Learning using Graph Structured Surrogate Models](https://mlsanity.com/paper/2102.08291/) (2021)
- [Group Equivariant Conditional Neural Processes](https://mlsanity.com/paper/2102.08759/) (2021)
- [Kernel Identification Through Transformers](https://mlsanity.com/paper/2106.08185/) (2021)

## Built on by (most cited first, 13 of 13)

- [Amortized Probabilistic Conditioning for Optimization, Simulation and Inference](https://mlsanity.com/paper/2410.15320/) (2024)
- [Amortized Bayesian Experimental Design for Decision-Making](https://mlsanity.com/paper/2411.02064/) (2024)
- [Translation Equivariant Transformer Neural Processes](https://mlsanity.com/paper/2406.12409/) (2024)
- [Approximately Equivariant Neural Processes](https://mlsanity.com/paper/2406.13488/) (2024)
- [PABBO: Preferential Amortized Black-Box Optimization](https://mlsanity.com/paper/2503.00924/) (2025)
- [ALINE: Joint Amortization for Bayesian Inference and Active Data Acquisition](https://mlsanity.com/paper/2506.07259/) (2025)
- [Spectral Convolutional Conditional Neural Processes](https://mlsanity.com/paper/2404.13182/) (2024)
- [Meta-Statistical Learning: Supervised Learning of Statistical Estimators](https://mlsanity.com/paper/2502.12088/) (2025)
- [Noise-Aware Differentially Private Regression via Meta-Learning](https://mlsanity.com/paper/2406.08569/) (2024)
- [R'enyi Neural Processes](https://mlsanity.com/paper/2405.15991/) (2024)
- [MIST: Mutual Information Estimation Via Supervised Training](https://mlsanity.com/paper/2511.18945/) (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)

## Abstract (arXiv)

Conditional Neural Processes (CNPs) are a class of metalearning models popular for combining the runtime efficiency of amortized inference with reliable uncertainty quantification. Many relevant machine learning tasks, such as in spatio-temporal modeling, Bayesian Optimization and continuous control, inherently contain equivariances -- for example to translation -- which the model can exploit for maximal performance. However, prior attempts to include equivariances in CNPs do not scale effectively beyond two input dimensions. In this work, we propose Relational Conditional Neural Processes (RCNPs), an effective approach to incorporate equivariances into any neural process model. Our proposed method extends the applicability and impact of equivariant neural processes to higher dimensions. We empirically demonstrate the competitive performance of RCNPs on a large array of tasks naturally containing equivariances.