# Autoregressive Conditional Neural Processes

arXiv: https://arxiv.org/abs/2303.14468 · HTML: https://mlsanity.com/paper/2303.14468/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- Builds on 61 of its 91 references that are in the map.
- First posted on arXiv 25 Mar 2023.

## Builds on (most cited first, 30 of 61)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [XLNet: Generalized Autoregressive Pretraining for Language Understanding](https://mlsanity.com/paper/1906.08237/) (2019)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Xception: Deep Learning with Depthwise Separable Convolutions](https://mlsanity.com/paper/1610.02357/) (2016)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Generating Long Sequences with Sparse Transformers](https://mlsanity.com/paper/1904.10509/) (2019)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Conditional Image Generation with PixelCNN Decoders](https://mlsanity.com/paper/1606.05328/) (2016)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [Self-Attention Generative Adversarial Networks](https://mlsanity.com/paper/1805.08318/) (2018)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Conditional Neural Processes](https://mlsanity.com/paper/1807.01613/) (2018)
- [PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications](https://mlsanity.com/paper/1701.05517/) (2017)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)

## Built on by (most cited first, 30 of 33)

- [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)
- [Practical Equivariances via Relational Conditional Neural Processes](https://mlsanity.com/paper/2306.10915/) (2023)
- [Geometric Neural Diffusion Processes](https://mlsanity.com/paper/2307.05431/) (2023)
- [Memory Efficient Neural Processes via Constant Memory Attention Block](https://mlsanity.com/paper/2305.14567/) (2023)
- [Episodic Multi-Task Learning with Heterogeneous Neural Processes](https://mlsanity.com/paper/2310.18713/) (2023)
- [ALINE: Joint Amortization for Bayesian Inference and Active Data Acquisition](https://mlsanity.com/paper/2506.07259/) (2025)
- [A Kernel-Based Conditional Two-Sample Test Using Nearest Neighbors (with Applications to Calibration, Regression Curves, and Simulation-Based Inference)](https://mlsanity.com/paper/2407.16550/) (2024)
- [Flow Matching Neural Processes](https://mlsanity.com/paper/2512.23853/) (2025)
- [Dimension Agnostic Neural Processes](https://mlsanity.com/paper/2502.20661/) (2025)
- [Spectral Convolutional Conditional Neural Processes](https://mlsanity.com/paper/2404.13182/) (2024)
- [Efficient Autoregressive Inference for Transformer Probabilistic Models](https://mlsanity.com/paper/2510.09477/) (2025)
- [Meta-Statistical Learning: Supervised Learning of Statistical Estimators](https://mlsanity.com/paper/2502.12088/) (2025)
- [PriorGuide: Test-Time Prior Adaptation for Simulation-Based Inference](https://mlsanity.com/paper/2510.13763/) (2025)
- [Diffusion-Augmented Neural Processes](https://mlsanity.com/paper/2311.09848/) (2023)
- [Noise-Aware Differentially Private Regression via Meta-Learning](https://mlsanity.com/paper/2406.08569/) (2024)
- [Reevaluating Meta-Learning Optimization Algorithms Through Contextual Self-Modulation](https://mlsanity.com/paper/2410.01655/) (2024)
- [Unsupervised Meta-Testing with Conditional Neural Processes for Hybrid Meta-Reinforcement Learning](https://mlsanity.com/paper/2506.04399/) (2025)
- [Incremental Transformer Neural Processes](https://mlsanity.com/paper/2602.18955/) (2026)
- [Neural Stochastic Processes for Satellite Precipitation Refinement](https://mlsanity.com/paper/2604.10414/) (2026)
- [R'enyi Neural Processes](https://mlsanity.com/paper/2405.15991/) (2024)
- [Context-Based Echo State Networks with Prediction Confidence for Human-Robot Shared Control](https://mlsanity.com/paper/2412.00541/) (2024)
- [MIST: Mutual Information Estimation Via Supervised Training](https://mlsanity.com/paper/2511.18945/) (2025)
- [Three Costs of Amortizing Gaussian Process Inference with Neural Processes](https://mlsanity.com/paper/2605.21798/) (2026)
- [Geometric Neural Process Fields](https://mlsanity.com/paper/2502.02338/) (2025)
- [Neural Bridge Processes](https://mlsanity.com/paper/2508.07220/) (2025)
- [Amortising Inference and Meta-Learning Priors in Neural Networks](https://mlsanity.com/paper/2602.08782/) (2026)
- [Optimising antibiotic switching via forecasting of patient physiology](https://mlsanity.com/paper/2603.08242/) (2026)
- [Gaussian Mixture Copula Processes for Irregular Time Series](https://mlsanity.com/paper/2605.23632/) (2026)
- [Revisiting Neural Processes via Fourier Transform and Volterra Series](https://mlsanity.com/paper/2606.01172/) (2026)

## Abstract (arXiv)

Conditional neural processes (CNPs; Garnelo et al., 2018a) are attractive meta-learning models which produce well-calibrated predictions and are trainable via a simple maximum likelihood procedure. Although CNPs have many advantages, they are unable to model dependencies in their predictions. Various works propose solutions to this, but these come at the cost of either requiring approximate inference or being limited to Gaussian predictions. In this work, we instead propose to change how CNPs are deployed at test time, without any modifications to the model or training procedure. Instead of making predictions independently for every target point, we autoregressively define a joint predictive distribution using the chain rule of probability, taking inspiration from the neural autoregressive density estimator (NADE) literature. We show that this simple procedure allows factorised Gaussian CNPs to model highly dependent, non-Gaussian predictive distributions. Perhaps surprisingly, in an extensive range of tasks with synthetic and real data, we show that CNPs in autoregressive (AR) mode not only significantly outperform non-AR CNPs, but are also competitive with more sophisticated models that are significantly more computationally expensive and challenging to train. This performance is remarkable given that AR CNPs are not trained to model joint dependencies. Our work provides an example of how ideas from neural distribution estimation can benefit neural processes, and motivates research into the AR deployment of other neural process models.