# The Functional Neural Process

arXiv: https://arxiv.org/abs/1906.08324 · HTML: https://mlsanity.com/paper/1906.08324/

## Key facts

- Cited by 43 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jun 2019.

## Built on by (most cited first, 30 of 43)

- [Priors in Bayesian Deep Learning: A Review](https://mlsanity.com/paper/2105.06868/) (2021)
- [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)
- [The Internet of Federated Things (IoFT): A Vision for the Future and In-depth Survey of Data-driven Approaches for Federated Learning](https://mlsanity.com/paper/2111.05326/) (2021)
- [The Neural Process Family: Survey, Applications and Perspectives](https://mlsanity.com/paper/2209.00517/) (2022)
- [What Matters For Meta-Learning Vision Regression Tasks?](https://mlsanity.com/paper/2203.04905/) (2022)
- [CAMul: Calibrated and Accurate Multi-view Time-Series Forecasting](https://mlsanity.com/paper/2109.07438/) (2021)
- [Group Equivariant Conditional Neural Processes](https://mlsanity.com/paper/2102.08759/) (2021)
- [When in Doubt: Neural Non-Parametric Uncertainty Quantification for Epidemic Forecasting](https://mlsanity.com/paper/2106.03904/) (2021)
- [Martingale Posterior Neural Processes](https://mlsanity.com/paper/2304.09431/) (2023)
- [Multi-fidelity Hierarchical Neural Processes](https://mlsanity.com/paper/2206.04872/) (2022)
- [Multi-Fidelity Residual Neural Processes for Scalable Surrogate Modeling](https://mlsanity.com/paper/2402.18846/) (2024)
- [Disentangled Multi-Fidelity Deep Bayesian Active Learning](https://mlsanity.com/paper/2305.04392/) (2023)
- [Geometric Neural Diffusion Processes](https://mlsanity.com/paper/2307.05431/) (2023)
- [Evidential Turing Processes](https://mlsanity.com/paper/2106.01216/) (2021)
- [Data-Centric Epidemic Forecasting: A Survey](https://mlsanity.com/paper/2207.09370/) (2022)
- [Bridge the Inference Gaps of Neural Processes via Expectation Maximization](https://mlsanity.com/paper/2501.03264/) (2025)
- [Deep Bayesian Active Learning for Accelerating Stochastic Simulation](https://mlsanity.com/paper/2106.02770/) (2021)
- [Meta-Learning Regrasping Strategies for Physical-Agnostic Objects](https://mlsanity.com/paper/2205.11110/) (2022)
- [Mini-Batch Consistent Slot Set Encoder for Scalable Set Encoding](https://mlsanity.com/paper/2103.01615/) (2021)
- [NP-SemiSeg: When Neural Processes meet Semi-Supervised Semantic Segmentation](https://mlsanity.com/paper/2308.02866/) (2023)
- [Dimension Agnostic Neural Processes](https://mlsanity.com/paper/2502.20661/) (2025)
- [ST-MAML: A Stochastic-Task based Method for Task-Heterogeneous Meta-Learning](https://mlsanity.com/paper/2109.13305/) (2021)
- [Category-Agnostic 6D Pose Estimation with Conditional Neural Processes](https://mlsanity.com/paper/2206.07162/) (2022)
- [When Rigidity Hurts: Soft Consistency Regularization for Probabilistic Hierarchical Time Series Forecasting](https://mlsanity.com/paper/2206.07940/) (2022)
- [Spectral Convolutional Conditional Neural Processes](https://mlsanity.com/paper/2404.13182/) (2024)
- [GP-ConvCNP: Better Generalization for Convolutional Conditional Neural Processes on Time Series Data](https://mlsanity.com/paper/2106.04967/) (2021)
- [Compositional Law Parsing with Latent Random Functions](https://mlsanity.com/paper/2209.09115/) (2022)
- [PEMS: Pre-trained Epidemic Time-series Models](https://mlsanity.com/paper/2311.07841/) (2023)
- [Distance-informed Neural Processes](https://mlsanity.com/paper/2508.18903/) (2025)

## Abstract (arXiv)

We present a new family of exchangeable stochastic processes, the Functional Neural Processes (FNPs). FNPs model distributions over functions by learning a graph of dependencies on top of latent representations of the points in the given dataset. In doing so, they define a Bayesian model without explicitly positing a prior distribution over latent global parameters; they instead adopt priors over the relational structure of the given dataset, a task that is much simpler. We show how we can learn such models from data, demonstrate that they are scalable to large datasets through mini-batch optimization and describe how we can make predictions for new points via their posterior predictive distribution. We experimentally evaluate FNPs on the tasks of toy regression and image classification and show that, when compared to baselines that employ global latent parameters, they offer both competitive predictions as well as more robust uncertainty estimates.