# Meta-Learning Stationary Stochastic Process Prediction with Convolutional Neural Processes

arXiv: https://arxiv.org/abs/2007.01332 · HTML: https://mlsanity.com/paper/2007.01332/

## Key facts

- Cited by 76 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jul 2020.

## Built on by (most cited first, 30 of 76)

- [Transformers Can Do Bayesian Inference](https://mlsanity.com/paper/2112.10510/) (2021)
- [Transformer Neural Processes: Uncertainty-Aware Meta Learning Via Sequence Modeling](https://mlsanity.com/paper/2207.04179/) (2022)
- [Priors in Bayesian Deep Learning: A Review](https://mlsanity.com/paper/2105.06868/) (2021)
- [Neural Diffusion Processes](https://mlsanity.com/paper/2206.03992/) (2022)
- [The Gaussian Neural Process](https://mlsanity.com/paper/2101.03606/) (2021)
- [Autoregressive Conditional Neural Processes](https://mlsanity.com/paper/2303.14468/) (2023)
- [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)
- [Spectral Diffusion Processes](https://mlsanity.com/paper/2209.14125/) (2022)
- [How Tight Can PAC-Bayes be in the Small Data Regime?](https://mlsanity.com/paper/2106.03542/) (2021)
- [The Neural Process Family: Survey, Applications and Perspectives](https://mlsanity.com/paper/2209.00517/) (2022)
- [Amortized Probabilistic Conditioning for Optimization, Simulation and Inference](https://mlsanity.com/paper/2410.15320/) (2024)
- [A Meta-Learning Approach to Bayesian Causal Discovery](https://mlsanity.com/paper/2412.16577/) (2024)
- [Model Predictive Task Sampling for Efficient and Robust Adaptation](https://mlsanity.com/paper/2501.11039/) (2025)
- [Graph Neural Processes for Spatio-Temporal Extrapolation](https://mlsanity.com/paper/2305.18719/) (2023)
- [Meta Temporal Point Processes](https://mlsanity.com/paper/2301.12023/) (2023)
- [Affective Processes: stochastic modelling of temporal context for emotion and facial expression recognition](https://mlsanity.com/paper/2103.13372/) (2021)
- [Neural Processes with Stochastic Attention: Paying more attention to the context dataset](https://mlsanity.com/paper/2204.05449/) (2022)
- [Martingale Posterior Neural Processes](https://mlsanity.com/paper/2304.09431/) (2023)
- [Environmental Sensor Placement with Convolutional Gaussian Neural Processes](https://mlsanity.com/paper/2211.10381/) (2022)
- [Practical Equivariances via Relational Conditional Neural Processes](https://mlsanity.com/paper/2306.10915/) (2023)
- [Translation Equivariant Transformer Neural Processes](https://mlsanity.com/paper/2406.12409/) (2024)
- [Contrastive Conditional Neural Processes](https://mlsanity.com/paper/2203.03978/) (2022)
- [Versatile Neural Processes for Learning Implicit Neural Representations](https://mlsanity.com/paper/2301.08883/) (2023)
- [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)
- [A Simple Yet Effective Strategy to Robustify the Meta Learning Paradigm](https://mlsanity.com/paper/2310.00708/) (2023)
- [Memory Efficient Neural Processes via Constant Memory Attention Block](https://mlsanity.com/paper/2305.14567/) (2023)
- [Evidential Turing Processes](https://mlsanity.com/paper/2106.01216/) (2021)
- [FNP: Fourier Neural Processes for Arbitrary-Resolution Data Assimilation](https://mlsanity.com/paper/2406.01645/) (2024)

## Abstract (arXiv)

Stationary stochastic processes (SPs) are a key component of many probabilistic models, such as those for off-the-grid spatio-temporal data. They enable the statistical symmetry of underlying physical phenomena to be leveraged, thereby aiding generalization. Prediction in such models can be viewed as a translation equivariant map from observed data sets to predictive SPs, emphasizing the intimate relationship between stationarity and equivariance. Building on this, we propose the Convolutional Neural Process (ConvNP), which endows Neural Processes (NPs) with translation equivariance and extends convolutional conditional NPs to allow for dependencies in the predictive distribution. The latter enables ConvNPs to be deployed in settings which require coherent samples, such as Thompson sampling or conditional image completion. Moreover, we propose a new maximum-likelihood objective to replace the standard ELBO objective in NPs, which conceptually simplifies the framework and empirically improves performance. We demonstrate the strong performance and generalization capabilities of ConvNPs on 1D regression, image completion, and various tasks with real-world spatio-temporal data.