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Convolutional Conditional Neural Processes

arXiv 1910.13556 ↗First posted 29 Oct 2019stat.ML cs.LGcited by 139

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Abstract (arXiv)

We introduce the Convolutional Conditional Neural Process (ConvCNP), a new member of the Neural Process family that models translation equivariance in the data. Translation equivariance is an important inductive bias for many learning problems including time series modelling, spatial data, and images. The model embeds data sets into an infinite-dimensional function space as opposed to a finite-dimensional vector space. To formalize this notion, we extend the theory of neural representations of sets to include functional representations, and demonstrate that any translation-equivariant embedding can be represented using a convolutional deep set. We evaluate ConvCNPs in several settings, demonstrating that they achieve state-of-the-art performance compared to existing NPs. We demonstrate that building in translation equivariance enables zero-shot generalization to challenging, out-of-domain tasks.

Key facts. Cited by 139 papers in the map (data through 7 Oct 2026). First posted on arXiv 29 Oct 2019.

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Citing papers per year: 2021: 21; 2022: 25; 2023: 27; 2024: 19; 2025: 26; 2026: 21.

139 papers.

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  1. 2023PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solverscited by 205
  2. 2022From data to functa: Your data point is a function and you can treat it like onecited by 183
  3. 2022Transformer Neural Processes: Uncertainty-Aware Meta Learning Via Sequence Modelingcited by 126
  4. 2022CARD: Classification and Regression Diffusion Modelscited by 102
  5. 2021Priors in Bayesian Deep Learning: A Reviewcited by 101
  6. 2021Generative Models as Distributions of Functionscited by 89
  7. 2024Position: Bayesian Deep Learning is Needed in the Age of Large-Scale AIcited by 60
  8. 2021Neural ODE Processescited by 57
  9. 2022Neural Diffusion Processescited by 50
  10. 2022Few-Shot Diffusion Modelscited by 37
  11. 2022Generative Pretraining for Black-Box Optimizationcited by 36
  12. 2021The Gaussian Neural Processcited by 34
38 more
  1. 2021Context-Aware Safe Reinforcement Learning for Non-Stationary Environmentscited by 33
  2. 2023Autoregressive Conditional Neural Processescited by 32
  3. 2023End-to-End Meta-Bayesian Optimisation with Transformer Neural Processescited by 31
  4. 2021Convolutional conditional neural processes for local climate downscalingcited by 29
  5. 2022Latent Bottlenecked Attentive Neural Processescited by 26
  6. 2024Learning to Defer to a Population: A Meta-Learning Approachcited by 26
  7. 2022Practical Conditional Neural Processes Via Tractable Dependent Predictionscited by 25
  8. 2022NP-Match: When Neural Processes meet Semi-Supervised Learningcited by 25
  9. 2021How Tight Can PAC-Bayes be in the Small Data Regime?cited by 24
  10. 2022Spectral Diffusion Processescited by 24
  11. 2022The Neural Process Family: Survey, Applications and Perspectivescited by 23
  12. 2023ExPT: Synthetic Pretraining for Few-Shot Experimental Designcited by 22
  13. 2024Amortized Probabilistic Conditioning for Optimization, Simulation and Inferencecited by 22
  14. 2025Model Predictive Task Sampling for Efficient and Robust Adaptationcited by 20
  15. 2022What Matters For Meta-Learning Vision Regression Tasks?cited by 18
  16. 2023Graph Neural Processes for Spatio-Temporal Extrapolationcited by 18
  17. 2021Group Equivariant Conditional Neural Processescited by 16
  18. 2022Neural Processes with Stochastic Attention: Paying more attention to the context datasetcited by 16
  19. 2023Meta Temporal Point Processescited by 16
  20. 2021Affective Processes: stochastic modelling of temporal context for emotion and facial expression recognitioncited by 15
  21. 2023Martingale Posterior Neural Processescited by 15
  22. 2022Environmental Sensor Placement with Convolutional Gaussian Neural Processescited by 14
  23. 2025Stochastic Process Learning via Operator Flow Matchingcited by 14
  24. 2023Practical Equivariances via Relational Conditional Neural Processescited by 13
  25. 2025Amortized In-Context Bayesian Posterior Estimationcited by 13
  26. 2024Does learning the right latent variables necessarily improve in-context learning?cited by 12
  27. 2024Translation Equivariant Transformer Neural Processescited by 12
  28. 2024Robust Fast Adaptation from Adversarially Explicit Task Distribution Generationcited by 12
  29. 2022Contrastive Conditional Neural Processescited by 11
  30. 2023Versatile Neural Processes for Learning Implicit Neural Representationscited by 11
  31. 2023Beyond Unimodal: Generalising Neural Processes for Multimodal Uncertainty Estimationcited by 11
  32. 2025Estimating Interventional Distributions with Uncertain Causal Graphs through Meta-Learningcited by 11
  33. 2021Efficient Gaussian Neural Processes for Regressioncited by 10
  34. 2022Evidential Conditional Neural Processescited by 10
  35. 2023Geometric Neural Diffusion Processescited by 10
  36. 2021Contrastive Neural Processes for Self-Supervised Learningcited by 9
  37. 2022Multidimensional Belief Quantification for Label-Efficient Meta-Learningcited by 9
  38. 2022Neural Implicit Dictionary via Mixture-of-Expert Trainingcited by 9

50 most cited of 139 All 139 (JSON)