mlsanityData to 7 Oct 2026

From data to functa: Your data point is a function and you can treat it like one

arXiv 2201.12204 ↗First posted 28 Jan 2022cs.LGcited by 183

Not on the map. Why?

Cited by 27 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

It is common practice in deep learning to represent a measurement of the world on a discrete grid, e.g. a 2D grid of pixels. However, the underlying signal represented by these measurements is often continuous, e.g. the scene depicted in an image. A powerful continuous alternative is then to represent these measurements using an implicit neural representation, a neural function trained to output the appropriate measurement value for any input spatial location. In this paper, we take this idea to its next level: what would it take to perform deep learning on these functions instead, treating them as data? In this context we refer to the data as functa, and propose a framework for deep learning on functa. This view presents a number of challenges around efficient conversion from data to functa, compact representation of functa, and effectively solving downstream tasks on functa. We outline a recipe to overcome these challenges and apply it to a wide range of data modalities including images, 3D shapes, neural radiance fields (NeRF) and data on manifolds. We demonstrate that this approach has various compelling properties across data modalities, in particular on the canonical tasks of generative modeling, data imputation, novel view synthesis and classification. Code: https://github.com/deepmind/functa

Key facts. Cited by 183 papers in the map (data through 7 Oct 2026). Builds on 72 of its 90 references that are in the map. First posted on arXiv 28 Jan 2022.

Builds on

72 of 90 references.

References · 72

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38 more
  1. 2017FiLM: Visual Reasoning with a General Conditioning Layercited by 2,286
  2. 2020Implicit Neural Representations with Periodic Activation Functionscited by 2,214
  3. 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,170
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50 most cited of 72 All 72 (JSON)

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 7; 2023: 43; 2024: 43; 2025: 53; 2026: 37.

183 papers.

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  1. 2023Shap-E: Generating Conditional 3D Implicit Functionscited by 379
  2. 2023LucidDreamer: Domain-free Generation of 3D Gaussian Splatting Scenescited by 228
  3. 2023Single-Stage Diffusion NeRF: A Unified Approach to 3D Generation and Reconstructioncited by 180
  4. 2022GAUDI: A Neural Architect for Immersive 3D Scene Generationcited by 136
  5. 2022Diffusion-SDF: Conditional Generative Modeling of Signed Distance Functionscited by 133
  6. 2023Equivariant Architectures for Learning in Deep Weight Spacescited by 106
  7. 2024LN3DIFF++: Scalable Latent Neural Fields Diffusion for Speedy 3D Generationcited by 91
  8. 2023ATT3D: Amortized Text-to-3D Object Synthesiscited by 87
  9. 2023Score-based Diffusion Models in Function Spacecited by 80
  10. 2023Operator Learning with Neural Fields: Tackling PDEs on General Geometriescited by 80
  11. 2022Continuous PDE Dynamics Forecasting with Implicit Neural Representationscited by 71
  12. 2023Deep Learning on Implicit Neural Representations of Shapescited by 62
38 more
  1. 2024Graph Neural Networks for Learning Equivariant Representations of Neural Networkscited by 59
  2. 2023Spatial Functa: Scaling Functa to ImageNet Classification and Generationcited by 55
  3. 2023Graph Metanetworks for Processing Diverse Neural Architecturescited by 55
  4. 2022Diffusion Generative Models in Infinite Dimensionscited by 49
  5. 2024Generic 3D Diffusion Adapter Using Controlled Multi-View Editingcited by 46
  6. 2023Continuous-Time Functional Diffusion Processescited by 39
  7. 2022Generalizable Implicit Neural Representations via Instance Pattern Composerscited by 38
  8. 2024AROMA: Preserving Spatial Structure for Latent PDE Modeling with Local Neural Fieldscited by 38
  9. 2023Conditional score-based diffusion models for Bayesian inference in infinite dimensionscited by 37
  10. 2024Parameterized Physics-informed Neural Networks for Parameterized PDEscited by 35
  11. 2025Symmetry in Neural Network Parameter Spacescited by 31
  12. 2023AI-Generated Content (AIGC) for Various Data Modalities: A Surveycited by 25
  13. 2024Aero-Nef: Neural Fields for Rapid Aircraft Aerodynamics Simulationscited by 24
  14. 2024Scale Equivariant Graph Metanetworkscited by 23
  15. 2023Gaussian3Diff: 3D Gaussian Diffusion for 3D Full Head Synthesis and Editingcited by 22
  16. 2023∞-Diff: Infinite Resolution Diffusion with Subsampled Mollified Statescited by 21
  17. 2025Neural Chaos: A Spectral Stochastic Neural Operatorcited by 21
  18. 2022UncertaINR: Uncertainty Quantification of End-to-End Implicit Neural Representations for Computed Tomographycited by 19
  19. 2024Atlas3D: Physically Constrained Self-Supporting Text-to-3D for Simulation and Fabricationcited by 19
  20. 2024Grounding Continuous Representations in Geometry: Equivariant Neural Fieldscited by 19
  21. 20243D-Adapter: Geometry-Consistent Multi-View Diffusion for High-Quality 3D Generationcited by 19
  22. 2025FunDiff: Diffusion Models over Function Spaces for Physics-Informed Generative Modelingcited by 19
  23. 2024Space-Time Continuous PDE Forecasting using Equivariant Neural Fieldscited by 18
  24. 2024Deep Linear Probe Generators for Weight Space Learningcited by 17
  25. 2023Time Series Continuous Modeling for Imputation and Forecasting with Implicit Neural Representationscited by 16
  26. 2023Locality-Aware Generalizable Implicit Neural Representationcited by 16
  27. 2024DDMI: Domain-Agnostic Latent Diffusion Models for Synthesizing High-Quality Implicit Neural Representationscited by 16
  28. 2024DIRECT-3D: Learning Direct Text-to-3D Generation on Massive Noisy 3D Datacited by 15
  29. 2024Monomial Matrix Group Equivariant Neural Functional Networkscited by 15
  30. 2024CINA: Conditional Implicit Neural Atlas for Spatio-Temporal Representation of Fetal Brainscited by 14
  31. 2023Partition Speeds Up Learning Implicit Neural Representations Based on Exponential-Increase Hypothesiscited by 13
  32. 2024Learning Useful Representations of Recurrent Neural Network Weight Matricescited by 13
  33. 2024Nonparametric Teaching of Implicit Neural Representationscited by 13
  34. 2022ProbNeRF: Uncertainty-Aware Inference of 3D Shapes from 2D Imagescited by 12
  35. 2023How to Train Neural Field Representations: A Comprehensive Study and Benchmarkcited by 12
  36. 2024Implicit-Zoo: A Large-Scale Dataset of Neural Implicit Functions for 2D Images and 3D Scenescited by 12
  37. 2023Neural Point Cloud Diffusion for Disentangled 3D Shape and Appearance Generationcited by 11
  38. 2025Fit Pixels, Get Labels: Meta-learned Implicit Networks for Image Segmentationcited by 11

50 most cited of 183 All 183 (JSON)