mlsanityData to 14 Oct 2026

Polynomial Neural Fields for Subband Decomposition and Manipulation

arXiv 2302.04862 ↗First posted 9 Feb 2023cs.CV cs.LGcited by 22

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Abstract (arXiv)

Neural fields have emerged as a new paradigm for representing signals, thanks to their ability to do it compactly while being easy to optimize. In most applications, however, neural fields are treated like black boxes, which precludes many signal manipulation tasks. In this paper, we propose a new class of neural fields called polynomial neural fields (PNFs). The key advantage of a PNF is that it can represent a signal as a composition of a number of manipulable and interpretable components without losing the merits of neural fields representation. We develop a general theoretical framework to analyze and design PNFs. We use this framework to design Fourier PNFs, which match state-of-the-art performance in signal representation tasks that use neural fields. In addition, we empirically demonstrate that Fourier PNFs enable signal manipulation applications such as texture transfer and scale-space interpolation. Code is available at https://github.com/stevenygd/PNF.

Key facts. Cited by 22 papers in the map (data through 14 Oct 2026). Builds on 50 of its 94 references that are in the map. First posted on arXiv 9 Feb 2023.

Builds on

50 of 94 references.

References · 50

  1. 2017Squeeze-and-Excitation Networkscited by 4,789
  2. 2019DeepSDF: Learning Continuous Signed Distance Functions for Shape Representationcited by 2,689
  3. 2017Non-local Neural Networkscited by 2,293
  4. 2020Implicit Neural Representations with Periodic Activation Functionscited by 2,238
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  11. 2020NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collectionscited by 1,232
  12. 2021Volume Rendering of Neural Implicit Surfacescited by 996
38 more
  1. 2020Neural Sparse Voxel Fieldscited by 959
  2. 2019Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representationscited by 864
  3. 2020NeRF++: Analyzing and Improving Neural Radiance Fieldscited by 861
  4. 2019PIFu: Pixel-Aligned Implicit Function for High-Resolution Clothed Human Digitizationcited by 818
  5. 2020Convolutional Occupancy Networkscited by 761
  6. 2020Implicit Geometric Regularization for Learning Shapescited by 710
  7. 2019Differentiable Volumetric Rendering: Learning Implicit 3D Representations without 3D Supervisioncited by 700
  8. 2021UNISURF: Unifying Neural Implicit Surfaces and Radiance Fields for Multi-View Reconstructioncited by 646
  9. 2021Ref-NeRF: Structured View-Dependent Appearance for Neural Radiance Fieldscited by 575
  10. 2020Learning Continuous Image Representation with Local Implicit Image Functioncited by 552
  11. 2021Neural Fields in Visual Computing and Beyondcited by 540
  12. 2021FastNeRF: High-Fidelity Neural Rendering at 200FPScited by 511
  13. 2020NeRV: Neural Reflectance and Visibility Fields for Relighting and View Synthesiscited by 496
  14. 2019PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flowscited by 488
  15. 2015A Neural Algorithm of Artistic Stylecited by 483
  16. 2020NeRD: Neural Reflectance Decomposition from Image Collectionscited by 449
  17. 2019SAL: Sign Agnostic Learning of Shapes from Raw Datacited by 390
  18. 2020Local Implicit Grid Representations for 3D Scenescited by 373
  19. 2021Text2Mesh: Text-Driven Neural Stylization for Meshescited by 334
  20. 2021COIN: COmpression with Implicit Neural representationscited by 233
  21. 2021DONeRF: Towards Real-Time Rendering of Compact Neural Radiance Fields using Depth Oracle Networkscited by 232
  22. 2019Texture Fields: Learning Texture Representations in Function Spacecited by 210
  23. 2021Neural-PIL: Neural Pre-Integrated Lighting for Reflectance Decompositioncited by 205
  24. 2020AutoInt: Automatic Integration for Fast Neural Volume Renderingcited by 204
  25. 2021CLIPstyler: Image Style Transfer with a Single Text Conditioncited by 203
  26. 2019DIST: Rendering Deep Implicit Signed Distance Function with Differentiable Sphere Tracingcited by 180
  27. 2019SDFDiff: Differentiable Rendering of Signed Distance Fields for 3D Shape Optimizationcited by 159
  28. 2021BACON: Band-limited Coordinate Networks for Multiscale Scene Representationcited by 143
  29. 2019On the Expressive Power of Deep Polynomial Neural Networkscited by 66
  30. 2020Pi-nets: Deep Polynomial Neural Networkscited by 39
  31. 2021Rethinking Positional Encodingcited by 37
  32. 2022MINER: Multiscale Implicit Neural Representationscited by 20
  33. 2022The Spectral Bias of Polynomial Neural Networkscited by 19
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  35. 2021CoPE: Conditional image generation using Polynomial Expansionscited by 12
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  37. 2022Adversarial Audio Synthesis with Complex-valued Polynomial Networkscited by 3
  38. 2016Survey of Expressivity in Deep Neural Networkscited by 2

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 7; 2024: 7; 2025: 6; 2026: 2.

22 papers.

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  1. 2023NeuRBF: A Neural Fields Representation with Adaptive Radial Basis Functionscited by 65
  2. 2023Disorder-invariant Implicit Neural Representationcited by 27
  3. 2024DGD: Dynamic 3D Gaussians Distillationcited by 23
  4. 2024Tuning the Frequencies: Robust Training for Sinusoidal Neural Networkscited by 19
  5. 2023Neural Spline Fields for Burst Image Fusion and Layer Separationcited by 16
  6. 2023Regularization of polynomial networks for image recognitioncited by 13
  7. 2024Multilinear Operator Networkscited by 12
  8. 2025Identifiability of Deep Polynomial Neural Networkscited by 12
  9. 2024BANF: Band-limited Neural Fields for Levels of Detail Reconstructioncited by 10
  10. 2023Neural Field Convolutions by Repeated Differentiationcited by 9
  11. 2023RHINO: Regularizing the Hash-based Implicit Neural Representationcited by 9
  12. 2024Grounding and Enhancing Grid-based Models for Neural Fieldscited by 9
10 more
  1. 2023Thera: Aliasing-Free Arbitrary-Scale Super-Resolution with Neural Heat Fieldscited by 6
  2. 2025The Alexander-Hirschowitz theorem for neurovarietiescited by 6
  3. 2025Towards Lossless Implicit Neural Representation via Bit Plane Decompositioncited by 5
  4. 2024Coarse-To-Fine Tensor Trains for Compact Visual Representationscited by 4
  5. 2026Calibrated Harmonic Overlaid Implicit Neural Representations for Multi-Dimensional Datacited by 3
  6. 2024A Latent Implicit 3D Shape Model for Multiple Levels of Detailcited by 2
  7. 2025MetricGrids: Arbitrary Nonlinear Approximation with Elementary Metric Grids based Implicit Neural Representationcited by 2
  8. 2025Frequency-Aware Gaussian Splatting Decompositioncited by 2
  9. 2025Spectral Prefiltering of Neural Fieldscited by 0
  10. 2026Exact Algebraic Computation of Learning Coefficients for Two-Dimensional Singular Modelscited by 0