mlsanityData to 7 Oct 2026

SAPE: Spatially-Adaptive Progressive Encoding for Neural Optimization

arXiv 2104.09125 ↗First posted 19 Apr 2021cs.LG cs.CV cs.GRcited by 59

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Abstract (arXiv)

Multilayer-perceptrons (MLP) are known to struggle with learning functions of high-frequencies, and in particular cases with wide frequency bands. We present a spatially adaptive progressive encoding (SAPE) scheme for input signals of MLP networks, which enables them to better fit a wide range of frequencies without sacrificing training stability or requiring any domain specific preprocessing. SAPE gradually unmasks signal components with increasing frequencies as a function of time and space. The progressive exposure of frequencies is monitored by a feedback loop throughout the neural optimization process, allowing changes to propagate at different rates among local spatial portions of the signal space. We demonstrate the advantage of SAPE on a variety of domains and applications, including regression of low dimensional signals and images, representation learning of occupancy networks, and a geometric task of mesh transfer between 3D shapes.

Key facts. Cited by 59 papers in the map (data through 7 Oct 2026). Builds on 33 of its 49 references that are in the map. First posted on arXiv 19 Apr 2021.

Builds on

33 of 49 references.

References · 33

  1. 2017Attention Is All You Needcited by 59,932
  2. 2019DeepSDF: Learning Continuous Signed Distance Functions for Shape Representationcited by 2,682
  3. 2020Implicit Neural Representations with Periodic Activation Functionscited by 2,214
  4. 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,170
  5. 2018Occupancy Networks: Learning 3D Reconstruction in Function Spacecited by 2,037
  6. 2020pixelNeRF: Neural Radiance Fields from One or Few Imagescited by 1,574
  7. 2018On the Spectral Bias of Neural Networkscited by 1,321
  8. 2020NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collectionscited by 1,230
  9. 2018Learning Implicit Fields for Generative Shape Modelingcited by 1,060
  10. 2019Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representationscited by 864
  11. 2019PIFu: Pixel-Aligned Implicit Function for High-Resolution Clothed Human Digitizationcited by 818
  12. 2020Convolutional Occupancy Networkscited by 760
21 more
  1. 2020Implicit Geometric Regularization for Learning Shapescited by 707
  2. 2021BARF: Bundle-Adjusting Neural Radiance Fieldscited by 641
  3. 2021Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapescited by 426
  4. 2019SAL: Sign Agnostic Learning of Shapes from Raw Datacited by 389
  5. 2020Local Implicit Grid Representations for 3D Scenescited by 372
  6. 2020Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstructioncited by 321
  7. 2019Learning Shape Templates with Structured Implicit Functionscited by 242
  8. 2020Learned Initializations for Optimizing Coordinate-Based Neural Representationscited by 240
  9. 2020Rethinking Positional Encoding in Language Pre-trainingcited by 197
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  12. 2018Training behavior of deep neural network in frequency domaincited by 174
  13. 2019Towards Understanding the Spectral Bias of Deep Learningcited by 173
  14. 2021Modulated Periodic Activations for Generalizable Local Functional Representationscited by 140
  15. 2019The Convergence Rate of Neural Networks for Learned Functions of Different Frequenciescited by 134
  16. 2020Points2Surf: Learning Implicit Surfaces from Point Cloud Patchescited by 122
  17. 2019Learning to Infer Implicit Surfaces without 3D Supervisioncited by 103
  18. 2020DualSDF: Semantic Shape Manipulation using a Two-Level Representationcited by 82
  19. 2020Learning to Encode Position for Transformer with Continuous Dynamical Modelcited by 61
  20. 2019Self-attention with Functional Time Representation Learningcited by 52
  21. 2020Better Patch Stitching for Parametric Surface Reconstructioncited by 21

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 5; 2022: 18; 2023: 13; 2024: 11; 2025: 6; 2026: 6.

59 papers.

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  1. 2021Neural Fields in Visual Computing and Beyondcited by 539
  2. 2022HumanNeRF: Free-viewpoint Rendering of Moving People from Monocular Videocited by 483
  3. 2021Extracting Triangular 3D Models, Materials, and Lighting From Imagescited by 363
  4. 2023FreeNeRF: Improving Few-shot Neural Rendering with Free Frequency Regularizationcited by 310
  5. 2021StyleGAN-V: A Continuous Video Generator with the Price, Image Quality and Perks of StyleGAN2cited by 300
  6. 2021BACON: Band-limited Coordinate Networks for Multiscale Scene Representationcited by 142
  7. 2022HF-NeuS: Improved Surface Reconstruction Using High-Frequency Detailscited by 120
  8. 2022GARF: Gaussian Activated Radiance Fields for High Fidelity Reconstruction and Pose Estimationcited by 86
  9. 2022E-NeRV: Expedite Neural Video Representation with Disentangled Spatial-Temporal Contextcited by 76
  10. 2023NeuRBF: A Neural Fields Representation with Adaptive Radial Basis Functionscited by 65
  11. 2022CROM: Continuous Reduced-Order Modeling of PDEs Using Implicit Neural Representationscited by 56
  12. 2023CamP: Camera Preconditioning for Neural Radiance Fieldscited by 55
38 more
  1. 2022Non-rigid Point Cloud Registration with Neural Deformation Pyramidcited by 41
  2. 2023PET-NeuS: Positional Encoding Tri-Planes for Neural Surfacescited by 37
  3. 2022Neural Fourier Filter Bankcited by 29
  4. 2022SPAGHETTI: Editing Implicit Shapes Through Part Aware Generationcited by 28
  5. 2022Residual Multiplicative Filter Networks for Multiscale Reconstructioncited by 25
  6. 2024Aero-Nef: Neural Fields for Rapid Aircraft Aerodynamics Simulationscited by 24
  7. 2024Neural Fields in Robotics: A Surveycited by 21
  8. 2022MINER: Multiscale Implicit Neural Representationscited by 20
  9. 2022Intrinsic Neural Fields: Learning Functions on Manifoldscited by 20
  10. 2022PINs: Progressive Implicit Networks for Multi-Scale Neural Representationscited by 19
  11. 2022Neural Residual Flow Fields for Efficient Video Representationscited by 16
  12. 2023NeRRF: 3D Reconstruction and View Synthesis for Transparent and Specular Objects with Neural Refractive-Reflective Fieldscited by 16
  13. 2024Fourier Amplitude and Correlation Loss: Beyond Using L2 Loss for Skillful Precipitation Nowcastingcited by 16
  14. 2023How to Train Neural Field Representations: A Comprehensive Study and Benchmarkcited by 12
  15. 2022PREF: Phasorial Embedding Fields for Compact Neural Representationscited by 10
  16. 2024BANF: Band-limited Neural Fields for Levels of Detail Reconstructioncited by 10
  17. 2023Neural Field Convolutions by Repeated Differentiationcited by 9
  18. 2022Semi-signed prioritized neural fitting for surface reconstruction from unoriented point cloudscited by 8
  19. 2023Implicit Shape and Appearance Priors for Few-Shot Full Head Reconstructioncited by 8
  20. 2024TriNeRFLet: A Wavelet Based Triplane NeRF Representationcited by 8
  21. 2025Stochastic Preconditioning for Neural Field Optimizationcited by 8
  22. 2024Neural Gaussian Scale-Space Fieldscited by 6
  23. 2025TetWeave: Isosurface Extraction using On-The-Fly Delaunay Tetrahedral Grids for Gradient-Based Mesh Optimizationcited by 6
  24. 2023Harnessing Low-Frequency Neural Fields for Few-Shot View Synthesiscited by 5
  25. 2023Coordinate Quantized Neural Implicit Representations for Multi-view Reconstructioncited by 5
  26. 2023MC-NeRF: Multi-Camera Neural Radiance Fields for Multi-Camera Image Acquisition Systemscited by 5
  27. 2024Preconditioners for the Stochastic Training of Neural Fieldscited by 5
  28. 2021Mesh Draping: Parametrization-Free Neural Mesh Transfercited by 4
  29. 2022PIP: Positional-encoding Image Priorcited by 3
  30. 2023Pose Modulated Avatars from Videocited by 3
  31. 2024MeshFeat: Multi-Resolution Features for Neural Fields on Meshescited by 3
  32. 2024Spatially-Adaptive Hash Encodings For Neural Surface Reconstructioncited by 3
  33. 2025SASNet: Spatially-Adaptive Sinusoidal Networks for INRscited by 3
  34. 2022Wassersplines for Neural Vector Field--Controlled Animationcited by 2
  35. 2022A Simple And Effective Filtering Scheme For Improving Neural Fieldscited by 2
  36. 2024A Latent Implicit 3D Shape Model for Multiple Levels of Detailcited by 2
  37. 2025MetricGrids: Arbitrary Nonlinear Approximation with Elementary Metric Grids based Implicit Neural Representationcited by 2
  38. 2025A View-consistent Sampling Method for Regularized Training of Neural Radiance Fieldscited by 1

50 most cited of 59 All 59 (JSON)