# Neural Fourier Filter Bank

arXiv: https://arxiv.org/abs/2212.01735 · HTML: https://mlsanity.com/paper/2212.01735/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Builds on 66 of its 92 references that are in the map.
- First posted on arXiv 4 Dec 2022.

## Builds on (most cited first, 30 of 66)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields](https://mlsanity.com/paper/2111.12077/) (2021)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [pixelNeRF: Neural Radiance Fields from One or Few Images](https://mlsanity.com/paper/2012.02190/) (2020)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [Magic3D: High-Resolution Text-to-3D Content Creation](https://mlsanity.com/paper/2211.10440/) (2022)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Direct Voxel Grid Optimization: Super-fast Convergence for Radiance Fields Reconstruction](https://mlsanity.com/paper/2111.11215/) (2021)
- [PlenOctrees for Real-time Rendering of Neural Radiance Fields](https://mlsanity.com/paper/2103.14024/) (2021)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [MVSNeRF: Fast Generalizable Radiance Field Reconstruction from Multi-View Stereo](https://mlsanity.com/paper/2103.15595/) (2021)
- [Block-NeRF: Scalable Large Scene Neural View Synthesis](https://mlsanity.com/paper/2202.05263/) (2022)
- [KiloNeRF: Speeding up Neural Radiance Fields with Thousands of Tiny MLPs](https://mlsanity.com/paper/2103.13744/) (2021)
- [Ref-NeRF: Structured View-Dependent Appearance for Neural Radiance Fields](https://mlsanity.com/paper/2112.03907/) (2021)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [FastNeRF: High-Fidelity Neural Rendering at 200FPS](https://mlsanity.com/paper/2103.10380/) (2021)
- [Point-NeRF: Point-based Neural Radiance Fields](https://mlsanity.com/paper/2201.08845/) (2022)

## Built on by (most cited first, 29 of 29)

- [FINER: Flexible spectral-bias tuning in Implicit NEural Representation by Variable-periodic Activation Functions](https://mlsanity.com/paper/2312.02434/) (2023)
- [NeuRBF: A Neural Fields Representation with Adaptive Radial Basis Functions](https://mlsanity.com/paper/2309.15426/) (2023)
- [Masked Wavelet Representation for Compact Neural Radiance Fields](https://mlsanity.com/paper/2212.09069/) (2022)
- [Tuning the Frequencies: Robust Training for Sinusoidal Neural Networks](https://mlsanity.com/paper/2407.21121/) (2024)
- [HIIF: Hierarchical Encoding based Implicit Image Function for Continuous Super-resolution](https://mlsanity.com/paper/2412.03748/) (2024)
- [Accelerating Neural Field Training via Soft Mining](https://mlsanity.com/paper/2312.00075/) (2023)
- [DaReNeRF: Direction-aware Representation for Dynamic Scenes](https://mlsanity.com/paper/2403.02265/) (2024)
- [FastSR-NeRF: Improving NeRF Efficiency on Consumer Devices with A Simple Super-Resolution Pipeline](https://mlsanity.com/paper/2312.11537/) (2023)
- [FINER++: Building a Family of Variable-periodic Functions for Activating Implicit Neural Representation](https://mlsanity.com/paper/2407.19434/) (2024)
- [Generative Neural Fields by Mixtures of Neural Implicit Functions](https://mlsanity.com/paper/2310.19464/) (2023)
- [ImFace++: A Sophisticated Nonlinear 3D Morphable Face Model with Implicit Neural Representations](https://mlsanity.com/paper/2312.04028/) (2023)
- [BANF: Band-limited Neural Fields for Levels of Detail Reconstruction](https://mlsanity.com/paper/2404.13024/) (2024)
- [Grounding and Enhancing Grid-based Models for Neural Fields](https://mlsanity.com/paper/2403.20002/) (2024)
- [ECRF: Entropy-Constrained Neural Radiance Fields Compression with Frequency Domain Optimization](https://mlsanity.com/paper/2311.14208/) (2023)
- [Thera: Aliasing-Free Arbitrary-Scale Super-Resolution with Neural Heat Fields](https://mlsanity.com/paper/2311.17643/) (2023)
- [Coordinate-Aware Modulation for Neural Fields](https://mlsanity.com/paper/2311.14993/) (2023)
- [A Unified Theory of Sinusoidal Activation Families for Implicit Neural Representations](https://mlsanity.com/paper/2502.00869/) (2025)
- [Pose Modulated Avatars from Video](https://mlsanity.com/paper/2308.11951/) (2023)
- [Deep Fourier-embedded Network for RGB and Thermal Salient Object Detection](https://mlsanity.com/paper/2411.18409/) (2024)
- [MetricGrids: Arbitrary Nonlinear Approximation with Elementary Metric Grids based Implicit Neural Representation](https://mlsanity.com/paper/2503.10000/) (2025)
- [Representing Animatable Avatar via Factorized Neural Fields](https://mlsanity.com/paper/2406.00637/) (2024)
- [Learning Two-factor Representation for Magnetic Resonance Image Super-resolution](https://mlsanity.com/paper/2409.09731/) (2024)
- [Factorized Multi-Resolution HashGrid for Efficient Neural Radiance Fields: Execution on Edge-Devices](https://mlsanity.com/paper/2604.02836/) (2026)
- [MDNF: Multi-Diffusion-Nets for Neural Fields on Meshes](https://mlsanity.com/paper/2409.03034/) (2024)
- [DaRePlane: Direction-aware Representations for Dynamic Scene Reconstruction](https://mlsanity.com/paper/2410.14169/) (2024)
- [FLAIR: Frequency- and Locality-Aware Implicit Neural Representations](https://mlsanity.com/paper/2508.13544/) (2025)
- [Adaptive Training of INRs via Pruning and Densification](https://mlsanity.com/paper/2510.23943/) (2025)
- [Adaptive Local Frequency Filtering for Fourier-Encoded Implicit Neural Representations](https://mlsanity.com/paper/2604.02846/) (2026)
- [CARA: Collision-Aware Resolution Adaptation for Multiresolution Hash Encoding Based Image Fitting](https://mlsanity.com/paper/2609.18554/) (2026)

## Abstract (arXiv)

We present a novel method to provide efficient and highly detailed reconstructions. Inspired by wavelets, we learn a neural field that decompose the signal both spatially and frequency-wise. We follow the recent grid-based paradigm for spatial decomposition, but unlike existing work, encourage specific frequencies to be stored in each grid via Fourier features encodings. We then apply a multi-layer perceptron with sine activations, taking these Fourier encoded features in at appropriate layers so that higher-frequency components are accumulated on top of lower-frequency components sequentially, which we sum up to form the final output. We demonstrate that our method outperforms the state of the art regarding model compactness and convergence speed on multiple tasks: 2D image fitting, 3D shape reconstruction, and neural radiance fields. Our code is available at https://github.com/ubc-vision/NFFB.