# Signal Processing for Implicit Neural Representations

arXiv: https://arxiv.org/abs/2210.08772 · HTML: https://mlsanity.com/paper/2210.08772/

## Key facts

- Cited by 46 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 91 references that are in the map.
- First posted on arXiv 17 Oct 2022.

## Builds on (most cited first, 30 of 44)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Xception: Deep Learning with Depthwise Separable Convolutions](https://mlsanity.com/paper/1610.02357/) (2016)
- [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)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [PIFu: Pixel-Aligned Implicit Function for High-Resolution Clothed Human Digitization](https://mlsanity.com/paper/1905.05172/) (2019)
- [Multi-Stage Progressive Image Restoration](https://mlsanity.com/paper/2102.02808/) (2021)
- [GIRAFFE: Representing Scenes as Compositional Generative Neural Feature Fields](https://mlsanity.com/paper/2011.12100/) (2020)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Resolution-robust Large Mask Inpainting with Fourier Convolutions](https://mlsanity.com/paper/2109.07161/) (2021)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [pi-GAN: Periodic Implicit Generative Adversarial Networks for 3D-Aware Image Synthesis](https://mlsanity.com/paper/2012.00926/) (2020)
- [GRAF: Generative Radiance Fields for 3D-Aware Image Synthesis](https://mlsanity.com/paper/2007.02442/) (2020)
- [Error bounds for approximations with deep ReLU networks](https://mlsanity.com/paper/1610.01145/) (2016)
- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [StyleNeRF: A Style-based 3D-Aware Generator for High-resolution Image Synthesis](https://mlsanity.com/paper/2110.08985/) (2021)
- [In-Place Scene Labelling and Understanding with Implicit Scene Representation](https://mlsanity.com/paper/2103.15875/) (2021)
- [CLIP-NeRF: Text-and-Image Driven Manipulation of Neural Radiance Fields](https://mlsanity.com/paper/2112.05139/) (2021)
- [NeRF in the Dark: High Dynamic Range View Synthesis from Noisy Raw Images](https://mlsanity.com/paper/2111.13679/) (2021)
- [Light Field Networks: Neural Scene Representations with Single-Evaluation Rendering](https://mlsanity.com/paper/2106.02634/) (2021)
- [PDE-Net: Learning PDEs from Data](https://mlsanity.com/paper/1710.09668/) (2017)
- [MAXIM: Multi-Axis MLP for Image Processing](https://mlsanity.com/paper/2201.02973/) (2022)
- [NeRV: Neural Representations for Videos](https://mlsanity.com/paper/2110.13903/) (2021)
- [Learning Shape Templates with Structured Implicit Functions](https://mlsanity.com/paper/1904.06447/) (2019)
- [Learned Initializations for Optimizing Coordinate-Based Neural Representations](https://mlsanity.com/paper/2012.02189/) (2020)
- [COIN: COmpression with Implicit Neural representations](https://mlsanity.com/paper/2103.03123/) (2021)
- [Editing Conditional Radiance Fields](https://mlsanity.com/paper/2105.06466/) (2021)

## Built on by (most cited first, 30 of 46)

- [Equivariant Architectures for Learning in Deep Weight Spaces](https://mlsanity.com/paper/2301.12780/) (2023)
- [GaussianImage: 1000 FPS Image Representation and Compression by 2D Gaussian Splatting](https://mlsanity.com/paper/2403.08551/) (2024)
- [Bidirectional Multi-Scale Implicit Neural Representations for Image Deraining](https://mlsanity.com/paper/2404.01547/) (2024)
- [Where Do We Stand with Implicit Neural Representations? A Technical and Performance Survey](https://mlsanity.com/paper/2411.03688/) (2024)
- [NeuralEditor: Editing Neural Radiance Fields via Manipulating Point Clouds](https://mlsanity.com/paper/2305.03049/) (2023)
- [INCODE: Implicit Neural Conditioning with Prior Knowledge Embeddings](https://mlsanity.com/paper/2310.18846/) (2023)
- [RecolorNeRF: Layer Decomposed Radiance Fields for Efficient Color Editing of 3D Scenes](https://mlsanity.com/paper/2301.07958/) (2023)
- [Scale Equivariant Graph Metanetworks](https://mlsanity.com/paper/2406.10685/) (2024)
- [Learning Useful Representations of Recurrent Neural Network Weight Matrices](https://mlsanity.com/paper/2403.11998/) (2024)
- [How to Train Neural Field Representations: A Comprehensive Study and Benchmark](https://mlsanity.com/paper/2312.10531/) (2023)
- [PNeRV: Enhancing Spatial Consistency via Pyramidal Neural Representation for Videos](https://mlsanity.com/paper/2404.08921/) (2024)
- [GIViC: Generative Implicit Video Compression](https://mlsanity.com/paper/2503.19604/) (2025)
- [Neural Field Convolutions by Repeated Differentiation](https://mlsanity.com/paper/2304.01834/) (2023)
- [Implicit Neural Representations for Robust Joint Sparse-View CT Reconstruction](https://mlsanity.com/paper/2405.02509/) (2024)
- [Scalable Implicit Graphon Learning](https://mlsanity.com/paper/2410.17464/) (2024)
- [Implicit Neural Representations and the Algebra of Complex Wavelets](https://mlsanity.com/paper/2310.00545/) (2023)
- [Stochastic Preconditioning for Neural Field Optimization](https://mlsanity.com/paper/2505.20473/) (2025)
- [In Search of a Data Transformation That Accelerates Neural Field Training](https://mlsanity.com/paper/2311.17094/) (2023)
- [Superpixel-informed Implicit Neural Representation for Multi-Dimensional Data](https://mlsanity.com/paper/2411.11356/) (2024)
- [End-to-End Implicit Neural Representations for Classification](https://mlsanity.com/paper/2503.18123/) (2025)
- [Towards Croppable Implicit Neural Representations](https://mlsanity.com/paper/2409.19472/) (2024)
- [SeamlessNeRF: Stitching Part NeRFs with Gradient Propagation](https://mlsanity.com/paper/2311.16127/) (2023)
- [Blind Video Super-Resolution based on Implicit Kernels](https://mlsanity.com/paper/2503.07856/) (2025)
- [Continuous Representation Methods, Theories, and Applications: An Overview and Perspectives](https://mlsanity.com/paper/2505.15222/) (2025)
- [Encoding Semantic Priors into the Weights of Implicit Neural Representation](https://mlsanity.com/paper/2406.04178/) (2024)
- [How to Design and Train Your Implicit Neural Representation for Video Compression](https://mlsanity.com/paper/2506.24127/) (2025)
- [Conv-INR: Convolutional Implicit Neural Representation for Multimodal Visual Signals](https://mlsanity.com/paper/2406.04249/) (2024)
- [Generalizable Physics-Informed Learning for Stochastic Safety-Critical Systems](https://mlsanity.com/paper/2407.08868/) (2024)
- [Towards the Spectral bias Alleviation by Normalizations in Coordinate Networks](https://mlsanity.com/paper/2407.17834/) (2024)
- [Few-shot Implicit Function Generation via Equivariance](https://mlsanity.com/paper/2501.01601/) (2025)

## Abstract (arXiv)

Implicit Neural Representations (INRs) encoding continuous multi-media data via multi-layer perceptrons has shown undebatable promise in various computer vision tasks. Despite many successful applications, editing and processing an INR remains intractable as signals are represented by latent parameters of a neural network. Existing works manipulate such continuous representations via processing on their discretized instance, which breaks down the compactness and continuous nature of INR. In this work, we present a pilot study on the question: how to directly modify an INR without explicit decoding? We answer this question by proposing an implicit neural signal processing network, dubbed INSP-Net, via differential operators on INR. Our key insight is that spatial gradients of neural networks can be computed analytically and are invariant to translation, while mathematically we show that any continuous convolution filter can be uniformly approximated by a linear combination of high-order differential operators. With these two knobs, INSP-Net instantiates the signal processing operator as a weighted composition of computational graphs corresponding to the high-order derivatives of INRs, where the weighting parameters can be data-driven learned. Based on our proposed INSP-Net, we further build the first Convolutional Neural Network (CNN) that implicitly runs on INRs, named INSP-ConvNet. Our experiments validate the expressiveness of INSP-Net and INSP-ConvNet in fitting low-level image and geometry processing kernels (e.g. blurring, deblurring, denoising, inpainting, and smoothening) as well as for high-level tasks on implicit fields such as image classification.