# Neural Field Convolutions by Repeated Differentiation

arXiv: https://arxiv.org/abs/2304.01834 · HTML: https://mlsanity.com/paper/2304.01834/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 69 references that are in the map.
- First posted on arXiv 4 Apr 2023.

## Builds on (most cited first, 30 of 33)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (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)
- [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)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Noise2Noise: Learning Image Restoration without Clean Data](https://mlsanity.com/paper/1803.04189/) (2018)
- [Non-Rigid Neural Radiance Fields: Reconstruction and Novel View Synthesis of a Dynamic Scene From Monocular Video](https://mlsanity.com/paper/2012.12247/) (2020)
- [Advances in Neural Rendering](https://mlsanity.com/paper/2111.05849/) (2021)
- [COIN: COmpression with Implicit Neural representations](https://mlsanity.com/paper/2103.03123/) (2021)
- [NeRF-Editing: Geometry Editing of Neural Radiance Fields](https://mlsanity.com/paper/2205.04978/) (2022)
- [AutoInt: Automatic Integration for Fast Neural Volume Rendering](https://mlsanity.com/paper/2012.01714/) (2020)
- [From data to functa: Your data point is a function and you can treat it like one](https://mlsanity.com/paper/2201.12204/) (2022)
- [Deep Parametric Continuous Convolutional Neural Networks](https://mlsanity.com/paper/2101.06742/) (2021)
- [HyperDiffusion: Generating Implicit Neural Fields with Weight-Space Diffusion](https://mlsanity.com/paper/2303.17015/) (2023)
- [BACON: Band-limited Coordinate Networks for Multiscale Scene Representation](https://mlsanity.com/paper/2112.04645/) (2021)
- [Generative Models as Distributions of Functions](https://mlsanity.com/paper/2102.04776/) (2021)
- [Neural Point Catacaustics for Novel-View Synthesis of Reflections](https://mlsanity.com/paper/2301.01087/) (2023)
- [Monte Carlo Convolution for Learning on Non-Uniformly Sampled Point Clouds](https://mlsanity.com/paper/1806.01759/) (2018)
- [SAPE: Spatially-Adaptive Progressive Encoding for Neural Optimization](https://mlsanity.com/paper/2104.09125/) (2021)
- [Signal Processing for Implicit Neural Representations](https://mlsanity.com/paper/2210.08772/) (2022)
- [Learning Signal-Agnostic Manifolds of Neural Fields](https://mlsanity.com/paper/2111.06387/) (2021)
- [Polynomial Neural Fields for Subband Decomposition and Manipulation](https://mlsanity.com/paper/2302.04862/) (2023)
- [Exact-NeRF: An Exploration of a Precise Volumetric Parameterization for Neural Radiance Fields](https://mlsanity.com/paper/2211.12285/) (2022)
- [Spelunking the Deep: Guaranteed Queries on General Neural Implicit Surfaces via Range Analysis](https://mlsanity.com/paper/2202.02444/) (2022)
- [NeRFocus: Neural Radiance Field for 3D Synthetic Defocus](https://mlsanity.com/paper/2203.05189/) (2022)

## Built on by (most cited first, 9 of 9)

- [Neural Geometry Processing via Spherical Neural Surfaces](https://mlsanity.com/paper/2407.07755/) (2024)
- [Stochastic Preconditioning for Neural Field Optimization](https://mlsanity.com/paper/2505.20473/) (2025)
- [Neural Gaussian Scale-Space Fields](https://mlsanity.com/paper/2405.20980/) (2024)
- [Neural Control Variates with Automatic Integration](https://mlsanity.com/paper/2409.15394/) (2024)
- [Towards Croppable Implicit Neural Representations](https://mlsanity.com/paper/2409.19472/) (2024)
- [Learnable Fractional Reaction-Diffusion Dynamics for Under-Display ToF Imaging and Beyond](https://mlsanity.com/paper/2511.01704/) (2025)
- [Neural Bounding](https://mlsanity.com/paper/2310.06822/) (2023)
- [Learning Neural Antiderivatives](https://mlsanity.com/paper/2509.17755/) (2025)
- [Spectral Prefiltering of Neural Fields](https://mlsanity.com/paper/2510.08394/) (2025)

## Abstract (arXiv)

Neural fields are evolving towards a general-purpose continuous representation for visual computing. Yet, despite their numerous appealing properties, they are hardly amenable to signal processing. As a remedy, we present a method to perform general continuous convolutions with general continuous signals such as neural fields. Observing that piecewise polynomial kernels reduce to a sparse set of Dirac deltas after repeated differentiation, we leverage convolution identities and train a repeated integral field to efficiently execute large-scale convolutions. We demonstrate our approach on a variety of data modalities and spatially-varying kernels.