# Neural Gaussian Scale-Space Fields

arXiv: https://arxiv.org/abs/2405.20980 · HTML: https://mlsanity.com/paper/2405.20980/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 98 references that are in the map.
- First posted on arXiv 31 May 2024.

## Builds on (most cited first, 30 of 41)

- [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)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [Alias-Free Generative Adversarial Networks](https://mlsanity.com/paper/2106.12423/) (2021)
- [BARF: Bundle-Adjusting Neural Radiance Fields](https://mlsanity.com/paper/2104.06405/) (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)
- [Advances in Neural Rendering](https://mlsanity.com/paper/2111.05849/) (2021)
- [Regularisation of Neural Networks by Enforcing Lipschitz Continuity](https://mlsanity.com/paper/1804.04368/) (2018)
- [FreeNeRF: Improving Few-shot Neural Rendering with Free Frequency Regularization](https://mlsanity.com/paper/2303.07418/) (2023)
- [Unitary Evolution Recurrent Neural Networks](https://mlsanity.com/paper/1511.06464/) (2015)
- [Sorting out Lipschitz function approximation](https://mlsanity.com/paper/1811.05381/) (2018)
- [Formal Guarantees on the Robustness of a Classifier against Adversarial Manipulation](https://mlsanity.com/paper/1705.08475/) (2017)
- [Spectral Norm Regularization for Improving the Generalizability of Deep Learning](https://mlsanity.com/paper/1705.10941/) (2017)
- [Deblur-NeRF: Neural Radiance Fields from Blurry Images](https://mlsanity.com/paper/2111.14292/) (2021)
- [Deep Parametric Continuous Convolutional Neural Networks](https://mlsanity.com/paper/2101.06742/) (2021)
- [Modulated Periodic Activations for Generalizable Local Functional Representations](https://mlsanity.com/paper/2104.03960/) (2021)
- [Orthogonal Weight Normalization: Solution to Optimization over Multiple Dependent Stiefel Manifolds in Deep Neural Networks](https://mlsanity.com/paper/1709.06079/) (2017)
- [Learning Smooth Neural Functions via Lipschitz Regularization](https://mlsanity.com/paper/2202.08345/) (2022)
- [Orthogonal Recurrent Neural Networks with Scaled Cayley Transform](https://mlsanity.com/paper/1707.09520/) (2017)
- [Tunable Efficient Unitary Neural Networks (EUNN) and their application to RNNs](https://mlsanity.com/paper/1612.05231/) (2016)
- [Monte Carlo Convolution for Learning on Non-Uniformly Sampled Point Clouds](https://mlsanity.com/paper/1806.01759/) (2018)

## Built on by (most cited first, 6 of 6)

- [VertexRegen: Mesh Generation with Continuous Level of Detail](https://mlsanity.com/paper/2508.09062/) (2025)
- [Neural Harmonic Textures for High-Quality Primitive Based Neural Reconstruction](https://mlsanity.com/paper/2604.01204/) (2026)
- [T-MLP: Tailed Multi-Layer Perceptron for Level-of-Detail Signal Representation](https://mlsanity.com/paper/2509.00066/) (2025)
- [Learning Neural Antiderivatives](https://mlsanity.com/paper/2509.17755/) (2025)
- [Spectral Prefiltering of Neural Fields](https://mlsanity.com/paper/2510.08394/) (2025)
- [HOSC: A Periodic Activation with Saturation Control for High-Fidelity Implicit Neural Representations](https://mlsanity.com/paper/2601.07870/) (2026)

## Abstract (arXiv)

Gaussian scale spaces are a cornerstone of signal representation and processing, with applications in filtering, multiscale analysis, anti-aliasing, and many more. However, obtaining such a scale space is costly and cumbersome, in particular for continuous representations such as neural fields. We present an efficient and lightweight method to learn the fully continuous, anisotropic Gaussian scale space of an arbitrary signal. Based on Fourier feature modulation and Lipschitz bounding, our approach is trained self-supervised, i.e., training does not require any manual filtering. Our neural Gaussian scale-space fields faithfully capture multiscale representations across a broad range of modalities, and support a diverse set of applications. These include images, geometry, light-stage data, texture anti-aliasing, and multiscale optimization.