# Intrinsic Neural Fields: Learning Functions on Manifolds

arXiv: https://arxiv.org/abs/2203.07967 · HTML: https://mlsanity.com/paper/2203.07967/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 67 references that are in the map.
- First posted on arXiv 15 Mar 2022.

## Builds on (most cited first, 30 of 38)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [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)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [A Generalization of Transformer Networks to Graphs](https://mlsanity.com/paper/2012.09699/) (2020)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [NeRD: Neural Reflectance Decomposition from Image Collections](https://mlsanity.com/paper/2012.03918/) (2020)
- [Advances in Neural Rendering](https://mlsanity.com/paper/2111.05849/) (2021)
- [PhySG: Inverse Rendering with Spherical Gaussians for Physics-based Material Editing and Relighting](https://mlsanity.com/paper/2104.00674/) (2021)
- [Text2Mesh: Text-Driven Neural Stylization for Meshes](https://mlsanity.com/paper/2112.03221/) (2021)
- [Texture Fields: Learning Texture Representations in Function Space](https://mlsanity.com/paper/1905.07259/) (2019)
- [Neural-PIL: Neural Pre-Integrated Lighting for Reflectance Decomposition](https://mlsanity.com/paper/2110.14373/) (2021)
- [DiffusionNet: Discretization Agnostic Learning on Surfaces](https://mlsanity.com/paper/2012.00888/) (2020)
- [Neural Tangents: Fast and Easy Infinite Neural Networks in Python](https://mlsanity.com/paper/1912.02803/) (2019)
- [Frequency Bias in Neural Networks for Input of Non-Uniform Density](https://mlsanity.com/paper/2003.04560/) (2020)
- [Modulated Periodic Activations for Generalizable Local Functional Representations](https://mlsanity.com/paper/2104.03960/) (2021)
- [Beyond Periodicity: Towards a Unifying Framework for Activations in Coordinate-MLPs](https://mlsanity.com/paper/2111.15135/) (2021)
- [Local Texture Estimator for Implicit Representation Function](https://mlsanity.com/paper/2111.08918/) (2021)
- [A Structured Dictionary Perspective on Implicit Neural Representations](https://mlsanity.com/paper/2112.01917/) (2021)
- [NeuTex: Neural Texture Mapping for Volumetric Neural Rendering](https://mlsanity.com/paper/2103.00762/) (2021)
- [NPMs: Neural Parametric Models for 3D Deformable Shapes](https://mlsanity.com/paper/2104.00702/) (2021)
- [BlenderProc](https://mlsanity.com/paper/1911.01911/) (2019)
- [Smooth Shells: Multi-Scale Shape Registration with Functional Maps](https://mlsanity.com/paper/1905.12512/) (2019)
- [Geometry-Consistent Neural Shape Representation with Implicit Displacement Fields](https://mlsanity.com/paper/2106.05187/) (2021)
- [SAPE: Spatially-Adaptive Progressive Encoding for Neural Optimization](https://mlsanity.com/paper/2104.09125/) (2021)
- [Seeing Implicit Neural Representations as Fourier Series](https://mlsanity.com/paper/2109.00249/) (2021)
- [Rethinking Positional Encoding](https://mlsanity.com/paper/2107.02561/) (2021)
- [Neural Surface Maps](https://mlsanity.com/paper/2103.16942/) (2021)
- [The Vector Heat Method](https://mlsanity.com/paper/1805.09170/) (2018)

## Built on by (most cited first, 20 of 20)

- [Geographic Location Encoding with Spherical Harmonics and Sinusoidal Representation Networks](https://mlsanity.com/paper/2310.06743/) (2023)
- [Swallowing the Bitter Pill: Simplified Scalable Conformer Generation](https://mlsanity.com/paper/2311.17932/) (2023)
- [Generalised Implicit Neural Representations](https://mlsanity.com/paper/2205.15674/) (2022)
- [NSF: Neural Surface Fields for Human Modeling from Monocular Depth](https://mlsanity.com/paper/2308.14847/) (2023)
- [Text2Scene: Text-driven Indoor Scene Stylization with Part-aware Details](https://mlsanity.com/paper/2308.16880/) (2023)
- [Manifold Diffusion Fields](https://mlsanity.com/paper/2305.15586/) (2023)
- [Single Mesh Diffusion Models with Field Latents for Texture Generation](https://mlsanity.com/paper/2312.09250/) (2023)
- [Explicit Neural Surfaces: Learning Continuous Geometry With Deformation Fields](https://mlsanity.com/paper/2306.02956/) (2023)
- [Leveraging Intrinsic Properties for Non-Rigid Garment Alignment](https://mlsanity.com/paper/2308.09519/) (2023)
- [Implicit Gaussian process representation of vector fields over arbitrary latent manifolds](https://mlsanity.com/paper/2309.16746/) (2023)
- [Hybrid Neural Representations for Spherical Data](https://mlsanity.com/paper/2402.05965/) (2024)
- [MeshFeat: Multi-Resolution Features for Neural Fields on Meshes](https://mlsanity.com/paper/2407.13592/) (2024)
- [FUSE: A Flow-based Mapping Between Shapes](https://mlsanity.com/paper/2511.13431/) (2025)
- [On Neural BRDFs: A Thorough Comparison of State-of-the-Art Approaches](https://mlsanity.com/paper/2502.15480/) (2025)
- [A survey of manifold learning and its applications for multimedia](https://mlsanity.com/paper/2310.12986/) (2023)
- [Inverse Neural Rendering for Explainable Multi-Object Tracking](https://mlsanity.com/paper/2404.12359/) (2024)
- [Heat Kernel Textures: the Geodesic Gaussians That Do Not Splat](https://mlsanity.com/paper/2609.07557/) (2026)
- [MDNF: Multi-Diffusion-Nets for Neural Fields on Meshes](https://mlsanity.com/paper/2409.03034/) (2024)
- [IG-GAN: A Generative Adversarial Network for Aerodynamic Data Generation Based on Intrinsic Geometry](https://mlsanity.com/paper/2607.11497/) (2026)
- [Accelerating HKTex without Mesh Eigensystems: Local Unfolding and Randomized Thermal Features](https://mlsanity.com/paper/2609.14105/) (2026)

## Abstract (arXiv)

Neural fields have gained significant attention in the computer vision community due to their excellent performance in novel view synthesis, geometry reconstruction, and generative modeling. Some of their advantages are a sound theoretic foundation and an easy implementation in current deep learning frameworks. While neural fields have been applied to signals on manifolds, e.g., for texture reconstruction, their representation has been limited to extrinsically embedding the shape into Euclidean space. The extrinsic embedding ignores known intrinsic manifold properties and is inflexible wrt. transfer of the learned function. To overcome these limitations, this work introduces intrinsic neural fields, a novel and versatile representation for neural fields on manifolds. Intrinsic neural fields combine the advantages of neural fields with the spectral properties of the Laplace-Beltrami operator. We show theoretically that intrinsic neural fields inherit many desirable properties of the extrinsic neural field framework but exhibit additional intrinsic qualities, like isometry invariance. In experiments, we show intrinsic neural fields can reconstruct high-fidelity textures from images with state-of-the-art quality and are robust to the discretization of the underlying manifold. We demonstrate the versatility of intrinsic neural fields by tackling various applications: texture transfer between deformed shapes & different shapes, texture reconstruction from real-world images with view dependence, and discretization-agnostic learning on meshes and point clouds.