# Generalised Implicit Neural Representations

arXiv: https://arxiv.org/abs/2205.15674 · HTML: https://mlsanity.com/paper/2205.15674/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 67 references that are in the map.
- First posted on arXiv 31 May 2022.

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

- [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)
- [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)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [A Generalization of Transformer Networks to Graphs](https://mlsanity.com/paper/2012.09699/) (2020)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [Graph Neural Networks with Learnable Structural and Positional Representations](https://mlsanity.com/paper/2110.07875/) (2021)
- [Community Detection and Stochastic Block Models](https://mlsanity.com/paper/1703.10146/) (2017)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [What graph neural networks cannot learn: depth vs width](https://mlsanity.com/paper/1907.03199/) (2019)
- [Sign and Basis Invariant Networks for Spectral Graph Representation Learning](https://mlsanity.com/paper/2202.13013/) (2022)
- [GraphiT: Encoding Graph Structure in Transformers](https://mlsanity.com/paper/2106.05667/) (2021)
- [Adversarial Generation of Continuous Images](https://mlsanity.com/paper/2011.12026/) (2020)
- [MeshSDF: Differentiable Iso-Surface Extraction](https://mlsanity.com/paper/2006.03997/) (2020)
- [3D Neural Scene Representations for Visuomotor Control](https://mlsanity.com/paper/2107.04004/) (2021)
- [Transferability of Spectral Graph Convolutional Neural Networks](https://mlsanity.com/paper/1907.12972/) (2019)
- [Beltrami Flow and Neural Diffusion on Graphs](https://mlsanity.com/paper/2110.09443/) (2021)
- [Convergence and Stability of Graph Convolutional Networks on Large Random Graphs](https://mlsanity.com/paper/2006.01868/) (2020)
- [Seeing Implicit Neural Representations as Fourier Series](https://mlsanity.com/paper/2109.00249/) (2021)
- [Phase Transitions, Distance Functions, and Implicit Neural Representations](https://mlsanity.com/paper/2106.07689/) (2021)
- [Network Geometry](https://mlsanity.com/paper/2001.03241/) (2020)
- [On the Universality of Graph Neural Networks on Large Random Graphs](https://mlsanity.com/paper/2105.13099/) (2021)
- [Intrinsic Neural Fields: Learning Functions on Manifolds](https://mlsanity.com/paper/2203.07967/) (2022)
- [A Unifying Generative Model for Graph Learning Algorithms: Label Propagation, Graph Convolutions, and Combinations](https://mlsanity.com/paper/2101.07730/) (2021)
- [Weisfeiler and Leman Go Infinite: Spectral and Combinatorial Pre-Colorings](https://mlsanity.com/paper/2201.13410/) (2022)

## Built on by (most cited first, 30 of 31)

- [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)
- [Modality-Agnostic Variational Compression of Implicit Neural Representations](https://mlsanity.com/paper/2301.09479/) (2023)
- [Nonparametric Teaching of Implicit Neural Representations](https://mlsanity.com/paper/2405.10531/) (2024)
- [Interpretable statistical representations of neural population dynamics and geometry](https://mlsanity.com/paper/2304.03376/) (2023)
- [Manifold Diffusion Fields](https://mlsanity.com/paper/2305.15586/) (2023)
- [Fast Training of Sinusoidal Neural Fields via Scaling Initialization](https://mlsanity.com/paper/2410.04779/) (2024)
- [Implicit Neural Representations for Robust Joint Sparse-View CT Reconstruction](https://mlsanity.com/paper/2405.02509/) (2024)
- [Implicit Neural Representations and the Algebra of Complex Wavelets](https://mlsanity.com/paper/2310.00545/) (2023)
- [Imaging Interiors: An Implicit Solution to Electromagnetic Inverse Scattering Problems](https://mlsanity.com/paper/2407.09352/) (2024)
- [NAISR: A 3D Neural Additive Model for Interpretable Shape Representation](https://mlsanity.com/paper/2303.09234/) (2023)
- [In Search of a Data Transformation That Accelerates Neural Field Training](https://mlsanity.com/paper/2311.17094/) (2023)
- [Spatiotemporal Implicit Neural Representation as a Generalized Traffic Data Learner](https://mlsanity.com/paper/2405.03185/) (2024)
- [Implicit Gaussian process representation of vector fields over arbitrary latent manifolds](https://mlsanity.com/paper/2309.16746/) (2023)
- [Variational Mixture of HyperGenerators for Learning Distributions Over Functions](https://mlsanity.com/paper/2302.06223/) (2023)
- [Reconstructing Historical Climate Fields With Deep Learning](https://mlsanity.com/paper/2311.18348/) (2023)
- [Continuous Representation Methods, Theories, and Applications: An Overview and Perspectives](https://mlsanity.com/paper/2505.15222/) (2025)
- [Breaking the Discretization Barrier of Continuous Physics Simulation Learning](https://mlsanity.com/paper/2509.17955/) (2025)
- [SAIR: Learning Semantic-aware Implicit Representation](https://mlsanity.com/paper/2310.09285/) (2023)
- [Hybrid Neural Representations for Spherical Data](https://mlsanity.com/paper/2402.05965/) (2024)
- [NeuroGauss4D-PCI: 4D Neural Fields and Gaussian Deformation Fields for Point Cloud Interpolation](https://mlsanity.com/paper/2405.14241/) (2024)
- [MeshFeat: Multi-Resolution Features for Neural Fields on Meshes](https://mlsanity.com/paper/2407.13592/) (2024)
- [NTK-Guided Implicit Neural Teaching](https://mlsanity.com/paper/2511.15487/) (2025)
- [Selective Test-Time Adaptation for Unsupervised Anomaly Detection using Neural Implicit Representations](https://mlsanity.com/paper/2410.03306/) (2024)
- [Continuous K-space Recovery Network with Image Guidance for Fast MRI Reconstruction](https://mlsanity.com/paper/2411.11282/) (2024)
- [Frequency-Aware Vision Transformers for High-Fidelity Super-Resolution of Earth System Models](https://mlsanity.com/paper/2502.12427/) (2025)
- [Enhancing Robustness of Implicit Neural Representations Against Weight Perturbations](https://mlsanity.com/paper/2508.13481/) (2025)
- [MDNF: Multi-Diffusion-Nets for Neural Fields on Meshes](https://mlsanity.com/paper/2409.03034/) (2024)
- [MING: A Functional Approach to Learning Molecular Generative Models](https://mlsanity.com/paper/2410.12522/) (2024)
- [ViSIR: Vision Transformer Single Image Reconstruction Method for Earth System Models](https://mlsanity.com/paper/2502.06741/) (2025)

## Abstract (arXiv)

We consider the problem of learning implicit neural representations (INRs) for signals on non-Euclidean domains. In the Euclidean case, INRs are trained on a discrete sampling of a signal over a regular lattice. Here, we assume that the continuous signal exists on some unknown topological space from which we sample a discrete graph. In the absence of a coordinate system to identify the sampled nodes, we propose approximating their location with a spectral embedding of the graph. This allows us to train INRs without knowing the underlying continuous domain, which is the case for most graph signals in nature, while also making the INRs independent of any choice of coordinate system. We show experiments with our method on various real-world signals on non-Euclidean domains.