# Hypernetwork functional image representation

arXiv: https://arxiv.org/abs/1902.10404 · HTML: https://mlsanity.com/paper/1902.10404/

## Key facts

- Cited by 65 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2019.

## Built on by (most cited first, 30 of 65)

- [Personalized Federated Learning using Hypernetworks](https://mlsanity.com/paper/2103.04628/) (2021)
- [Modulated Periodic Activations for Generalizable Local Functional Representations](https://mlsanity.com/paper/2104.03960/) (2021)
- [Similarity of Neural Network Models: A Survey of Functional and Representational Measures](https://mlsanity.com/paper/2305.06329/) (2023)
- [A Brief Review of Hypernetworks in Deep Learning](https://mlsanity.com/paper/2306.06955/) (2023)
- [A Structured Dictionary Perspective on Implicit Neural Representations](https://mlsanity.com/paper/2112.01917/) (2021)
- [HyperMorph: Amortized Hyperparameter Learning for Image Registration](https://mlsanity.com/paper/2101.01035/) (2021)
- [CSP: Self-Supervised Contrastive Spatial Pre-Training for Geospatial-Visual Representations](https://mlsanity.com/paper/2305.01118/) (2023)
- [UltraSR: Spatial Encoding is a Missing Key for Implicit Image Function-based Arbitrary-Scale Super-Resolution](https://mlsanity.com/paper/2103.12716/) (2021)
- [Cascaded Local Implicit Transformer for Arbitrary-Scale Super-Resolution](https://mlsanity.com/paper/2303.16513/) (2023)
- [Sphere2Vec: A General-Purpose Location Representation Learning over a Spherical Surface for Large-Scale Geospatial Predictions](https://mlsanity.com/paper/2306.17624/) (2023)
- [Improved Implicit Neural Representation with Fourier Reparameterized Training](https://mlsanity.com/paper/2401.07402/) (2024)
- [Learning the Effect of Registration Hyperparameters with HyperMorph](https://mlsanity.com/paper/2203.16680/) (2022)
- [INCODE: Implicit Neural Conditioning with Prior Knowledge Embeddings](https://mlsanity.com/paper/2310.18846/) (2023)
- [Implicit Full Waveform Inversion with Deep Neural Representation](https://mlsanity.com/paper/2209.03525/) (2022)
- [HyperDeepONet: learning operator with complex target function space using the limited resources via hypernetwork](https://mlsanity.com/paper/2312.15949/) (2023)
- [Block Contextual MDPs for Continual Learning](https://mlsanity.com/paper/2110.06972/) (2021)
- [Pareto Set Learning for Multi-Objective Reinforcement Learning](https://mlsanity.com/paper/2501.06773/) (2025)
- [HyperINR: A Fast and Predictive Hypernetwork for Implicit Neural Representations via Knowledge Distillation](https://mlsanity.com/paper/2304.04188/) (2023)
- [Principled Weight Initialization for Hypernetworks](https://mlsanity.com/paper/2312.08399/) (2023)
- [HyperDynamics: Meta-Learning Object and Agent Dynamics with Hypernetworks](https://mlsanity.com/paper/2103.09439/) (2021)
- [Instant GaussianImage: A Generalizable and Self-Adaptive Image Representation via 2D Gaussian Splatting](https://mlsanity.com/paper/2506.23479/) (2025)
- [HIIF: Hierarchical Encoding based Implicit Image Function for Continuous Super-resolution](https://mlsanity.com/paper/2412.03748/) (2024)
- [Example-based Hypernetworks for Out-of-Distribution Generalization](https://mlsanity.com/paper/2203.14276/) (2022)
- [TINC: Tree-structured Implicit Neural Compression](https://mlsanity.com/paper/2211.06689/) (2022)
- [FreSh: Frequency Shifting for Accelerated Neural Representation Learning](https://mlsanity.com/paper/2410.05050/) (2024)
- [SCI: A Spectrum Concentrated Implicit Neural Compression for Biomedical Data](https://mlsanity.com/paper/2209.15180/) (2022)
- [HyperPocket: Generative Point Cloud Completion](https://mlsanity.com/paper/2102.05973/) (2021)
- [HyperSound: Generating Implicit Neural Representations of Audio Signals with Hypernetworks](https://mlsanity.com/paper/2211.01839/) (2022)
- [HAIR: Hypernetworks-based All-in-One Image Restoration](https://mlsanity.com/paper/2408.08091/) (2024)
- [MiraGe: Editable 2D Images using Gaussian Splatting](https://mlsanity.com/paper/2410.01521/) (2024)

## Abstract (arXiv)

Motivated by the human way of memorizing images we introduce their functional representation, where an image is represented by a neural network. For this purpose, we construct a hypernetwork which takes an image and returns weights to the target network, which maps point from the plane (representing positions of the pixel) into its corresponding color in the image. Since the obtained representation is continuous, one can easily inspect the image at various resolutions and perform on it arbitrary continuous operations. Moreover, by inspecting interpolations we show that such representation has some properties characteristic to generative models. To evaluate the proposed mechanism experimentally, we apply it to image super-resolution problem. Despite using a single model for various scaling factors, we obtained results comparable to existing super-resolution methods.