# NOIR: Neural Operator mapping for Implicit Representations

arXiv: https://arxiv.org/abs/2603.13118 · HTML: https://mlsanity.com/paper/2603.13118/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 61 references that are in the map.
- First posted on arXiv 13 Mar 2026.

## Builds on (most cited first, 30 of 44)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [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)
- [TransUNet: Transformers Make Strong Encoders for Medical Image Segmentation](https://mlsanity.com/paper/2102.04306/) (2021)
- [Attention U-Net: Learning Where to Look for the Pancreas](https://mlsanity.com/paper/1804.03999/) (2018)
- [Semantic Image Synthesis with Spatially-Adaptive Normalization](https://mlsanity.com/paper/1903.07291/) (2019)
- [Swin-Unet: Unet-like Pure Transformer for Medical Image Segmentation](https://mlsanity.com/paper/2105.05537/) (2021)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (2021)
- [nnU-Net: Self-adapting Framework for U-Net-Based Medical Image Segmentation](https://mlsanity.com/paper/1809.10486/) (2018)
- [Learning Shape Templates with Structured Implicit Functions](https://mlsanity.com/paper/1904.06447/) (2019)
- [A Deep Cascade of Convolutional Neural Networks for Dynamic MR Image Reconstruction](https://mlsanity.com/paper/1704.02422/) (2017)
- [Image reconstruction by domain transform manifold learning](https://mlsanity.com/paper/1704.08841/) (2017)
- [MetaSDF: Meta-learning Signed Distance Functions](https://mlsanity.com/paper/2006.09662/) (2020)
- [Convolutional Neural Operators for robust and accurate learning of PDEs](https://mlsanity.com/paper/2302.01178/) (2023)
- [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 Functional Maps: Structured Prediction for Dense Shape Correspondence](https://mlsanity.com/paper/1704.08686/) (2017)
- [Implicit Neural Representation in Medical Imaging: A Comparative Survey](https://mlsanity.com/paper/2307.16142/) (2023)
- [Framing U-Net via Deep Convolutional Framelets: Application to Sparse-view CT](https://mlsanity.com/paper/1708.08333/) (2017)
- [Operator Learning with Neural Fields: Tackling PDEs on General Geometries](https://mlsanity.com/paper/2306.07266/) (2023)
- [COIN++: Neural Compression Across Modalities](https://mlsanity.com/paper/2201.12904/) (2022)
- [Representation Equivalent Neural Operators: a Framework for Alias-free Operator Learning](https://mlsanity.com/paper/2305.19913/) (2023)
- [WDM: 3D Wavelet Diffusion Models for High-Resolution Medical Image Synthesis](https://mlsanity.com/paper/2402.19043/) (2024)
- [textttGradICON: Approximate Diffeomorphisms via Gradient Inverse Consistency](https://mlsanity.com/paper/2206.05897/) (2022)

## Built on by (most cited first, 1 of 1)

- [CATO: Charted Attention for Neural PDE Operators](https://mlsanity.com/paper/2605.09016/) (2026)

## Abstract (arXiv)

This paper presents NOIR, a framework that reframes core medical imaging tasks as operator learning between continuous function spaces, challenging the prevailing paradigm of discrete grid-based deep learning. Instead of operating on fixed pixel or voxel grids, NOIR embeds discrete medical signals into shared Implicit Neural Representations and learns a Neural Operator that maps between their latent modulations, enabling resolution-independent function-to-function transformations. We evaluate NOIR across multiple 2D and 3D downstream tasks, including segmentation, shape completion, image-to-image translation, and image synthesis, on several public datasets such as Shenzhen, OASIS-4, SkullBreak, fastMRI, as well as an in-house clinical dataset. It achieves competitive performance at native resolution while demonstrating strong robustness to unseen discretizations, and empirically satisfies key theoretical properties of neural operators. The project page is available here: https://github.com/Sidaty1/NOIR-io.