# Neural Space-filling Curves

arXiv: https://arxiv.org/abs/2204.08453 · HTML: https://mlsanity.com/paper/2204.08453/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 46 references that are in the map.
- First posted on arXiv 18 Apr 2022.

## Builds on (most cited first, 15 of 15)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [NeRV: Neural Representations for Videos](https://mlsanity.com/paper/2110.13903/) (2021)
- [Order Matters: Sequence to sequence for sets](https://mlsanity.com/paper/1511.06391/) (2015)
- [TGIF: A New Dataset and Benchmark on Animated GIF Description](https://mlsanity.com/paper/1604.02748/) (2016)
- [Data-Driven Space-Filling Curves](https://mlsanity.com/paper/2009.06309/) (2020)

## Built on by (most cited first, 3 of 3)

- [Machine learning for modelling unstructured grid data in computational physics: a review](https://mlsanity.com/paper/2502.09346/) (2025)
- [LOOPE: Learnable Optimal Patch Order in Positional Embeddings for Vision Transformers](https://mlsanity.com/paper/2504.14386/) (2025)
- [Spatial Priors via Space Filling Curves for Small and Limited Data Vision Transformers](https://mlsanity.com/paper/2606.14757/) (2026)

## Abstract (arXiv)

We present Neural Space-filling Curves (SFCs), a data-driven approach to infer a context-based scan order for a set of images. Linear ordering of pixels forms the basis for many applications such as video scrambling, compression, and auto-regressive models that are used in generative modeling for images. Existing algorithms resort to a fixed scanning algorithm such as Raster scan or Hilbert scan. Instead, our work learns a spatially coherent linear ordering of pixels from the dataset of images using a graph-based neural network. The resulting Neural SFC is optimized for an objective suitable for the downstream task when the image is traversed along with the scan line order. We show the advantage of using Neural SFCs in downstream applications such as image compression. Code and additional results will be made available at https://hywang66.github.io/publication/neuralsfc.