# HashEncoding: Autoencoding with Multiscale Coordinate Hashing

arXiv: https://arxiv.org/abs/2211.15894 · HTML: https://mlsanity.com/paper/2211.15894/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 21 references that are in the map.
- First posted on arXiv 29 Nov 2022.

## Builds on (most cited first, 11 of 11)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [SegFormer: Simple and Efficient Design for Semantic Segmentation with Transformers](https://mlsanity.com/paper/2105.15203/) (2021)
- [An Intriguing Failing of Convolutional Neural Networks and the CoordConv Solution](https://mlsanity.com/paper/1807.03247/) (2018)
- ["Zero-Shot" Super-Resolution using Deep Internal Learning](https://mlsanity.com/paper/1712.06087/) (2017)
- [Adversarial Generation of Continuous Images](https://mlsanity.com/paper/2011.12026/) (2020)
- [Image Generators with Conditionally-Independent Pixel Synthesis](https://mlsanity.com/paper/2011.13775/) (2020)
- [COCO-GAN: Generation by Parts via Conditional Coordinating](https://mlsanity.com/paper/1904.00284/) (2019)
- [Linearized Multi-Sampling for Differentiable Image Transformation](https://mlsanity.com/paper/1901.07124/) (2019)

## Abstract (arXiv)

We present HashEncoding, a novel autoencoding architecture that leverages a non-parametric multiscale coordinate hash function to facilitate a per-pixel decoder without convolutions. By leveraging the space-folding behaviour of hashing functions, HashEncoding allows for an inherently multiscale embedding space that remains much smaller than the original image. As a result, the decoder requires very few parameters compared with decoders in traditional autoencoders, approaching a non-parametric reconstruction of the original image and allowing for greater generalizability. Finally, by allowing backpropagation directly to the coordinate space, we show that HashEncoding can be exploited for geometric tasks such as optical flow.