# Locally orderless networks

arXiv: https://arxiv.org/abs/2406.13514 · HTML: https://mlsanity.com/paper/2406.13514/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 19 references that are in the map.
- First posted on arXiv 19 Jun 2024.

## Builds on (most cited first, 3 of 3)

- [The Earth Mover's Pinball Loss: Quantiles for Histogram-Valued Regression](https://mlsanity.com/paper/2106.02051/) (2021)
- [Information-Theoretic Registration with Explicit Reorientation of Diffusion-Weighted Images](https://mlsanity.com/paper/1905.12056/) (2019)
- [First Order Locally Orderless Registration](https://mlsanity.com/paper/2108.04926/) (2021)

## Abstract (arXiv)

We present Locally Orderless Networks (LON) and its theoretic foundation which links it to Convolutional Neural Networks (CNN), to Scale-space histograms, and measurement theory. The key elements are a regular sampling of the bias and the derivative of the activation function. We compare LON, CNN, and Scale-space histograms on prototypical single-layer networks. We show how LON and CNN can emulate each other, how LON expands the set of functionals computable to non-linear functions such as squaring. We demonstrate simple networks which illustrate the improved performance of LON over CNN on simple tasks for estimating the gradient magnitude squared, for regressing shape area and perimeter lengths, and for explainability of individual pixels' influence on the result.