Locally orderless networks

Jon Sporring*, Peidi Xu, Jiahao Lu, Francois Bernard Lauze, Sune Darkner

*Corresponding author for this work

Research output: Working paperPreprintResearch

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Abstract

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.
Original languageEnglish
Publisherarxiv.org
Number of pages12
Publication statusPublished - 19 Jun 2024

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