Locally orderless networks

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

Keywords: Convolutional Neural Networks, Locally Orderless Images, histograms, saliency maps, explainability

TL;DR: Locally Orderless Networks (LON) extend Convolutional Neural Networks (CNN) by enabling non-linear function computation and improved performance on tasks like gradient estimation and shape regression, while offering better pixel-level explainability.

Abstract: We present Locally Orderless Networks (LON) and the theoretical foundation that links them to Convolutional Neural Networks (CNN), 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 and how LON expands the set of functions computable to non-linear functions such as squaring. We demonstrate simple networks that 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.

Submission Number: 40