Locally orderless networks

TL;DR

Locally Orderless Networks (LON) are introduced as a new neural network framework that extends CNN capabilities, offering improved performance and explainability by linking to scale-space histograms and measurement theory.

Contribution

LON provides a novel theoretical foundation connecting CNNs to scale-space histograms and measurement theory, enabling emulation and expansion of functional capabilities.

Findings

LON can emulate CNNs and expand their functional set.

LON outperforms CNN on simple gradient and shape regression tasks.

LON enhances explainability of pixel influence in network outputs.

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.