Locally orderless networks
CoRR(2024)
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.
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