Locally orderless networks
This work addresses a specific bottleneck in neural network design for researchers in computer vision and machine learning, offering an incremental improvement over existing methods.
The paper introduces Locally Orderless Networks (LON) to tackle the limitation of CNNs in computing non-linear functionals, showing improved performance on tasks like gradient magnitude squared estimation and shape regression with concrete gains in accuracy.
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.