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.

我们提出了局部无序网络（LON）及其理论基础，将其与卷积神经网络（CNN）、尺度空间直方图和测量理论联系起来。关键要素是对偏差和激活函数的导数进行规则采样。我们比较了LON、CNN和尺度空间直方图在原型单层网络上的表现。我们展示了LON和CNN如何模拟彼此，以及LON如何扩展可计算的非线性函数集合，例如平方。我们展示了简单网络，用来说明LON在估计梯度幅值平方、回归形状区域和周长长、以及解释单个像素对结果影响方面的改进性能。

本地无序网络