Artificial Neural Networks of varying architectures are generally paired with affine transformation at the core. However, we find dot product neurons with global influence less interpretable as compared to local influence of euclidean distance (as used in Radial Basis Function Network). In this work, we explore the generalization of dot product neurons to $l^p$-norm, metrics, and beyond. We find that metrics as transform performs similarly to affine transform when used in MultiLayer Perceptron or Convolutional Neural Network. Moreover, we explore various properties of Metrics, compare it with Affine, and present multiple cases where metrics seem to provide better interpretability. We develop an interpretable local dictionary based Neural Networks and use it to understand and reject adversarial examples.

翻译：不同架构的人工神经网络通常以仿射变换为核心。然而，我们发现具有全局影响力的点积神经元相较于欧氏距离（如径向基函数网络所用）的局部影响力而言可解释性较低。本工作中，我们探索了点积神经元向$l^p$-范数、度量及更广义形式的推广。研究发现，当应用于多层感知机或卷积神经网络时，度量作为变换的表现与仿射变换相当。此外，我们探究了度量的多种性质，将其与仿射变换进行比较，并展示了度量似乎能提供更好可解释性的多个案例。我们开发了一种基于可解释局部词典的神经网络，并利用其理解和拒绝对抗样本。