用度量替换传统变换，提升神经网络可解释性
Metric as Transform: Exploring beyond Affine Transform for Interpretable Neural Network
- 将点积神经元推广至lp范数与度量空间
- 在MLP/CNN中度量变换性能接近仿射变换
- 构建局部字典网络，有效识别对抗样本
不同架构的神经网络通常依赖仿射变换为核心。然而我们发现，具有全局影响的点积神经元比径向基函数网络中欧氏距离的局部影响更难解释。本文探索点积神经元向lp-范数、度量及更广义形式的推广。结果表明，在多层感知机或卷积神经网络中，以度量为变换的模型性能与仿射变换相当。我们进一步分析度量的多种性质，对比其与仿射变换的差异，并展示多个度量带来更好可解释性的案例。基于此，我们构建了一种可解释的局部字典神经网络，用于理解并拒绝对抗样本。
原文摘要 · Abstract (English)
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.
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