The standard approach to verify representations learned by Deep Neural Networks is to use them in specific tasks such as classification or regression, and measure their performance based on accuracy in such tasks. However, in many cases, we would want to verify more complex properties of a learned representation. To do this, we propose a framework based on a probabilistic first-order language, namely, Hybrid Markov Logic Networks (HMLNs) where we specify properties over embeddings mixed with symbolic domain knowledge. We present an approach to learn parameters for the properties within this framework. Further, we develop a verification method to test embeddings in this framework by encoding this task as a Mixed Integer Linear Program for which we can leverage existing state-of-the-art solvers. We illustrate verification in Graph Neural Networks, Deep Knowledge Tracing and Intelligent Tutoring Systems to demonstrate the generality of our approach.

翻译：标准方法通过将深度神经网络学到的表征用于分类或回归等特定任务，并基于准确率评估其性能。然而在许多情况下，我们需要验证学到的表征具有更复杂的性质。为此，我们提出一个基于概率一阶语言的框架——混合马尔可夫逻辑网络（HMLNs），在此框架中，我们将嵌入与符号化领域知识混合，并指定其应满足的性质。我们提出一种在该框架内学习性质参数的方法，并开发了一种验证方法，通过将该任务编码为混合整数线性规划问题，可利用现有最先进的求解器检验嵌入。我们在图神经网络、深度知识追踪和智能辅导系统中进行了验证，展示了所提方法的普适性。