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.

我们提出了一种基于概率一阶语言的框架，即混合马尔可夫逻辑网络（HMLNs），用于验证学习得到的表示，并通过编码为混合整数线性规划的方式来进行嵌入的验证。我们使用现有的先进求解器测试了该方法，在图神经网络、深度知识追踪和智能辅导系统中展示了其广泛适用性。