  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.
