On the verification of Embeddings using Hybrid Markov Logic
This addresses the need for more rigorous verification of embeddings in machine learning, particularly for domains requiring symbolic reasoning, though it appears incremental as it builds on existing probabilistic logic methods.
The paper tackles the problem of verifying complex properties of learned embeddings beyond standard task performance, proposing a framework using Hybrid Markov Logic Networks to specify and test properties combined with symbolic knowledge, and demonstrates its applicability in Graph Neural Networks, Deep Knowledge Tracing, and Intelligent Tutoring Systems.
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.