Incorporating Expert Rules into Neural Networks in the Framework of Concept-Based Learning
This work addresses the challenge of combining inductive and deductive learning for researchers in machine learning, offering a way to incorporate domain knowledge into neural networks, though it appears incremental in extending concept-based learning.
The paper tackles the problem of integrating expert rules into neural networks for concept-based learning, proposing methods to combine logical rules with neural networks to ensure concept probabilities satisfy expert constraints, and demonstrates the approaches with numerical examples.
A problem of incorporating the expert rules into machine learning models for extending the concept-based learning is formulated in the paper. It is proposed how to combine logical rules and neural networks predicting the concept probabilities. The first idea behind the combination is to form constraints for a joint probability distribution over all combinations of concept values to satisfy the expert rules. The second idea is to represent a feasible set of probability distributions in the form of a convex polytope and to use its vertices or faces. We provide several approaches for solving the stated problem and for training neural networks which guarantee that the output probabilities of concepts would not violate the expert rules. The solution of the problem can be viewed as a way for combining the inductive and deductive learning. Expert rules are used in a broader sense when any logical function that connects concepts and class labels or just concepts with each other can be regarded as a rule. This feature significantly expands the class of the proposed results. Numerical examples illustrate the approaches. The code of proposed algorithms is publicly available.