Incorporating Expert Rules into Neural Networks in the Framework of Concept-Based Learning

TL;DR

This paper introduces methods to incorporate expert logical rules into neural networks for concept-based learning, ensuring rule compliance and combining inductive and deductive reasoning.

Contribution

It proposes novel approaches to embed expert rules into neural networks by formulating constraints on probability distributions, expanding concept-based learning capabilities.

Findings

Methods guarantee neural network outputs adhere to expert rules

Approaches effectively combine inductive and deductive learning

Numerical examples demonstrate the effectiveness of the methods

Abstract

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.