Generalized Constraints as A New Mathematical Problem in Artificial Intelligence: A Review and Perspective

TL;DR

This paper introduces the concept of Generalized Constraints (GCs) as a broad mathematical framework for AI modeling, emphasizing their importance over conventional constraints and exploring their role in knowledge-driven and data-driven AI systems.

Contribution

It defines GCs as a unifying mathematical problem in AI, compares them with conventional constraints, and discusses their significance in AI modeling and future research directions.

Findings

GCs are more prevalent than CCs in AI modeling.

Incorporating GCs enhances understanding of AI transparency and interpretability.

Studies on GCs can lead to novel AI and mathematical research areas.

Abstract

In this comprehensive review, we describe a new mathematical problem in artificial intelligence (AI) from a mathematical modeling perspective, following the philosophy stated by Rudolf E. Kalman that "Once you get the physics right, the rest is mathematics". The new problem is called "Generalized Constraints (GCs)", and we adopt GCs as a general term to describe any type of prior information in modelings. To understand better about GCs to be a general problem, we compare them with the conventional constraints (CCs) and list their extra challenges over CCs. In the construction of AI machines, we basically encounter more often GCs for modeling, rather than CCs with well-defined forms. Furthermore, we discuss the ultimate goals of AI and redefine transparent, interpretable, and explainable AI in terms of comprehension levels about machines. We review the studies in relation to the GC problems although most of them do not take the notion of GCs. We demonstrate that if AI machines are simplified by a coupling with both knowledge-driven submodel and data-driven submodel, GCs will play a critical role in a knowledge-driven submodel as well as in the coupling form between the two submodels. Examples are given to show that the studies in view of a generalized constraint problem will help us perceive and explore novel subjects in AI, or even in mathematics, such as generalized constraint learning (GCL).