Generalized Constraints as A New Mathematical Problem in Artificial Intelligence: A Review and Perspective
This work proposes a foundational problem for AI researchers, aiming to redefine interpretable AI and explore novel subjects, but it is a conceptual review without new empirical results.
The paper introduces Generalized Constraints (GCs) as a new mathematical problem in AI, describing them as a general term for prior information in modeling, and argues that GCs are more common than conventional constraints in AI construction, playing a critical role in knowledge-driven submodels and their coupling with data-driven models.
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).