论文标题
普遍的约束是人工智能中的新数学问题：评论和观点
Generalized Constraints as A New Mathematical Problem in Artificial Intelligence: A Review and Perspective
论文作者
论文摘要
在这篇全面的评论中，我们从数学建模的角度描述了一个新的数学问题（AI），遵循鲁道夫·E·卡尔曼（Rudolf E.新问题称为“广义约束（GCS）”，我们采用GC作为一般术语来描述模型中任何类型的先验信息。为了更好地了解GC是一个普遍的问题，我们将它们与常规约束（CC）进行比较，并列出了对CCS的额外挑战。在AI机器的构建中，我们基本上遇到了建模的GC，而不是具有明确形式的CC。此外，我们讨论了人工智能的最终目标，并从对机器的理解水平方面重新定义了透明，可解释和可解释的AI。我们审查了与GC问题有关的研究，尽管其中大多数没有接受GC的概念。我们证明，如果通过与知识驱动的子模型和数据驱动的子模型的耦合来简化AI机器，那么GCS将在知识驱动的子模型以及两个子模型之间的耦合形式中发挥关键作用。举例说明，有关广义约束问题的研究将有助于我们感知和探索AI甚至数学中的新主题，例如广义约束学习（GCL）。
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).
