Shell theory: A statistical model of reality

• Main Authors: LIN, Wen-yan, LIU, Siying, REN, Changhao, CHEUNG, Ngai-Man, LI, Hongdong, MATSUSHITA, Yasuyuki
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2022
• Subjects: Semantics; Mathematical model; Machine learning; Random variables; Manifolds; Machine learning algorithms; Prediction algorithms; Artificial Intelligence and Robotics
• Online Access: https://ink.library.smu.edu.sg/sis_research/6222; https://ink.library.smu.edu.sg/context/sis_research/article/7225/viewcontent/again27.pdf
• Institution: Singapore Management University

Machine learning's grand ambition is the mathematical modeling of reality. The recent years have seen major advances using deep-learned techniques that model reality implicitly; however, corresponding advances in explicit mathematical models have been noticeably lacking. We believe this dichotomy is rooted in the limitations of the current statistical tools, which struggle to make sense of the high dimensional generative processes that natural data seems to originate from. This paper proposes a new, distance based statistical technique which allows us to develop elegant mathematical models of such generative processes. Our model suggests that each semantic concept has an associated distinctive-shell which encapsulates almost-all instances of itself and excludes almost-all others. creating the first, explicit mathematical representation of the constraints which make machine learning possible.