Can machines think? Since Alan Turing asked this question in 1950, nobody is able to give a direct answer, due to the lack of solid mathematical foundations for general intelligence. In this paper, we introduce a categorical framework towards this goal, with two main results. First, we investigate object representation through presheaves, introducing the notion of self-state awareness as a categorical analogue to self-consciousness, along with corresponding algorithms for its enforcement and evaluation. Secondly, we extend object representation to scenario representation using diagrams and limits, which then become building blocks for mathematical modeling, interpretability and AI safety. As an ancillary result, our framework introduces various categorical invariance properties that can serve as the alignment signals for model training.
Understanding Critical Thinking in Generative Artificial Intelligence Use: Development, Validation, and Correlates of the Critical Thinking in AI Use Scale
School of Social Sciences, Nanyang Technological University（南洋理工大学社会科学学院）；Interdisciplinary Graduate Programme, Nanyang Technological University（南洋理工大学跨学科研究生项目）；College of Health and Human Sciences, Purdue University（普渡大学健康与人类科学学院）；School of Social Sciences, Singapore Management University（新加坡管理学院社会科学学院）；Faculty of Information Technology, Monash University（墨尔本大学信息技术学院）
How Do Artificial Intelligences Think? The Three Mathematico-Cognitive Factors of Categorical Segmentation Operated by Synthetic Neurons
Neocognition & Faculties of Philosophy and Psychology, Paris（巴黎新认知与哲学心理学学院）；Neocognition and NP - Phelma, UGA（佐治亚大学新认知与NP-Phelma学院）；Neocognition（新认知机构）；Neocognition and Faculty of Medicine of Lyon East, University Lyon 1（里昂第一大学里昂东部医学院新认知机构）；Neocognition (Chrysippe R&D) and Department of Psychology, University of Paris 8（巴黎第八大学心理学系新认知机构（克吕西普研发中心））；Neocognition (Chrysippe R&D) and Epitech Paris（巴黎Epitech新认知机构（克吕西普研发中心））
Brain-inspired and Self-based Artificial Intelligence
Brain-inspired Cognitive AI Lab, Institute of Automation, Chinese Academy of Sciences, China.；Beijing Key Laboratory of Safe AI；Beijing Institute of AI Safety；Key Laboratory of Brain Cognition；Brain-inspired Intelligence Technology, Chinese Academy of Sciences, China.；University of Chinese Academy of Sciences, China.；Department of Philosophy, School of Humanities, University of Chinese Academy of Sciences, China.
Building Machines that Learn and Think with People
University of Cambridge（剑桥大学）；Princeton University（普林斯顿大学）；NYU（纽约大学）；The Alan Turing Institute（艾伦·图灵研究所）；MIT（麻省理工学院）；Microsoft Research（微软研究院）；University of Chicago（芝加哥大学）
Self-Revising Discovery Systems for Science: A Categorical Framework for Agentic Artificial Intelligence
Laboratory for Atomistic and Molecular Mechanics（原子分子力学实验室）；Department of Biological Engineering（生物工程系）；Massachusetts Institute of Technology（麻省理工学院）；Department of Civil and Environmental Engineering（土木与环境工程系）；Department of Mechanical Engineering（机械工程系）；Center for Computational Science and Engineering（计算科学与工程中心）；Schwarzman College of Computing（施瓦茨曼计算学院）
Empowering Machines to Think Like Chemists: Unveiling Molecular Structure-Polarity Relationships with Hierarchical Symbolic Regression
Shanghai Jiao Tong University（上海交通大学）；Peking University（北京大学）；Ningbo Institute of Digital Twin, Eastern Institute of Technology（东方理工宁波数字孪生研究院）；Peking University Shenzhen Graduate School（北京大学深圳研究生院）
