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.

翻译：机器能够思考吗？自艾伦·图灵于1950年提出这一问题以来，由于缺乏通用智能的坚实数学基础，无人能给出直接答案。本文提出一个面向该目标的范畴论框架，主要贡献有两方面。首先，我们通过预层研究对象表征，引入"自我状态意识"概念作为自我意识在范畴论中的类比，并给出其强制执行与评估的相应算法。其次，我们利用图与极限将对象表征扩展至场景表征，这些结构成为数学建模、可解释性与AI安全的基本构件。作为辅助成果，本框架引入了多种范畴论不变性性质，可作为模型训练的对齐信号。