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, consisting of four components: the sensor, world category, planner with objectives, and actor. By leveraging category theory, many important notions in general intelligence can be rigorously defined and analyzed. For instance, we introduce the concept of self-state awareness as a categorical analogy for self-consciousness and provide algorithms for learning and evaluating it. For communication with other agents, we propose to use diagrams that capture the exact representation of the context, instead of using natural languages. Additionally, we demonstrate that by designing the objectives as the output of function over self-state, the model's human-friendliness is guaranteed. Most importantly, our framework naturally introduces various constraints based on categorical invariance that can serve as the alignment signals for training a model that fits into the framework.

翻译：机器能思考吗？自艾伦·图灵于1950年提出这个问题以来，由于缺乏坚实的数学基础来定义通用智能，至今无人能给出直接答案。本文介绍了一个旨在解决该问题的范畴论框架，该框架由四个组成部分构成：传感器、世界范畴、带目标规划器以及执行器。通过运用范畴论，通用智能中的诸多重要概念得以严格定义与分析。例如，我们引入自我状态感知的概念作为自我意识的范畴类比，并提供了对其进行学习与评估的算法。在与其它智能体的通信中，我们提议使用能精确捕捉语境表示的图示而非自然语言。此外，我们证明，通过将目标设计为自我状态上的函数输出，可保证模型对人类友好。最为关键的是，我们的框架基于范畴不变性自然引入了多种约束，这些约束可作为对齐信号，用于训练符合本框架的模型。