A Mathematical Formulation of AGI in the (C, U, V) Framework

This article seeks to explore a general formulation of artificial general intelligence (AGI) under a unified framework that defines AGI agents as points in a joint ($C,U,V$$C,U,V$) space. An agent is characterized by three components: ① a cognitive architecture $C,$$C,$ which represents the modules (mathematical functions) inside the agent’s mind, as well as the connections and communication protocols between these modules, including the theory of mind (ToM); ② a set of potential functions $U$$U$, which represents the skills of perception, cognition, and planning (e.g., a potential function can be a neural network trained for visual object recognition, or embodied motion planning); and ③ a set of value functions $V$$V$, which includes the agent’s urges, preferences, and social affections, as well as benefits for individual agents or a group of agents. In this setting, “intelligence” is defined as a wide range of phenomena exhibited by agents when they interact with complex environments (i.e., physical intelligence) and other agents (i.e., social intelligence). Given an initial point in the ($C,U,V$$C,U,V$) space, an agent can explore new $V$$V$-dimensions, which in turn drives the acquisition and learning of skills by enabling the learning of new potential functions $U$$U$ in the environment and by updating the cognitive model. We have developed a Tong test as a benchmark and evaluation criteria: An agent that has reached the human level ($C,U,V$$C,U,V$) is called a “Tong Agent.” The convergence of this process defines the limits of the agent’s evolution; we name this the “stopping problem” of Tong Agents, based on the analogy of the halting problem in a Turing machine.