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arXiv 2303.04571cs.AI
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通用智能的范畴论框架

A Categorical Framework of General Intelligence

Tsinghua University(清华大学);Shanghai Artificial Intelligence Laboratory(上海人工智能实验室);Shanghai Qi Zhi Institute(上海期智研究院)

Yang Yuan

AI总结:

针对通用智能缺乏坚实数学基础的问题,本文提出一个范畴论框架,通过预层研究对象表征并提出自我状态觉知概念及相关算法,用图表和极限扩展为场景表征以支撑AI建模、可解释性与安全,还提出可作训练对齐信号的范畴不变性性质。

摘要:

机器能思考吗?自1950年艾伦·图灵提出这一问题以来,由于通用智能缺乏坚实的数学基础,无人能给出直接答案。本文为此目标引入了一个范畴论框架,包含两项主要成果。第一,我们通过预层(presheaves)研究对象表征,提出了自我状态觉知的概念,它是自我意识的范畴论对应物,同时给出了实现与评估该特性的对应算法。第二,我们利用图表(diagrams)和极限(limits)将对象表征扩展为场景表征,这些场景表征可作为数学建模、可解释性与AI安全的基础构件。作为附带成果,我们的框架提出了多种范畴不变性性质,可作为模型训练的对齐信号。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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