用张量方程统一神经与符号AI，让机器既会学又会推理。
Tensor Logic: The Language of AI
- 以张量方程为唯一语法，融合逻辑规则与张量运算
- 可无缝实现Transformer、图模型等主流AI架构
- 支持嵌入空间中的可靠推理，适合追求可解释性的研究者
AI发展受限于缺乏具备完整特性的编程语言。现有框架如PyTorch和TensorFlow虽支持自动微分与GPU加速，但依附于本非为AI设计的Python，且无法原生支持自动化推理与知识获取，导致大量补丁式尝试。而传统AI语言如LISP、Prolog则缺乏可扩展性与学习能力。本文提出张量逻辑（Tensor Logic），通过观察逻辑规则与爱因斯坦求和本质相同，将所有AI形式归约为张量方程。该语言能优雅实现Transformer、形式推理、核机器与图模型。更重要的是，它使嵌入空间中的可靠推理成为可能，结合神经网络的可扩展性与符号推理的可靠性，或为更广泛采纳AI提供基础。
原文摘要 · Abstract (English)
Progress in AI is hindered by the lack of a programming language with all the requisite features. Libraries like PyTorch and TensorFlow provide automatic differentiation and efficient GPU implementation, but are additions to Python, which was never intended for AI. Their lack of support for automated reasoning and knowledge acquisition has led to a long and costly series of hacky attempts to tack them on. On the other hand, AI languages like LISP and Prolog lack scalability and support for learning. This paper proposes tensor logic, a language that solves these problems by unifying neural and symbolic AI at a fundamental level. The sole construct in tensor logic is the tensor equation, based on the observation that logical rules and Einstein summation are essentially the same operation, and all else can be reduced to them. I show how to elegantly implement key forms of neural, symbolic and statistical AI in tensor logic, including transformers, formal reasoning, kernel machines and graphical models. Most importantly, tensor logic makes new directions possible, such as sound reasoning in embedding space. This combines the scalability and learnability of neural networks with the reliability and transparency of symbolic reasoning, and is potentially a basis for the wider adoption of AI.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。