用张量网络统一神经与符号AI，实现高效逻辑概率推理。
A tensor network formalism for neuro-symbolic AI
- 将神经网络分解视为张量分解，融合符号逻辑的稀疏性
- 提出可训练的混合逻辑网络，支持概率与逻辑联合推理
- 适合研究神经符号系统、推理算法的开发者使用
神经与符号人工智能的统一仍是核心挑战。本文提出一种张量网络形式化框架，通过张量分解捕捉两类方法的稀疏性原理。我们设计函数的基编码方案，将神经分解建模为张量分解，并将逻辑公式与概率分布表示为结构化张量分解。该框架将张量网络收缩定义为基本推理类别，将源自概率论和命题逻辑的高效推理算法转化为收缩消息传递机制。框架支持混合逻辑与概率模型的构建与训练，我们称之为混合逻辑网络（Hybrid Logic Network）。理论成果配套提供 Python 库 tnreason，支持实际架构的实现与应用。
原文摘要 · Abstract (English)
The unification of neural and symbolic approaches to artificial intelligence remains a central open challenge. In this work, we introduce a tensor network formalism, which captures sparsity principles originating in the different approaches in tensor decompositions. In particular, we describe a basis encoding scheme for functions and model neural decompositions as tensor decompositions. The proposed formalism can be applied to represent logical formulas and probability distributions as structured tensor decompositions. This unified treatment identifies tensor network contractions as a fundamental inference class and formulates efficiently scaling reasoning algorithms, originating from probability theory and propositional logic, as contraction message passing schemes. The framework enables the definition and training of hybrid logical and probabilistic models, which we call Hybrid Logic Network. The theoretical concepts are accompanied by the python library tnreason, which enables the implementation and practical use of the proposed architectures.
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