A tensor network formalism for neuro-symbolic AI
This work addresses the central open problem of neuro-symbolic AI integration for researchers and practitioners, offering a novel framework that is foundational but incremental in building on existing tensor methods.
The paper tackles the challenge of unifying neural and symbolic AI by introducing a tensor network formalism that represents logical formulas and probability distributions as structured tensor decompositions, enabling the definition and training of hybrid logical and probabilistic models called Hybrid Logic Network, with a provided python library for implementation.
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.