A tensor network formalism for neuro-symbolic AI

TL;DR

This paper introduces a tensor network formalism that unifies neural and symbolic AI approaches, enabling structured reasoning and hybrid models through tensor decompositions and a new Python library.

Contribution

It presents a novel tensor network framework for representing and reasoning with logical and probabilistic models in AI, along with a practical implementation tool.

Findings

Unified tensor formalism for neural and symbolic AI

Efficient inference algorithms via tensor contraction schemes

Implementation of hybrid logical-probabilistic models with tnreason

Abstract

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.