A tensor network formalism for neuro-symbolic AI
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866918299397259264 |
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| author | Goessmann, Alex Schütte, Janina Fröhlich, Maximilian Eigel, Martin |
| author_facet | Goessmann, Alex Schütte, Janina Fröhlich, Maximilian Eigel, Martin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_15442 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A tensor network formalism for neuro-symbolic AI Goessmann, Alex Schütte, Janina Fröhlich, Maximilian Eigel, Martin Artificial Intelligence Machine Learning Logic in Computer Science Numerical Analysis 15A69, 68T27 G.3; F.1.2 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. |
| title | A tensor network formalism for neuro-symbolic AI |
| topic | Artificial Intelligence Machine Learning Logic in Computer Science Numerical Analysis 15A69, 68T27 G.3; F.1.2 |
| url | https://arxiv.org/abs/2601.15442 |