Product Interaction: An Algebraic Formalism for Deep Learning Architectures
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866908807731347456 |
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| author | Dong, Haonan Cheng, Chun-Wun Aviles-Rivero, Angelica I. |
| author_facet | Dong, Haonan Cheng, Chun-Wun Aviles-Rivero, Angelica I. |
| contents | In this paper, we introduce product interactions, an algebraic formalism in which neural network layers are constructed from compositions of a multiplication operator defined over suitable algebras. Product interactions provide a principled way to generate and organize algebraic expressions by increasing interaction order. Our central observation is that algebraic expressions in modern neural networks admit a unified construction in terms of linear, quadratic, and higher-order product interactions. Convolutional and equivariant networks arise as symmetry-constrained linear product interactions, while attention and Mamba correspond to higher-order product interactions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_02573 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Product Interaction: An Algebraic Formalism for Deep Learning Architectures Dong, Haonan Cheng, Chun-Wun Aviles-Rivero, Angelica I. Machine Learning Artificial Intelligence In this paper, we introduce product interactions, an algebraic formalism in which neural network layers are constructed from compositions of a multiplication operator defined over suitable algebras. Product interactions provide a principled way to generate and organize algebraic expressions by increasing interaction order. Our central observation is that algebraic expressions in modern neural networks admit a unified construction in terms of linear, quadratic, and higher-order product interactions. Convolutional and equivariant networks arise as symmetry-constrained linear product interactions, while attention and Mamba correspond to higher-order product interactions. |
| title | Product Interaction: An Algebraic Formalism for Deep Learning Architectures |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2602.02573 |