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This results in a diagrammatic approach to constructing novel neural network architectures. When applied to particles within a given local neighborhood, the resulting components, which we term \u2018fusion blocks,\u2019 serve as universal approximators of any continuous equivariant function defined on the neighborhood. We incorporate a fusion block into pre-existing equivariant architectures (Cormorant and MACE), leading to improved performance with fewer parameters on a range of challenging chemical problems. Furthermore, we apply group-equivariant neural networks to study non-adiabatic molecular dynamics of stilbene cis-trans isomerization. Our approach, which combines tensor networks with equivariant neural networks, suggests a potentially fruitful direction for designing more expressive equivariant neural networks.<\/jats:p>","DOI":"10.1088\/2632-2153\/ad4a04","type":"journal-article","created":{"date-parts":[[2024,5,11]],"date-time":"2024-05-11T02:11:58Z","timestamp":1715393518000},"page":"025044","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Unifying O(3) equivariant neural networks design with tensor-network formalism"],"prefix":"10.1088","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1473-6492","authenticated-orcid":true,"given":"Zimu","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zihan","family":"Pengmei","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Han","family":"Zheng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Erik","family":"Thiede","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1669-8039","authenticated-orcid":true,"given":"Junyu","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Risi","family":"Kondor","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"266","published-online":{"date-parts":[[2024,5,21]]},"reference":[{"key":"mlstad4a04bib1","doi-asserted-by":"publisher","first-page":"178","DOI":"10.1016\/j.cpc.2018.03.016","article-title":"Deepmd-kit: a deep learning package for many-body potential energy representation and molecular dynamics","volume":"228","author":"Wang","year":"2018","journal-title":"Comput. 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