{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/higher-rank-irreducible-cartesian-tensors-for","title":"Higher-Rank Irreducible Cartesian Tensors for Equivariant Message Passing","arxiv_id":"2405.14253","date":"2024-05-23","proceeding":null,"authors":["Viktor Zaverkin","Francesco Alesiani","Takashi Maruyama","Federico Errica","Henrik Christiansen","Makoto Takamoto","Nicolas Weber","Mathias Niepert"],"abstract":"The ability to perform fast and accurate atomistic simulations is crucial for advancing the chemical sciences. By learning from high-quality data, machine-learned interatomic potentials achieve accuracy on par with ab initio and first-principles methods at a fraction of their computational cost. The success of machine-learned interatomic potentials arises from integrating inductive biases such as equivariance to group actions on an atomic system, e.g., equivariance to rotations and reflections. In particular, the field has notably advanced with the emergence of equivariant message passing. Most of these models represent an atomic system using spherical tensors, tensor products of which require complicated numerical coefficients and can be computationally demanding. Cartesian tensors offer a promising alternative, though state-of-the-art methods lack flexibility in message-passing mechanisms, restricting their architectures and expressive power. This work explores higher-rank irreducible Cartesian tensors to address these limitations. We integrate irreducible Cartesian tensor products into message-passing neural networks and prove the equivariance and traceless property of the resulting layers. Through empirical evaluations on various benchmark data sets, we consistently observe on-par or better performance than that of state-of-the-art spherical and Cartesian models.","url_abs":"https://arxiv.org/abs/2405.14253v2","url_pdf":"https://arxiv.org/pdf/2405.14253v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"higher-rank-irreducible-cartesian-tensors-for","repo_url":"https://github.com/nec-research/ictp","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"NOASSERTION"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2405.14253","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2405.14253"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/nec-research/ictp","reach":{"status":"ok","spdx":"NOASSERTION"}}],"summary":{"ran":3},"by_repo_kind":{"official":{"samples":3,"ran":3,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":3,"samples":[{"code_sha256_prefix":"922fc0ab9c8faa06","entry":"full_3x3_to_5_quadrupole","repo":"nec-research/ictp","repo_kind":"official","path":"ictp/training/loss_fns.py","file_url":"https://github.com/nec-research/ictp/blob/HEAD/ictp/training/loss_fns.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":true,"licence":"NOASSERTION","inline_ok":false,"mcp_get_code":{"code_sha256":"922fc0ab9c8faa06"}},{"code_sha256_prefix":"9b5d4c58d732261e","entry":"full_3x3_to_voigt_6_stress","repo":"nec-research/ictp","repo_kind":"official","path":"ictp/training/loss_fns.py","file_url":"https://github.com/nec-research/ictp/blob/HEAD/ictp/training/loss_fns.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":true,"licence":"NOASSERTION","inline_ok":false,"mcp_get_code":{"code_sha256":"9b5d4c58d732261e"}},{"code_sha256_prefix":"c02ce04cec624797","entry":"normalized_dot_product","repo":"nec-research/ictp","repo_kind":"official","path":"ictp/training/loss_fns.py","file_url":"https://github.com/nec-research/ictp/blob/HEAD/ictp/training/loss_fns.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":true,"licence":"NOASSERTION","inline_ok":false,"mcp_get_code":{"code_sha256":"c02ce04cec624797"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}