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They do not, however, consider the spatial direction from one atom to another, despite directional information playing a central role in empirical potentials for molecules, e.g. in angular potentials. To alleviate this limitation we propose directional message passing, in which we embed the messages passed between atoms instead of the atoms themselves. Each message is associated with a direction in coordinate space. These directional message embeddings are rotationally equivariant since the associated directions rotate with the molecule. We propose a message passing scheme analogous to belief propagation, which uses the directional information by transforming messages based on the angle between them. Additionally, we use spherical Bessel functions and spherical harmonics to construct theoretically well-founded, orthogonal representations that achieve better performance than the currently prevalent Gaussian radial basis representations while using fewer than 1/4 of the parameters. We leverage these innovations to construct the directional message passing neural network (DimeNet). DimeNet outperforms previous GNNs on average by 76% on MD17 and by 31% on QM9. Our implementation is available online.","url_abs":"https://arxiv.org/abs/2003.03123v2","url_pdf":"https://arxiv.org/pdf/2003.03123v2.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":"directional-message-passing-for-molecular-1","repo_url":"https://github.com/klicperajo/dimenet","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"tf","reach":null},{"paper_slug":"directional-message-passing-for-molecular-1","repo_url":"https://github.com/akirasosa/pytorch-dimenet","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"directional-message-passing-for-molecular-1","repo_url":"https://github.com/intellabs/matsciml","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"gone","observed_at":"2026-09-17","how":"tree_404+repo_404"}},{"paper_slug":"directional-message-passing-for-molecular-1","repo_url":"https://github.com/dmlc/dgl/tree/master/examples/pytorch/dimenet","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"drug-discovery","task_name":"Drug Discovery"},{"task_slug":"formation-energy","task_name":"Formation Energy"}],"methods":[{"method_slug":"mpnn","method_name":"MPNN"}],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/drug-discovery-on-qm9","task":"Drug Discovery","dataset":"QM9","model":"DimeNet","rank_in_archive_order":7,"of":11,"metrics":{"Error ratio":"0.44"},"uses_additional_data":false},{"leaderboard":"/sota/formation-energy-on-qm9","task":"Formation Energy","dataset":"QM9","model":"DimeNet","rank_in_archive_order":9,"of":18,"metrics":{"MAE":"0.185"},"uses_additional_data":false}],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2003.03123","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2003.03123"}},"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. 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