{"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/roto-translated-local-coordinate-frames-for","title":"Roto-translated Local Coordinate Frames For Interacting Dynamical Systems","arxiv_id":"2110.14961","date":"2021-10-28","proceeding":"NeurIPS 2021 12","authors":["Miltiadis Kofinas","Naveen Shankar Nagaraja","Efstratios Gavves"],"abstract":"Modelling interactions is critical in learning complex dynamical systems, namely systems of interacting objects with highly non-linear and time-dependent behaviour. A large class of such systems can be formalized as $\\textit{geometric graphs}$, $\\textit{i.e.}$, graphs with nodes positioned in the Euclidean space given an $\\textit{arbitrarily}$ chosen global coordinate system, for instance vehicles in a traffic scene. Notwithstanding the arbitrary global coordinate system, the governing dynamics of the respective dynamical systems are invariant to rotations and translations, also known as $\\textit{Galilean invariance}$. As ignoring these invariances leads to worse generalization, in this work we propose local coordinate frames per node-object to induce roto-translation invariance to the geometric graph of the interacting dynamical system. Further, the local coordinate frames allow for a natural definition of anisotropic filtering in graph neural networks. Experiments in traffic scenes, 3D motion capture, and colliding particles demonstrate that the proposed approach comfortably outperforms the recent state-of-the-art.","url_abs":"https://arxiv.org/abs/2110.14961v3","url_pdf":"https://arxiv.org/pdf/2110.14961v3.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":"roto-translated-local-coordinate-frames-for","repo_url":"https://github.com/mkofinas/locs","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"trajectory-forecasting","task_name":"Trajectory Forecasting"},{"task_slug":"trajectory-prediction","task_name":"Trajectory Prediction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2110.14961","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2110.14961"}},"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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