{"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/efficient-long-range-convolutions-for-point-1","title":"Efficient Long-Range Convolutions for Point Clouds","arxiv_id":"2010.05295","date":"2020-10-11","proceeding":null,"authors":["Yifan Peng","Lin Lin","Lexing Ying","Leonardo Zepeda-Núñez"],"abstract":"The efficient treatment of long-range interactions for point clouds is a challenging problem in many scientific machine learning applications. To extract global information, one usually needs a large window size, a large number of layers, and/or a large number of channels. This can often significantly increase the computational cost. In this work, we present a novel neural network layer that directly incorporates long-range information for a point cloud. This layer, dubbed the long-range convolutional (LRC)-layer, leverages the convolutional theorem coupled with the non-uniform Fourier transform. In a nutshell, the LRC-layer mollifies the point cloud to an adequately sized regular grid, computes its Fourier transform, multiplies the result by a set of trainable Fourier multipliers, computes the inverse Fourier transform, and finally interpolates the result back to the point cloud. The resulting global all-to-all convolution operation can be performed in nearly-linear time asymptotically with respect to the number of input points. The LRC-layer is a particularly powerful tool when combined with local convolution as together they offer efficient and seamless treatment of both short and long range interactions. We showcase this framework by introducing a neural network architecture that combines LRC-layers with short-range convolutional layers to accurately learn the energy and force associated with a $N$-body potential. We also exploit the induced two-level decomposition and propose an efficient strategy to train the combined architecture with a reduced number of samples.","url_abs":"https://arxiv.org/abs/2010.05295v1","url_pdf":"https://arxiv.org/pdf/2010.05295v1.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":"efficient-long-range-convolutions-for-point-1","repo_url":"https://github.com/Forgotten/Efficient_Long-Range_Convolutions_for_Point_Clouds","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"tf","reach":null}],"tasks":[],"methods":[{"method_slug":"convolution","method_name":"Convolution"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}