[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-117854-en":3,"doc-seo-117854-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},117854,34359740700684,"Finn","https://ap-avatar.wpscdn.com/avatar/1f400023980c374ae676?_k=1777273430885731487",8,"Research & Report","Group invariant machine learning - by fundamental domain projections","Supervised group invariant and equivariant machine learning is addressed through geometric topology. A novel pre-processing strategy projects inputs into a geometric space that parametrises symmetry-group orbits, enabling subsequent use of arbitrary learning models such as neural networks, random forests, or support-vector machines. An efficient algorithm for computing the geometric projection is provided. Example applications include prediction of Hodge numbers of CICY matrices, where the method yields improved accuracy compared with approaches reported in the literature.","King’s Research Portal  \nDocument Version  \nPublisher's PDF, also known as Version of record  \nLink to publication record in King's Research Portal  \nCitation for published version (APA):  \nSheard, D. , Platt, D. , & Aslan, B. (2023) . Group invariant machine learning by fundamental domain projections. Proceedings of Machine Learning Research, 197, 182-218 . [https://proceedings.mlr.press/v197/aslan23a.html](https://proceedings.mlr.press/v197/aslan23a.html)  \nCiting this paper  \nPlease note that where the full-text provided on King's Research Portal is the Author Accepted Manuscript or Post-Print version this may differ from the final Published version. If citing, it is advised that you check and use the publisher's definitive version for pagination, volume/issue, and date of publication details. 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Oct. 2023  \nGroup invariant machine learning by fundamental domain projections  \nBenjamin Aslan∗ [ucahbas@ucl.ac.uk](ucahbas@ucl.ac.uk)  \nUniversity College London  \nDaniel Platt∗ [daniel.1.platt@kcl.ac.uk](daniel.1.platt@kcl.ac.uk)  \nKing’s College London, Strand Campus  \nDavid Sheard∗ [david.sheard.17@ucl.ac.uk](david.sheard.17@ucl.ac.uk)  \nUniversity College London  \nEditors: Sophia Sanborn, Christian Shewmake, Simone Azeglio, Arianna Di Bernardo, Nina Miolane  \nAbstract  \nWe approach the well-studied problem of supervised group invariant and equivariant machine learning from the point of view of geometric topology. We propose a novel approach using a pre-processing step, which involves projecting the input data into a geometric space which parametrises the orbits of the symmetry group. This new data can then be the input for an arbitrary machine learning model (neural network, random forest, support-vector machine etc) . We give an algorithm to compute the geometric projection, which is efficient to implement, and we illustrate our approach on some example machine learning problems (including the well-studied problem of predicting Hodge numbers of CICY matrices), finding an improvement in accuracy versus others in the literature.  \nKeywords: Group invariant, group equivariant, geometric deep learning, fundamental domain, geometric topology  \n1. Introduction  \nMany tasks in machine learning can be understood as approximating a function α : X → Y between a feature space and an output space. Typically, these may be subsets of Rn, but could be more complicated like Riemannian manifolds. We consider the problem in the presence of symmetries—more precisely, suppose a group G that acts on X on the left, and α satisfies the invariance property  \nα (g · x) = α(x) for all x ∈ X, g ∈ G. (1)  \nA simple example is recognising a single handwritten digit which may have been rotated by 90◦ , 180◦ , or 270◦ , so the problem is invariant under the action of Z4 .  \nMachine learning models such as neural networks or random forests can approximate α but the resulting function β will not generally be G-invariant. The key t","cbCainYLVyBDzU0M","https://ap.wps.com/l/cbCainYLVyBDzU0M","pdf",904324,1,38,"English","en",105,"# Introduction\n## Previous work","[{\"question\":\"What is the core idea behind group invariant learning in this work?\",\"answer\":\"The method enforces invariance by projecting inputs into a geometric space that parametrises group orbits, then feeding this representation to standard machine learning models.\"},{\"question\":\"How does the proposed approach relate to existing techniques like data augmentation?\",\"answer\":\"The document contrasts symmetrisation methods such as data augmentation and pooling with intrinsic approaches that build invariance into the model structure, then proposes an alternative via geometric pre-processing.\"},{\"question\":\"What algorithm is presented, and why is it important?\",\"answer\":\"An algorithm is provided to compute the geometric projection efficiently, making the pre-processing step practical to implement.\"}]","Group invariant machine learning - 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