{"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/a-neural-network-for-semigroups","title":"A Neural Network for Semigroups","arxiv_id":"2103.07388","date":"2021-03-12","proceeding":null,"authors":["Edouard Balzin","Boris Shminke"],"abstract":"Tasks like image reconstruction in computer vision, matrix completion in recommender systems and link prediction in graph theory, are well studied in machine learning literature. In this work, we apply a denoising autoencoder-based neural network architecture to the task of completing partial multiplication (Cayley) tables of finite semigroups. We suggest a novel loss function for that task based on the algebraic nature of the semigroup data. We also provide a software package for conducting experiments similar to those carried out in this work. Our experiments showed that with only about 10% of the available data, it is possible to build a model capable of reconstructing a full Cayley from only half of it in about 80% of cases.","url_abs":"https://arxiv.org/abs/2103.07388v1","url_pdf":"https://arxiv.org/pdf/2103.07388v1.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":"a-neural-network-for-semigroups","repo_url":"https://github.com/inpefess/neural-semigroups","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"denoising","task_name":"Denoising"},{"task_slug":"image-reconstruction","task_name":"Image Reconstruction"},{"task_slug":"link-prediction","task_name":"Link Prediction"},{"task_slug":"matrix-completion","task_name":"Matrix Completion"},{"task_slug":"recommendation-systems","task_name":"Recommendation Systems"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}