{"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/quantifying-and-learning-disentangled-1","title":"Quantifying and Learning Linear Symmetry-Based Disentanglement","arxiv_id":"2011.06070","date":"2020-11-11","proceeding":"NeurIPS 2021 12","authors":["Loek Tonnaer","Luis A. Pérez Rey","Vlado Menkovski","Mike Holenderski","Jacobus W. Portegies"],"abstract":"The definition of Linear Symmetry-Based Disentanglement (LSBD) formalizes the notion of linearly disentangled representations, but there is currently no metric to quantify LSBD. Such a metric is crucial to evaluate LSBD methods and to compare to previous understandings of disentanglement. We propose $\\mathcal{D}_\\mathrm{LSBD}$, a mathematically sound metric to quantify LSBD, and provide a practical implementation for $\\mathrm{SO}(2)$ groups. Furthermore, from this metric we derive LSBD-VAE, a semi-supervised method to learn LSBD representations. We demonstrate the utility of our metric by showing that (1) common VAE-based disentanglement methods don't learn LSBD representations, (2) LSBD-VAE as well as other recent methods can learn LSBD representations, needing only limited supervision on transformations, and (3) various desirable properties expressed by existing disentanglement metrics are also achieved by LSBD representations.","url_abs":"https://arxiv.org/abs/2011.06070v4","url_pdf":"https://arxiv.org/pdf/2011.06070v4.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":"quantifying-and-learning-disentangled-1","repo_url":"https://github.com/luis-armando-perez-rey/lsbd-vae","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"tf","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"disentanglement","task_name":"Disentanglement"},{"task_slug":"interpretable-machine-learning","task_name":"Interpretable Machine Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2011.06070","atlas_url":"https://app.syntology.ai/?focus=2011.06070","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}