{"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/learning-interpretable-low-dimensional-1","title":"Learning Interpretable Low-dimensional Representation via Physical Symmetry","arxiv_id":"2302.10890","date":"2023-02-05","proceeding":"NeurIPS 2023 11","authors":["Xuanjie Liu","Daniel Chin","Yichen Huang","Gus Xia"],"abstract":"We have recently seen great progress in learning interpretable music representations, ranging from basic factors, such as pitch and timbre, to high-level concepts, such as chord and texture. However, most methods rely heavily on music domain knowledge. It remains an open question what general computational principles give rise to interpretable representations, especially low-dim factors that agree with human perception. In this study, we take inspiration from modern physics and use physical symmetry as a self consistency constraint for the latent space of time-series data. Specifically, it requires the prior model that characterises the dynamics of the latent states to be equivariant with respect to certain group transformations. We show that physical symmetry leads the model to learn a linear pitch factor from unlabelled monophonic music audio in a self-supervised fashion. In addition, the same methodology can be applied to computer vision, learning a 3D Cartesian space from videos of a simple moving object without labels. Furthermore, physical symmetry naturally leads to counterfactual representation augmentation, a new technique which improves sample efficiency.","url_abs":"https://arxiv.org/abs/2302.10890v4","url_pdf":"https://arxiv.org/pdf/2302.10890v4.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":"learning-interpretable-low-dimensional-1","repo_url":"https://github.com/xuanjieliu/self-supervised-learning-via-physical-symmetry","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"time-series-1","task_name":"Time Series"},{"task_slug":null,"task_name":"counterfactual"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2302.10890","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2302.10890"}},"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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