{"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/on-the-fundamental-trade-offs-in-learning","title":"On Characterizing the Trade-off in Invariant Representation Learning","arxiv_id":"2109.03386","date":"2021-09-08","proceeding":"NeurIPS 2021 12","authors":["Bashir Sadeghi","Sepehr Dehdashtian","Vishnu Boddeti"],"abstract":"Many applications of representation learning, such as privacy preservation, algorithmic fairness, and domain adaptation, desire explicit control over semantic information being discarded. This goal is formulated as satisfying two objectives: maximizing utility for predicting a target attribute while simultaneously being invariant (independent) to a known semantic attribute. Solutions to invariant representation learning (IRepL) problems lead to a trade-off between utility and invariance when they are competing. While existing works study bounds on this trade-off, two questions remain outstanding: 1) What is the exact trade-off between utility and invariance? and 2) What are the encoders (mapping the data to a representation) that achieve the trade-off, and how can we estimate it from training data? This paper addresses these questions for IRepLs in reproducing kernel Hilbert spaces (RKHS)s. Under the assumption that the distribution of a low-dimensional projection of high-dimensional data is approximately normal, we derive a closed-form solution for the global optima of the underlying optimization problem for encoders in RKHSs. This yields closed formulae for a near-optimal trade-off, corresponding optimal representation dimensionality, and the corresponding encoder(s). We also numerically quantify the trade-off on representative problems and compare them to those achieved by baseline IRepL algorithms.","url_abs":"https://arxiv.org/abs/2109.03386v4","url_pdf":"https://arxiv.org/pdf/2109.03386v4.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":"on-the-fundamental-trade-offs-in-learning","repo_url":"https://github.com/human-analysis/tradeoff-invariant-representation-learning","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"attribute","task_name":"Attribute"},{"task_slug":"domain-adaptation","task_name":"Domain Adaptation"},{"task_slug":"fairness","task_name":"Fairness"},{"task_slug":"representation-learning","task_name":"Representation Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2109.03386","atlas_url":"https://app.syntology.ai/?focus=2109.03386","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}