{"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/the-lovasz-hinge-a-novel-convex-surrogate-for","title":"The Lovász Hinge: A Novel Convex Surrogate for Submodular Losses","arxiv_id":"1512.07797","date":"2015-12-24","proceeding":null,"authors":["Jiaqian Yu","Matthew Blaschko"],"abstract":"Learning with non-modular losses is an important problem when sets of\npredictions are made simultaneously. The main tools for constructing convex\nsurrogate loss functions for set prediction are margin rescaling and slack\nrescaling. In this work, we show that these strategies lead to tight convex\nsurrogates iff the underlying loss function is increasing in the number of\nincorrect predictions. However, gradient or cutting-plane computation for these\nfunctions is NP-hard for non-supermodular loss functions. We propose instead a\nnovel surrogate loss function for submodular losses, the Lov\\'asz hinge, which\nleads to O(p log p) complexity with O(p) oracle accesses to the loss function\nto compute a gradient or cutting-plane. We prove that the Lov\\'asz hinge is\nconvex and yields an extension. As a result, we have developed the first\ntractable convex surrogates in the literature for submodular losses. We\ndemonstrate the utility of this novel convex surrogate through several set\nprediction tasks, including on the PASCAL VOC and Microsoft COCO datasets.","url_abs":"http://arxiv.org/abs/1512.07797v2","url_pdf":"http://arxiv.org/pdf/1512.07797v2.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":"the-lovasz-hinge-a-novel-convex-surrogate-for","repo_url":"https://github.com/yjq8812/lovaszhinge","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"the-lovasz-hinge-a-novel-convex-surrogate-for","repo_url":"https://github.com/kornia/kornia","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=1512.07797","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}