{"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/squared-earth-movers-distance-based-loss-for","title":"Squared Earth Mover's Distance-based Loss for Training Deep Neural Networks","arxiv_id":"1611.05916","date":"2016-11-17","proceeding":null,"authors":["Le Hou","Chen-Ping Yu","Dimitris Samaras"],"abstract":"In the context of single-label classification, despite the huge success of\ndeep learning, the commonly used cross-entropy loss function ignores the\nintricate inter-class relationships that often exist in real-life tasks such as\nage classification. In this work, we propose to leverage these relationships\nbetween classes by training deep nets with the exact squared Earth Mover's\nDistance (also known as Wasserstein distance) for single-label classification.\nThe squared EMD loss uses the predicted probabilities of all classes and\npenalizes the miss-predictions according to a ground distance matrix that\nquantifies the dissimilarities between classes. We demonstrate that on datasets\nwith strong inter-class relationships such as an ordering between classes, our\nexact squared EMD losses yield new state-of-the-art results. Furthermore, we\npropose a method to automatically learn this matrix using the CNN's own\nfeatures during training. We show that our method can learn a ground distance\nmatrix efficiently with no inter-class relationship priors and yield the same\nperformance gain. Finally, we show that our method can be generalized to\napplications that lack strong inter-class relationships and still maintain\nstate-of-the-art performance. Therefore, with limited computational overhead,\none can always deploy the proposed loss function on any dataset over the\nconventional cross-entropy.","url_abs":"http://arxiv.org/abs/1611.05916v4","url_pdf":"http://arxiv.org/pdf/1611.05916v4.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":"squared-earth-movers-distance-based-loss-for","repo_url":"https://github.com/MilesGrey/emd","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok"}},{"paper_slug":"squared-earth-movers-distance-based-loss-for","repo_url":"https://github.com/glanceable-io/ordinal-log-loss","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}},{"paper_slug":"squared-earth-movers-distance-based-loss-for","repo_url":"https://github.com/luke321321/portfolio","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"age-classification","task_name":"Age Classification"},{"task_slug":"classification","task_name":"General Classification"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1611.05916","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}