{"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/smooth-loss-functions-for-deep-top-k","title":"Smooth Loss Functions for Deep Top-k Classification","arxiv_id":"1802.07595","date":"2018-02-21","proceeding":"ICLR 2018 1","authors":["Leonard Berrada","Andrew Zisserman","M. Pawan Kumar"],"abstract":"The top-k error is a common measure of performance in machine learning and\ncomputer vision. In practice, top-k classification is typically performed with\ndeep neural networks trained with the cross-entropy loss. Theoretical results\nindeed suggest that cross-entropy is an optimal learning objective for such a\ntask in the limit of infinite data. In the context of limited and noisy data\nhowever, the use of a loss function that is specifically designed for top-k\nclassification can bring significant improvements. Our empirical evidence\nsuggests that the loss function must be smooth and have non-sparse gradients in\norder to work well with deep neural networks. Consequently, we introduce a\nfamily of smoothed loss functions that are suited to top-k optimization via\ndeep learning. The widely used cross-entropy is a special case of our family.\nEvaluating our smooth loss functions is computationally challenging: a na\\\"ive\nalgorithm would require $\\mathcal{O}(\\binom{n}{k})$ operations, where n is the\nnumber of classes. Thanks to a connection to polynomial algebra and a\ndivide-and-conquer approach, we provide an algorithm with a time complexity of\n$\\mathcal{O}(k n)$. Furthermore, we present a novel approximation to obtain\nfast and stable algorithms on GPUs with single floating point precision. We\ncompare the performance of the cross-entropy loss and our margin-based losses\nin various regimes of noise and data size, for the predominant use case of k=5.\nOur investigation reveals that our loss is more robust to noise and overfitting\nthan cross-entropy.","url_abs":"http://arxiv.org/abs/1802.07595v1","url_pdf":"http://arxiv.org/pdf/1802.07595v1.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":"smooth-loss-functions-for-deep-top-k","repo_url":"https://github.com/oval-group/smooth-topk","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"classification-1","task_name":"Classification"},{"task_slug":"classification","task_name":"General Classification"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1802.07595","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1802.07595"}},"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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