{"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/an-exploration-of-softmax-alternatives","title":"An Exploration of Softmax Alternatives Belonging to the Spherical Loss Family","arxiv_id":"1511.05042","date":"2015-11-16","proceeding":null,"authors":["Alexandre de Brébisson","Pascal Vincent"],"abstract":"In a multi-class classification problem, it is standard to model the output\nof a neural network as a categorical distribution conditioned on the inputs.\nThe output must therefore be positive and sum to one, which is traditionally\nenforced by a softmax. This probabilistic mapping allows to use the maximum\nlikelihood principle, which leads to the well-known log-softmax loss. However\nthe choice of the softmax function seems somehow arbitrary as there are many\nother possible normalizing functions. It is thus unclear why the log-softmax\nloss would perform better than other loss alternatives. In particular Vincent\net al. (2015) recently introduced a class of loss functions, called the\nspherical family, for which there exists an efficient algorithm to compute the\nupdates of the output weights irrespective of the output size. In this paper,\nwe explore several loss functions from this family as possible alternatives to\nthe traditional log-softmax. In particular, we focus our investigation on\nspherical bounds of the log-softmax loss and on two spherical log-likelihood\nlosses, namely the log-Spherical Softmax suggested by Vincent et al. (2015) and\nthe log-Taylor Softmax that we introduce. Although these alternatives do not\nyield as good results as the log-softmax loss on two language modeling tasks,\nthey surprisingly outperform it in our experiments on MNIST and CIFAR-10,\nsuggesting that they might be relevant in a broad range of applications.","url_abs":"http://arxiv.org/abs/1511.05042v3","url_pdf":"http://arxiv.org/pdf/1511.05042v3.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":"an-exploration-of-softmax-alternatives","repo_url":"https://github.com/pascal20100/factored_output_layer","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"language-modeling","task_name":"Language Modeling"},{"task_slug":"language-modelling","task_name":"Language Modelling"},{"task_slug":"multi-class-classification","task_name":"Multi-class Classification"}],"methods":[{"method_slug":"softmax","method_name":"Softmax"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1511.05042","atlas_url":"https://app.syntology.ai/?focus=1511.05042","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}