{"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-two-pass-softmax-algorithm","title":"The Two-Pass Softmax Algorithm","arxiv_id":"2001.04438","date":"2020-01-13","proceeding":null,"authors":["Marat Dukhan","Artsiom Ablavatski"],"abstract":"The softmax (also called softargmax) function is widely used in machine learning models to normalize real-valued scores into a probability distribution. To avoid floating-point overflow, the softmax function is conventionally implemented in three passes: the first pass to compute the normalization constant, and two other passes to compute outputs from normalized inputs. We analyze two variants of the Three-Pass algorithm and demonstrate that in a well-optimized implementation on HPC-class processors performance of all three passes is limited by memory bandwidth. We then present a novel algorithm for softmax computation in just two passes. The proposed Two-Pass algorithm avoids both numerical overflow and the extra normalization pass by employing an exotic representation for intermediate values, where each value is represented as a pair of floating-point numbers: one representing the \"mantissa\" and another representing the \"exponent\". Performance evaluation demonstrates that on out-of-cache inputs on an Intel Skylake-X processor the new Two-Pass algorithm outperforms the traditional Three-Pass algorithm by up to 28% in AVX512 implementation, and by up to 18% in AVX2 implementation. The proposed Two-Pass algorithm also outperforms the traditional Three-Pass algorithm on Intel Broadwell and AMD Zen 2 processors. To foster reproducibility, we released an open-source implementation of the new Two-Pass Softmax algorithm and other experiments in this paper as a part of XNNPACK library at GitHub.com/google/XNNPACK.","url_abs":"https://arxiv.org/abs/2001.04438v1","url_pdf":"https://arxiv.org/pdf/2001.04438v1.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-two-pass-softmax-algorithm","repo_url":"https://github.com/google/XNNPACK","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"NOASSERTION"}},{"paper_slug":"the-two-pass-softmax-algorithm","repo_url":"https://github.com/TinkerBoard2-Android/external-XNNPACK","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"NOASSERTION"}},{"paper_slug":"the-two-pass-softmax-algorithm","repo_url":"https://github.com/annxingyuan/XNNPACK","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"NOASSERTION"}},{"paper_slug":"the-two-pass-softmax-algorithm","repo_url":"https://github.com/liuluyang530/XNNPACK-gpt","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"NOASSERTION"}}],"tasks":[{"task_slug":"two","task_name":"Vocal Bursts Valence Prediction"}],"methods":[{"method_slug":"softmax","method_name":"Softmax"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}