{"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-matrix-calculus-you-need-for-deep","title":"The Matrix Calculus You Need For Deep Learning","arxiv_id":"1802.01528","date":"2018-02-05","proceeding":null,"authors":["Terence Parr","Jeremy Howard"],"abstract":"This paper is an attempt to explain all the matrix calculus you need in order\nto understand the training of deep neural networks. We assume no math knowledge\nbeyond what you learned in calculus 1, and provide links to help you refresh\nthe necessary math where needed. Note that you do not need to understand this\nmaterial before you start learning to train and use deep learning in practice;\nrather, this material is for those who are already familiar with the basics of\nneural networks, and wish to deepen their understanding of the underlying math.\nDon't worry if you get stuck at some point along the way---just go back and\nreread the previous section, and try writing down and working through some\nexamples. And if you're still stuck, we're happy to answer your questions in\nthe Theory category at forums.fast.ai. Note: There is a reference section at\nthe end of the paper summarizing all the key matrix calculus rules and\nterminology discussed here. See related articles at http://explained.ai","url_abs":"http://arxiv.org/abs/1802.01528v3","url_pdf":"http://arxiv.org/pdf/1802.01528v3.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-matrix-calculus-you-need-for-deep","repo_url":"https://github.com/parrt/bookish","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"the-matrix-calculus-you-need-for-deep","repo_url":"https://github.com/ChrominskiMateusz/LSTM_layer_with_kernel_fusion","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":null},{"paper_slug":"the-matrix-calculus-you-need-for-deep","repo_url":"https://github.com/fr3fou/gone","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":null},{"paper_slug":"the-matrix-calculus-you-need-for-deep","repo_url":"https://github.com/leandromineti/ml-curriculum","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"the-matrix-calculus-you-need-for-deep","repo_url":"https://github.com/leandromineti/ml-knowledge-graph","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"articles","task_name":"Articles"},{"task_slug":"deep-learning","task_name":"Deep Learning"},{"task_slug":"math","task_name":"Math"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}