{"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/orthogonal-recurrent-neural-networks-with","title":"Orthogonal Recurrent Neural Networks with Scaled Cayley Transform","arxiv_id":"1707.09520","date":"2017-07-29","proceeding":"ICML 2018 7","authors":["Kyle Helfrich","Devin Willmott","Qiang Ye"],"abstract":"Recurrent Neural Networks (RNNs) are designed to handle sequential data but\nsuffer from vanishing or exploding gradients. Recent work on Unitary Recurrent\nNeural Networks (uRNNs) have been used to address this issue and in some cases,\nexceed the capabilities of Long Short-Term Memory networks (LSTMs). We propose\na simpler and novel update scheme to maintain orthogonal recurrent weight\nmatrices without using complex valued matrices. This is done by parametrizing\nwith a skew-symmetric matrix using the Cayley transform. Such a parametrization\nis unable to represent matrices with negative one eigenvalues, but this\nlimitation is overcome by scaling the recurrent weight matrix by a diagonal\nmatrix consisting of ones and negative ones. The proposed training scheme\ninvolves a straightforward gradient calculation and update step. In several\nexperiments, the proposed scaled Cayley orthogonal recurrent neural network\n(scoRNN) achieves superior results with fewer trainable parameters than other\nunitary RNNs.","url_abs":"http://arxiv.org/abs/1707.09520v3","url_pdf":"http://arxiv.org/pdf/1707.09520v3.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":"orthogonal-recurrent-neural-networks-with","repo_url":"https://github.com/SpartinStuff/scoRNN","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":null},{"paper_slug":"orthogonal-recurrent-neural-networks-with","repo_url":"https://github.com/HUJI-Deep/Long-Term-Memory-of-Deep-RNNs","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1707.09520","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1707.09520"}},"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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