{"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/complex-unitary-recurrent-neural-networks","title":"Complex Unitary Recurrent Neural Networks using Scaled Cayley Transform","arxiv_id":"1811.04142","date":"2018-11-09","proceeding":null,"authors":["Kehelwala D. G. Maduranga","Kyle E. Helfrich","Qiang Ye"],"abstract":"Recurrent neural networks (RNNs) have been successfully used on a wide range\nof sequential data problems. A well known difficulty in using RNNs is the\n\\textit{vanishing or exploding gradient} problem. Recently, there have been\nseveral different RNN architectures that try to mitigate this issue by\nmaintaining an orthogonal or unitary recurrent weight matrix. One such\narchitecture is the scaled Cayley orthogonal recurrent neural network (scoRNN)\nwhich parameterizes the orthogonal recurrent weight matrix through a scaled\nCayley transform. This parametrization contains a diagonal scaling matrix\nconsisting of positive or negative one entries that can not be optimized by\ngradient descent. Thus the scaling matrix is fixed before training and a\nhyperparameter is introduced to tune the matrix for each particular task. In\nthis paper, we develop a unitary RNN architecture based on a complex scaled\nCayley transform. Unlike the real orthogonal case, the transformation uses a\ndiagonal scaling matrix consisting of entries on the complex unit circle which\ncan be optimized using gradient descent and no longer requires the tuning of a\nhyperparameter. We also provide an analysis of a potential issue of the modReLU\nactiviation function which is used in our work and several other unitary RNNs.\nIn the experiments conducted, the scaled Cayley unitary recurrent neural\nnetwork (scuRNN) achieves comparable or better results than scoRNN and other\nunitary RNNs without fixing the scaling matrix.","url_abs":"http://arxiv.org/abs/1811.04142v2","url_pdf":"http://arxiv.org/pdf/1811.04142v2.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":"complex-unitary-recurrent-neural-networks","repo_url":"https://github.com/Gayan225/scuRNN","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"NOASSERTION"}}],"tasks":[],"methods":[{"method_slug":"unitary-rnn","method_name":"Unitary RNN"},{"method_slug":"modrelu","method_name":"modReLU"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1811.04142","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}