{"url":"/method/unitary-rnn","slug":"unitary-rnn","name":"Unitary RNN","full_name":"Unitary RNN","full_name_withheld":false,"description_markdown":"A **Unitary RNN** is a recurrent neural network architecture that uses a unitary hidden to hidden matrix. Specifically they concern dynamics of the form:\r\n\r\n$$ h\\_{t} = f\\left(Wh\\_{t−1} + Vx\\_{t}\\right) $$\r\n\r\nwhere $W$ is a unitary matrix $\\left(W^{†}W = I\\right)$. The product of unitary matrices is a unitary matrix, so $W$ can be parameterised as a product of simpler unitary matrices:\r\n\r\n$$ h\\_{t} = f\\left(D\\_{3}R\\_{2}F^{−1}D\\_{2}PR\\_{1}FD\\_{1}h\\_{t−1} + Vxt\\right) $$\r\n\r\nwhere $D\\_{3}$, $D\\_{2}$, $D\\_{1}$ are learned diagonal complex matrices, and $R\\_{2}$, $R\\_{1}$ are learned reflection matrices. Matrices $F$ and $F^{−1}$ are the discrete Fourier transformation and its inverse. P is any constant random permutation. The activation function $f\\left(h\\right)$ applies a rectified linear unit with a learned bias to the modulus of each complex number. Only\r\nthe diagonal and reflection matrices, $D$ and $R$, are learned, so Unitary RNNs have fewer parameters than [LSTMs](https://paperswithcode.com/method/lstm) with comparable numbers of hidden units.\r\n\r\nSource: [Associative LSTMs](https://arxiv.org/pdf/1602.03032.pdf)","description_state":"present","introduced_year":null,"introduced_by":{"title":"Unitary Evolution Recurrent Neural Networks","paper":"/paper/unitary-evolution-recurrent-neural-networks","first_author":"Martin Arjovsky","n_authors":3,"url_abs":null,"archive_paper_url":"https://paperswithcode.com/paper/unitary-evolution-recurrent-neural-networks"},"source":{"url":"http://arxiv.org/abs/1511.06464v4","title":"Unitary Evolution Recurrent Neural Networks","url_on_a_paper_host":true},"code_snippet_url":null,"code_snippet_url_on_a_code_host":false,"categories":[{"area":"Sequential","area_id":"sequential","collection":"Recurrent Neural Networks","url":"/methods/category/recurrent-neural-networks","pwc_aliases":[]}],"n_papers_tagged":3,"archive_num_papers":3,"papers_newest_first":[{"paper":"/paper/an-automl-based-approach-to-multimodal-image","title":"An AutoML-based Approach to Multimodal Image Sentiment Analysis","date":"2021-02-16","arxiv_id":"2102.08092","n_code_links":0,"syntology":null},{"paper":"/paper/complex-unitary-recurrent-neural-networks","title":"Complex Unitary Recurrent Neural Networks using Scaled Cayley Transform","date":"2018-11-09","arxiv_id":"1811.04142","n_code_links":1,"syntology":null},{"paper":"/paper/unitary-evolution-recurrent-neural-networks","title":"Unitary Evolution Recurrent Neural Networks","date":"2015-11-20","arxiv_id":"1511.06464","n_code_links":2,"syntology":{"ran":1,"of":1,"unverified":0,"pointer_only":1}}],"papers_shown":3,"tasks":[{"task":"/task/automl","name":"AutoML","papers":1},{"task":"/task/marketing","name":"Marketing","papers":1},{"task":"/task/multimodal-sentiment-analysis","name":"Multimodal Sentiment Analysis","papers":1},{"task":"/task/recommendation-systems","name":"Recommendation Systems","papers":1},{"task":"/task/sentiment-analysis","name":"Sentiment Analysis","papers":1},{"task":"/task/sequential-image-classification","name":"Sequential Image Classification","papers":1}],"tasks_shown":6,"n_tasks":6,"usage_by_year":[{"year":"2015","papers":1},{"year":"2018","papers":1},{"year":"2021","papers":1}],"row_source":"methods_table","archive":{"source":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","archive_url":"https://paperswithcode.com/method/unitary-rnn"},"syntology_read_at":"2026-09-24T18:15:14+00:00"}