{"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/deep-complex-networks","title":"Deep Complex Networks","arxiv_id":"1705.09792","date":"2017-05-27","proceeding":"ICLR 2018 1","authors":["Chiheb Trabelsi","Olexa Bilaniuk","Ying Zhang","Dmitriy Serdyuk","Sandeep Subramanian","João Felipe Santos","Soroush Mehri","Negar Rostamzadeh","Yoshua Bengio","Christopher J. Pal"],"abstract":"At present, the vast majority of building blocks, techniques, and\narchitectures for deep learning are based on real-valued operations and\nrepresentations. However, recent work on recurrent neural networks and older\nfundamental theoretical analysis suggests that complex numbers could have a\nricher representational capacity and could also facilitate noise-robust memory\nretrieval mechanisms. Despite their attractive properties and potential for\nopening up entirely new neural architectures, complex-valued deep neural\nnetworks have been marginalized due to the absence of the building blocks\nrequired to design such models. In this work, we provide the key atomic\ncomponents for complex-valued deep neural networks and apply them to\nconvolutional feed-forward networks and convolutional LSTMs. More precisely, we\nrely on complex convolutions and present algorithms for complex\nbatch-normalization, complex weight initialization strategies for\ncomplex-valued neural nets and we use them in experiments with end-to-end\ntraining schemes. We demonstrate that such complex-valued models are\ncompetitive with their real-valued counterparts. We test deep complex models on\nseveral computer vision tasks, on music transcription using the MusicNet\ndataset and on Speech Spectrum Prediction using the TIMIT dataset. We achieve\nstate-of-the-art performance on these audio-related tasks.","url_abs":"http://arxiv.org/abs/1705.09792v4","url_pdf":"http://arxiv.org/pdf/1705.09792v4.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":"deep-complex-networks","repo_url":"https://github.com/ChihebTrabelsi/deep_complex_networks","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}},{"paper_slug":"deep-complex-networks","repo_url":"https://github.com/Doyosae/Deep-Complex-Networks","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"unanswered"}},{"paper_slug":"deep-complex-networks","repo_url":"https://github.com/JesperDramsch/keras-complex","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"NOASSERTION"}},{"paper_slug":"deep-complex-networks","repo_url":"https://github.com/MRSRL/complex-networks-release","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"unanswered"}},{"paper_slug":"deep-complex-networks","repo_url":"https://github.com/Medabid1/ComplexValuedCNN","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"unanswered"}},{"paper_slug":"deep-complex-networks","repo_url":"https://github.com/QinggangSUN/keras_complex_valued_networks","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"unanswered"}},{"paper_slug":"deep-complex-networks","repo_url":"https://github.com/ispamm/htorch","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"deep-complex-networks","repo_url":"https://github.com/omrijsharon/torchlex","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"deep-complex-networks","repo_url":"https://github.com/ypeleg/komplex","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"image-classification","task_name":"Image Classification"},{"task_slug":"music-transcription","task_name":"Music Transcription"},{"task_slug":"retrieval","task_name":"Retrieval"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/image-classification-on-cifar-10","task":"Image Classification","dataset":"CIFAR-10","model":"Deep Complex","rank_in_archive_order":158,"of":265,"metrics":{"Percentage correct":"94.4"},"uses_additional_data":false},{"leaderboard":"/sota/image-classification-on-svhn","task":"Image Classification","dataset":"SVHN","model":"Deep Complex","rank_in_archive_order":40,"of":62,"metrics":{"Percentage error":"3.3"},"uses_additional_data":false},{"leaderboard":"/sota/music-transcription-on-musicnet","task":"Music Transcription","dataset":"MusicNet","model":"Deep Complex Network","rank_in_archive_order":3,"of":6,"metrics":{"APS":"72.9","Number of params":"8.8M"},"uses_additional_data":false},{"leaderboard":"/sota/music-transcription-on-musicnet","task":"Music Transcription","dataset":"MusicNet","model":"Deep Real Network","rank_in_archive_order":5,"of":6,"metrics":{"APS":"69.6","Number of params":"10.0M"},"uses_additional_data":false}],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1705.09792","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1705.09792"}},"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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