{"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/tunable-efficient-unitary-neural-networks","title":"Tunable Efficient Unitary Neural Networks (EUNN) and their application to RNNs","arxiv_id":"1612.05231","date":"2016-12-15","proceeding":"ICML 2017 8","authors":["Li Jing","Yichen Shen","Tena Dubček","John Peurifoy","Scott Skirlo","Yann Lecun","Max Tegmark","Marin Soljačić"],"abstract":"Using unitary (instead of general) matrices in artificial neural networks\n(ANNs) is a promising way to solve the gradient explosion/vanishing problem, as\nwell as to enable ANNs to learn long-term correlations in the data. This\napproach appears particularly promising for Recurrent Neural Networks (RNNs).\nIn this work, we present a new architecture for implementing an Efficient\nUnitary Neural Network (EUNNs); its main advantages can be summarized as\nfollows. Firstly, the representation capacity of the unitary space in an EUNN\nis fully tunable, ranging from a subspace of SU(N) to the entire unitary space.\nSecondly, the computational complexity for training an EUNN is merely\n$\\mathcal{O}(1)$ per parameter. Finally, we test the performance of EUNNs on\nthe standard copying task, the pixel-permuted MNIST digit recognition benchmark\nas well as the Speech Prediction Test (TIMIT). We find that our architecture\nsignificantly outperforms both other state-of-the-art unitary RNNs and the LSTM\narchitecture, in terms of the final performance and/or the wall-clock training\nspeed. EUNNs are thus promising alternatives to RNNs and LSTMs for a wide\nvariety of applications.","url_abs":"http://arxiv.org/abs/1612.05231v3","url_pdf":"http://arxiv.org/pdf/1612.05231v3.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":"tunable-efficient-unitary-neural-networks","repo_url":"https://github.com/jingli9111/EUNN-tensorflow","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":{"status":"gone","observed_at":"2026-09-18","how":"tree_404+repo_404"}},{"paper_slug":"tunable-efficient-unitary-neural-networks","repo_url":"https://github.com/iguanaus/EUNN-theano","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"tunable-efficient-unitary-neural-networks","repo_url":"https://github.com/flaport/torch_eunn","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"tunable-efficient-unitary-neural-networks","repo_url":"https://github.com/solgaardlab/neurophox","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":null,"task_name":"Permuted-MNIST"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1612.05231","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1612.05231"}},"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. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/flaport/torch_eunn","reach":null},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/solgaardlab/neurophox","reach":{"status":"ok","spdx":"MIT"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/jingli9111/EUNN-tensorflow","reach":{"status":"gone","observed_at":"2026-09-18","how":"tree_404+repo_404"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/iguanaus/EUNN-theano","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"ran_violates":1,"ran_fixture":1,"unverified":20},"by_repo_kind":{"official":{"samples":5,"ran":0,"repositories":1},"listed":{"samples":17,"ran":2,"repositories":2}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"2d824fe3cb24d6a2","entry":"cmm","repo":"flaport/torch_eunn","repo_kind":"listed","path":"torch_eunn.py","file_url":"https://github.com/flaport/torch_eunn/blob/HEAD/torch_eunn.py","link_basis":"first_harvest_node","language":"python","status":"ran_violates","verification_level":1,"contract_check":"VIOLATES","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"2d824fe3cb24d6a2"}},{"code_sha256_prefix":"6f86da6493673239","entry":"eunn","repo":"flaport/torch_eunn","repo_kind":"listed","path":"torch_eunn.py","file_url":"https://github.com/flaport/torch_eunn/blob/HEAD/torch_eunn.py","link_basis":"first_harvest_node","language":"python","status":"ran_fixture","verification_level":1,"contract_check":"RAISES","metamorphic_tier":"invariant","behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"6f86da6493673239"}},{"code_sha256_prefix":"0f9745926384036b","entry":"bptrs","repo":"iguanaus/EUNN-theano","repo_kind":"official","path":"fftconv.py","file_url":"https://github.com/iguanaus/EUNN-theano/blob/HEAD/fftconv.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"0f9745926384036b"}},{"code_sha256_prefix":"2f5ba97abdeb258c","entry":"checkerboard_to_param","repo":"solgaardlab/neurophox","repo_kind":"listed","path":"neurophox/decompositions.py","file_url":"https://github.com/solgaardlab/neurophox/blob/HEAD/neurophox/decompositions.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"2f5ba97abdeb258c"}},{"code_sha256_prefix":"b03f07ab4d8a044b","entry":"cnorm","repo":"solgaardlab/neurophox","repo_kind":"listed","path":"neurophox/ml/nonlinearities.py","file_url":"https://github.com/solgaardlab/neurophox/blob/HEAD/neurophox/ml/nonlinearities.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"b03f07ab4d8a044b"}},{"code_sha256_prefix":"b0024b3700fafa76","entry":"cnormsq","repo":"solgaardlab/neurophox","repo_kind":"listed","path":"neurophox/ml/nonlinearities.py","file_url":"https://github.com/solgaardlab/neurophox/blob/HEAD/neurophox/ml/nonlinearities.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"b0024b3700fafa76"}},{"code_sha256_prefix":"a7c7c0f896248555","entry":"complex_mse","repo":"solgaardlab/neurophox","repo_kind":"listed","path":"neurophox/ml/linear.py","file_url":"https://github.com/solgaardlab/neurophox/blob/HEAD/neurophox/ml/linear.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"a7c7c0f896248555"}},{"code_sha256_prefix":"2e25840573fd6123","entry":"generate_keras_batch","repo":"solgaardlab/neurophox","repo_kind":"listed","path":"neurophox/ml/linear.py","file_url":"https://github.com/solgaardlab/neurophox/blob/HEAD/neurophox/ml/linear.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"2e25840573fd6123"}},{"code_sha256_prefix":"3268829a2be85b3d","entry":"get_haar_diagonal_sequence","repo":"solgaardlab/neurophox","repo_kind":"listed","path":"neurophox/helpers.py","file_url":"https://github.com/solgaardlab/neurophox/blob/HEAD/neurophox/helpers.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"3268829a2be85b3d"}},{"code_sha256_prefix":"fe084038a9330dac","entry":"get_haar_theta","repo":"solgaardlab/neurophox","repo_kind":"listed","path":"neurophox/initializers.py","file_url":"https://github.com/solgaardlab/neurophox/blob/HEAD/neurophox/initializers.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"fe084038a9330dac"}},{"code_sha256_prefix":"d958ae5b8ac823b4","entry":"get_initializer","repo":"solgaardlab/neurophox","repo_kind":"listed","path":"neurophox/initializers.py","file_url":"https://github.com/solgaardlab/neurophox/blob/HEAD/neurophox/initializers.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"d958ae5b8ac823b4"}},{"code_sha256_prefix":"58bc45ee4257a1b3","entry":"get_mzi_transfer_matrix","repo":"solgaardlab/neurophox","repo_kind":"listed","path":"neurophox/components/mzi.py","file_url":"https://github.com/solgaardlab/neurophox/blob/HEAD/neurophox/components/mzi.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"58bc45ee4257a1b3"}},{"code_sha256_prefix":"2947f55793f40d77","entry":"get_ortho_haar_theta","repo":"solgaardlab/neurophox","repo_kind":"listed","path":"neurophox/initializers.py","file_url":"https://github.com/solgaardlab/neurophox/blob/HEAD/neurophox/initializers.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"2947f55793f40d77"}},{"code_sha256_prefix":"eda08eb52c0cc327","entry":"get_tdc_transfer_matrix","repo":"solgaardlab/neurophox","repo_kind":"listed","path":"neurophox/components/mzi.py","file_url":"https://github.com/solgaardlab/neurophox/blob/HEAD/neurophox/components/mzi.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"eda08eb52c0cc327"}},{"code_sha256_prefix":"f0abdf7c350a7acc","entry":"gradient_descent","repo":"iguanaus/EUNN-theano","repo_kind":"official","path":"optimizations.py","file_url":"https://github.com/iguanaus/EUNN-theano/blob/HEAD/optimizations.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"f0abdf7c350a7acc"}},{"code_sha256_prefix":"9a1cc22fc4bebe7b","entry":"normalized_fidelity","repo":"solgaardlab/neurophox","repo_kind":"listed","path":"neurophox/ml/linear.py","file_url":"https://github.com/solgaardlab/neurophox/blob/HEAD/neurophox/ml/linear.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"9a1cc22fc4bebe7b"}},{"code_sha256_prefix":"b89a8b25a57a4ce1","entry":"permute_approx","repo":"iguanaus/EUNN-theano","repo_kind":"official","path":"widget.py","file_url":"https://github.com/iguanaus/EUNN-theano/blob/HEAD/widget.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"b89a8b25a57a4ce1"}},{"code_sha256_prefix":"e48f79c125c0bb57","entry":"permute_list12","repo":"iguanaus/EUNN-theano","repo_kind":"official","path":"widget.py","file_url":"https://github.com/iguanaus/EUNN-theano/blob/HEAD/widget.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"e48f79c125c0bb57"}},{"code_sha256_prefix":"7f653a85312e6df6","entry":"reck_decomposition","repo":"solgaardlab/neurophox","repo_kind":"listed","path":"neurophox/decompositions.py","file_url":"https://github.com/solgaardlab/neurophox/blob/HEAD/neurophox/decompositions.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"7f653a85312e6df6"}},{"code_sha256_prefix":"f69ddd5f6086c06f","entry":"to_absolute_theta","repo":"solgaardlab/neurophox","repo_kind":"listed","path":"neurophox/helpers.py","file_url":"https://github.com/solgaardlab/neurophox/blob/HEAD/neurophox/helpers.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"f69ddd5f6086c06f"}},{"code_sha256_prefix":"71587416e135f94f","entry":"to_complex_gpuarray","repo":"iguanaus/EUNN-theano","repo_kind":"official","path":"fftconv.py","file_url":"https://github.com/iguanaus/EUNN-theano/blob/HEAD/fftconv.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"71587416e135f94f"}},{"code_sha256_prefix":"c9c896b7297dde56","entry":"to_stripe_array","repo":"solgaardlab/neurophox","repo_kind":"listed","path":"neurophox/helpers.py","file_url":"https://github.com/solgaardlab/neurophox/blob/HEAD/neurophox/helpers.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"c9c896b7297dde56"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}