{"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/hope-high-order-polynomial-expansion-of-black","title":"HOPE: High-order Polynomial Expansion of Black-box Neural Networks","arxiv_id":"2307.08192","date":"2023-07-17","proceeding":null,"authors":["Tingxiong Xiao","Weihang Zhang","Yuxiao Cheng","Jinli Suo"],"abstract":"Despite their remarkable performance, deep neural networks remain mostly ``black boxes'', suggesting inexplicability and hindering their wide applications in fields requiring making rational decisions. Here we introduce HOPE (High-order Polynomial Expansion), a method for expanding a network into a high-order Taylor polynomial on a reference input. Specifically, we derive the high-order derivative rule for composite functions and extend the rule to neural networks to obtain their high-order derivatives quickly and accurately. From these derivatives, we can then derive the Taylor polynomial of the neural network, which provides an explicit expression of the network's local interpretations. Numerical analysis confirms the high accuracy, low computational complexity, and good convergence of the proposed method. Moreover, we demonstrate HOPE's wide applications built on deep learning, including function discovery, fast inference, and feature selection. The code is available at https://github.com/HarryPotterXTX/HOPE.git.","url_abs":"https://arxiv.org/abs/2307.08192v1","url_pdf":"https://arxiv.org/pdf/2307.08192v1.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":"hope-high-order-polynomial-expansion-of-black","repo_url":"https://github.com/harrypotterxtx/hope","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"feature-selection","task_name":"feature selection"}],"methods":[{"method_slug":"hope","method_name":"HOPE"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2307.08192","atlas_url":"https://app.syntology.ai/?focus=2307.08192","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2307.08192"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+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/harrypotterxtx/hope","reach":{"status":"ok"}}],"summary":{"ran":16,"unverified":2},"by_repo_kind":{"official":{"samples":18,"ran":16,"repositories":1}},"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":18,"samples":[{"code_sha256_prefix":"a6212c5c5a7f9674","entry":"Activation","repo":"harrypotterxtx/hope","repo_kind":"official","path":"utils/Network.py","file_url":"https://github.com/harrypotterxtx/hope/blob/HEAD/utils/Network.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"a6212c5c5a7f9674"}},{"code_sha256_prefix":"e9954d5dd966b612","entry":"JudgeAct","repo":"harrypotterxtx/hope","repo_kind":"official","path":"utils/Activation.py","file_url":"https://github.com/harrypotterxtx/hope/blob/HEAD/utils/Activation.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"e9954d5dd966b612"}},{"code_sha256_prefix":"5d1cb3ffe100f152","entry":"ModuleDict","repo":"harrypotterxtx/hope","repo_kind":"official","path":"utils/Network.py","file_url":"https://github.com/harrypotterxtx/hope/blob/HEAD/utils/Network.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"5d1cb3ffe100f152"}},{"code_sha256_prefix":"147b9c268f1914b8","entry":"MultiFormula","repo":"harrypotterxtx/hope","repo_kind":"official","path":"utils/ChainMatrix.py","file_url":"https://github.com/harrypotterxtx/hope/blob/HEAD/utils/ChainMatrix.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"147b9c268f1914b8"}},{"code_sha256_prefix":"7d7cfb17f0c88bb4","entry":"SingleStrFormula","repo":"harrypotterxtx/hope","repo_kind":"official","path":"utils/ChainMatrix.py","file_url":"https://github.com/harrypotterxtx/hope/blob/HEAD/utils/ChainMatrix.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":true,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"7d7cfb17f0c88bb4"}},{"code_sha256_prefix":"c3a28942febbdd0c","entry":"StrFormula","repo":"harrypotterxtx/hope","repo_kind":"official","path":"utils/ChainMatrix.py","file_url":"https://github.com/harrypotterxtx/hope/blob/HEAD/utils/ChainMatrix.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"c3a28942febbdd0c"}},{"code_sha256_prefix":"5b7715594984b84e","entry":"cald","repo":"harrypotterxtx/hope","repo_kind":"official","path":"auto.py","file_url":"https://github.com/harrypotterxtx/hope/blob/HEAD/auto.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"5b7715594984b84e"}},{"code_sha256_prefix":"285713efc578efa9","entry":"create_code","repo":"harrypotterxtx/hope","repo_kind":"official","path":"utils/Global.py","file_url":"https://github.com/harrypotterxtx/hope/blob/HEAD/utils/Global.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"285713efc578efa9"}},{"code_sha256_prefix":"b10d037ab889007a","entry":"create_coords","repo":"harrypotterxtx/hope","repo_kind":"official","path":"utils/Global.py","file_url":"https://github.com/harrypotterxtx/hope/blob/HEAD/utils/Global.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"b10d037ab889007a"}},{"code_sha256_prefix":"33b1630ff701ffed","entry":"create_flattened_coords","repo":"harrypotterxtx/hope","repo_kind":"official","path":"utils/Samplers.py","file_url":"https://github.com/harrypotterxtx/hope/blob/HEAD/utils/Samplers.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"33b1630ff701ffed"}},{"code_sha256_prefix":"7b0462e7cb6c3b67","entry":"create_lr_scheduler","repo":"harrypotterxtx/hope","repo_kind":"official","path":"utils/Optimizer.py","file_url":"https://github.com/harrypotterxtx/hope/blob/HEAD/utils/Optimizer.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"7b0462e7cb6c3b67"}},{"code_sha256_prefix":"553590ed9758f52c","entry":"create_optim","repo":"harrypotterxtx/hope","repo_kind":"official","path":"utils/Optimizer.py","file_url":"https://github.com/harrypotterxtx/hope/blob/HEAD/utils/Optimizer.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"553590ed9758f52c"}},{"code_sha256_prefix":"949763c8466649d3","entry":"get_taylor_coef","repo":"harrypotterxtx/hope","repo_kind":"official","path":"global.py","file_url":"https://github.com/harrypotterxtx/hope/blob/HEAD/global.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"949763c8466649d3"}},{"code_sha256_prefix":"49307138b9a6ff3c","entry":"invnormalize_data","repo":"harrypotterxtx/hope","repo_kind":"official","path":"utils/Samplers.py","file_url":"https://github.com/harrypotterxtx/hope/blob/HEAD/utils/Samplers.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"49307138b9a6ff3c"}},{"code_sha256_prefix":"a08f4c11483ef0c6","entry":"judge_exist","repo":"harrypotterxtx/hope","repo_kind":"official","path":"global.py","file_url":"https://github.com/harrypotterxtx/hope/blob/HEAD/global.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"a08f4c11483ef0c6"}},{"code_sha256_prefix":"42bca2074e6a5608","entry":"normalize_data","repo":"harrypotterxtx/hope","repo_kind":"official","path":"utils/Samplers.py","file_url":"https://github.com/harrypotterxtx/hope/blob/HEAD/utils/Samplers.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"42bca2074e6a5608"}},{"code_sha256_prefix":"4ac749f921b31097","entry":"autograd","repo":"harrypotterxtx/hope","repo_kind":"official","path":"auto.py","file_url":"https://github.com/harrypotterxtx/hope/blob/HEAD/auto.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"4ac749f921b31097"}},{"code_sha256_prefix":"981cd9c1fb3b7dd6","entry":"taylor_output","repo":"harrypotterxtx/hope","repo_kind":"official","path":"utils/Global.py","file_url":"https://github.com/harrypotterxtx/hope/blob/HEAD/utils/Global.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"981cd9c1fb3b7dd6"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}