{"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/beta-crown-efficient-bound-propagation-with","title":"Beta-CROWN: Efficient Bound Propagation with Per-neuron Split Constraints for Complete and Incomplete Neural Network Robustness Verification","arxiv_id":"2103.06624","date":"2021-03-11","proceeding":"NeurIPS 2021 12","authors":["Shiqi Wang","huan zhang","Kaidi Xu","Xue Lin","Suman Jana","Cho-Jui Hsieh","J. Zico Kolter"],"abstract":"Bound propagation based incomplete neural network verifiers such as CROWN are very efficient and can significantly accelerate branch-and-bound (BaB) based complete verification of neural networks. However, bound propagation cannot fully handle the neuron split constraints introduced by BaB commonly handled by expensive linear programming (LP) solvers, leading to loose bounds and hurting verification efficiency. In this work, we develop $\\beta$-CROWN, a new bound propagation based method that can fully encode neuron splits via optimizable parameters $\\beta$ constructed from either primal or dual space. When jointly optimized in intermediate layers, $\\beta$-CROWN generally produces better bounds than typical LP verifiers with neuron split constraints, while being as efficient and parallelizable as CROWN on GPUs. Applied to complete robustness verification benchmarks, $\\beta$-CROWN with BaB is up to three orders of magnitude faster than LP-based BaB methods, and is notably faster than all existing approaches while producing lower timeout rates. By terminating BaB early, our method can also be used for efficient incomplete verification. We consistently achieve higher verified accuracy in many settings compared to powerful incomplete verifiers, including those based on convex barrier breaking techniques. Compared to the typically tightest but very costly semidefinite programming (SDP) based incomplete verifiers, we obtain higher verified accuracy with three orders of magnitudes less verification time. Our algorithm empowered the $\\alpha,\\!\\beta$-CROWN (alpha-beta-CROWN) verifier, the winning tool in VNN-COMP 2021. Our code is available at http://PaperCode.cc/BetaCROWN","url_abs":"https://arxiv.org/abs/2103.06624v2","url_pdf":"https://arxiv.org/pdf/2103.06624v2.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":"beta-crown-efficient-bound-propagation-with","repo_url":"https://github.com/KaidiXu/Beta-CROWN","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"unanswered"}},{"paper_slug":"beta-crown-efficient-bound-propagation-with","repo_url":"https://github.com/eth-sri/eran","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":null},{"paper_slug":"beta-crown-efficient-bound-propagation-with","repo_url":"https://github.com/Verified-Intelligence/alpha-beta-CROWN_vnncomp2024","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"beta-crown-efficient-bound-propagation-with","repo_url":"https://github.com/avrahamraviv/formal-verification-of-object-detection","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"beta-crown-efficient-bound-propagation-with","repo_url":"https://github.com/huanzhang12/alpha-beta-CROWN","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"NOASSERTION"}},{"paper_slug":"beta-crown-efficient-bound-propagation-with","repo_url":"https://github.com/verified-intelligence/alpha-beta-crown","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"NOASSERTION"}}],"tasks":[{"task_slug":"adversarial-attack","task_name":"Adversarial Attack"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2103.06624","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2103.06624"}},"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/Verified-Intelligence/alpha-beta-CROWN_vnncomp2024","reach":null},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/verified-intelligence/alpha-beta-crown","reach":{"status":"ok","spdx":"NOASSERTION"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/huanzhang12/alpha-beta-CROWN","reach":{"status":"ok","spdx":"NOASSERTION"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/eth-sri/eran","reach":null},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/avrahamraviv/formal-verification-of-object-detection","reach":null},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/KaidiXu/Beta-CROWN","reach":{"status":"unanswered"}}],"summary":{"ran":1,"ran_draft_wrong":1,"ran_honours":1,"ran_violates":1,"unverified":1},"by_repo_kind":{"official":{"samples":4,"ran":4,"repositories":1},"listed":{"samples":1,"ran":0,"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":1,"samples":[{"code_sha256_prefix":"ed7f6744c1db4625","entry":"Optimizer","repo":"eth-sri/eran","repo_kind":"official","path":"tf_verify/optimizer.py","file_url":"https://github.com/eth-sri/eran/blob/HEAD/tf_verify/optimizer.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"ed7f6744c1db4625"}},{"code_sha256_prefix":"0c0bc63904f889b0","entry":"isnetworkfile","repo":"eth-sri/eran","repo_kind":"official","path":"tf_verify/__main__.py","file_url":"https://github.com/eth-sri/eran/blob/HEAD/tf_verify/__main__.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":"deterministic","behaviour_fingerprint":false,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"0c0bc63904f889b0"}},{"code_sha256_prefix":"473beca3aa6713e4","entry":"parse_input_box","repo":"eth-sri/eran","repo_kind":"official","path":"tf_verify/__main__.py","file_url":"https://github.com/eth-sri/eran/blob/HEAD/tf_verify/__main__.py","link_basis":"first_harvest_node","language":"python","status":"ran_honours","verification_level":1,"contract_check":"HONOURS","metamorphic_tier":"well_formed","behaviour_fingerprint":true,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"473beca3aa6713e4"}},{"code_sha256_prefix":"f017532fc389cbfe","entry":"str2bool","repo":"eth-sri/eran","repo_kind":"official","path":"tf_verify/__main__.py","file_url":"https://github.com/eth-sri/eran/blob/HEAD/tf_verify/__main__.py","link_basis":"first_harvest_node","language":"python","status":"ran_violates","verification_level":1,"contract_check":"VIOLATES","metamorphic_tier":"deterministic","behaviour_fingerprint":false,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"f017532fc389cbfe"}},{"code_sha256_prefix":"522597fedc59dae8","entry":"beta_crown_backward_bound","repo":"Verified-Intelligence/alpha-beta-CROWN_vnncomp2024","repo_kind":"listed","path":"auto_LiRPA/beta_crown.py","file_url":"https://github.com/Verified-Intelligence/alpha-beta-CROWN_vnncomp2024/blob/HEAD/auto_LiRPA/beta_crown.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NOASSERTION","inline_ok":false,"mcp_get_code":{"code_sha256":"522597fedc59dae8"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}