{"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/probabilistic-verification-of-neural-networks-1","title":"Probabilistic Verification of Neural Networks using Branch and Bound","arxiv_id":"2405.17556","date":"2024-05-27","proceeding":null,"authors":["David Boetius","Stefan Leue","Tobias Sutter"],"abstract":"Probabilistic verification of neural networks is concerned with formally analysing the output distribution of a neural network under a probability distribution of the inputs. Examples of probabilistic verification include verifying the demographic parity fairness notion or quantifying the safety of a neural network. We present a new algorithm for the probabilistic verification of neural networks based on an algorithm for computing and iteratively refining lower and upper bounds on probabilities over the outputs of a neural network. By applying state-of-the-art bound propagation and branch and bound techniques from non-probabilistic neural network verification, our algorithm significantly outpaces existing probabilistic verification algorithms, reducing solving times for various benchmarks from the literature from tens of minutes to tens of seconds. Furthermore, our algorithm compares favourably even to dedicated algorithms for restricted subsets of probabilistic verification. We complement our empirical evaluation with a theoretical analysis, proving that our algorithm is sound and, under mildly restrictive conditions, also complete when using a suitable set of heuristics.","url_abs":"https://arxiv.org/abs/2405.17556v2","url_pdf":"https://arxiv.org/pdf/2405.17556v2.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":"probabilistic-verification-of-neural-networks-1","repo_url":"https://github.com/sen-uni-kn/probspecs","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"fairness","task_name":"Fairness"}],"methods":[{"method_slug":"set","method_name":"SET"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2405.17556","atlas_url":"https://app.syntology.ai/?focus=2405.17556","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2405.17556"}},"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/sen-uni-kn/probspecs","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"ran":3},"by_repo_kind":{"official":{"samples":3,"ran":3,"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":0,"samples":[{"code_sha256_prefix":"24efb96a2400ff7e","entry":"clamp","repo":"sen-uni-kn/probspecs","repo_kind":"official","path":"probspecs/operations/clamp.py","file_url":"https://github.com/sen-uni-kn/probspecs/blob/HEAD/probspecs/operations/clamp.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"24efb96a2400ff7e"}},{"code_sha256_prefix":"d09f3fc9e92b15b0","entry":"maximum","repo":"sen-uni-kn/probspecs","repo_kind":"official","path":"probspecs/operations/clamp.py","file_url":"https://github.com/sen-uni-kn/probspecs/blob/HEAD/probspecs/operations/clamp.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"d09f3fc9e92b15b0"}},{"code_sha256_prefix":"9ea33d3e1efa71a0","entry":"minimum","repo":"sen-uni-kn/probspecs","repo_kind":"official","path":"probspecs/operations/clamp.py","file_url":"https://github.com/sen-uni-kn/probspecs/blob/HEAD/probspecs/operations/clamp.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"9ea33d3e1efa71a0"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}