{"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/efficient-bound-of-lipschitz-constant-for","title":"Efficient Bound of Lipschitz Constant for Convolutional Layers by Gram Iteration","arxiv_id":"2305.16173","date":"2023-05-25","proceeding":null,"authors":["Blaise Delattre","Quentin Barthélemy","Alexandre Araujo","Alexandre Allauzen"],"abstract":"Since the control of the Lipschitz constant has a great impact on the training stability, generalization, and robustness of neural networks, the estimation of this value is nowadays a real scientific challenge. In this paper we introduce a precise, fast, and differentiable upper bound for the spectral norm of convolutional layers using circulant matrix theory and a new alternative to the Power iteration. Called the Gram iteration, our approach exhibits a superlinear convergence. First, we show through a comprehensive set of experiments that our approach outperforms other state-of-the-art methods in terms of precision, computational cost, and scalability. Then, it proves highly effective for the Lipschitz regularization of convolutional neural networks, with competitive results against concurrent approaches. Code is available at https://github.com/blaisedelattre/lip4conv.","url_abs":"https://arxiv.org/abs/2305.16173v3","url_pdf":"https://arxiv.org/pdf/2305.16173v3.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":"efficient-bound-of-lipschitz-constant-for","repo_url":"https://github.com/blaisedelattre/lip4conv","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2305.16173","atlas_url":"https://app.syntology.ai/?focus=2305.16173","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2305.16173"}},"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":"deterministic:regex_extraction","url":"https://github.com/blaisedelattre/lip4conv","reach":null}],"summary":{"ran":1,"ran_fixture":1},"by_repo_kind":{"official":{"samples":2,"ran":2,"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":"f5c1160a25c0ebfe","entry":"GramIterationConvBackward","repo":"blaisedelattre/lip4conv","repo_kind":"official","path":"bounds.py","file_url":"https://github.com/blaisedelattre/lip4conv/blob/HEAD/bounds.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"f5c1160a25c0ebfe"}},{"code_sha256_prefix":"a0bc8891dc6bdee6","entry":"estimate_dense","repo":"blaisedelattre/lip4conv","repo_kind":"official","path":"bounds.py","file_url":"https://github.com/blaisedelattre/lip4conv/blob/HEAD/bounds.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":"a0bc8891dc6bdee6"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}