{"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/chordal-sparsity-for-lipschitz-constant","title":"Chordal Sparsity for Lipschitz Constant Estimation of Deep Neural Networks","arxiv_id":"2204.00846","date":"2022-04-02","proceeding":null,"authors":["Anton Xue","Lars Lindemann","Alexander Robey","Hamed Hassani","George J. Pappas","Rajeev Alur"],"abstract":"Lipschitz constants of neural networks allow for guarantees of robustness in image classification, safety in controller design, and generalizability beyond the training data. As calculating Lipschitz constants is NP-hard, techniques for estimating Lipschitz constants must navigate the trade-off between scalability and accuracy. In this work, we significantly push the scalability frontier of a semidefinite programming technique known as LipSDP while achieving zero accuracy loss. We first show that LipSDP has chordal sparsity, which allows us to derive a chordally sparse formulation that we call Chordal-LipSDP. The key benefit is that the main computational bottleneck of LipSDP, a large semidefinite constraint, is now decomposed into an equivalent collection of smaller ones: allowing Chordal-LipSDP to outperform LipSDP particularly as the network depth grows. Moreover, our formulation uses a tunable sparsity parameter that enables one to gain tighter estimates without incurring a significant computational cost. We illustrate the scalability of our approach through extensive numerical experiments.","url_abs":"https://arxiv.org/abs/2204.00846v2","url_pdf":"https://arxiv.org/pdf/2204.00846v2.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":"chordal-sparsity-for-lipschitz-constant","repo_url":"https://github.com/antonxue/chordal-lipsdp","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"image-classification","task_name":"Image Classification"},{"task_slug":"navigate","task_name":"Navigate"},{"task_slug":"image-classification","task_name":"image-classification"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2204.00846","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}