{"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/provably-bounding-neural-network-preimages-1","title":"Provably Bounding Neural Network Preimages","arxiv_id":"2302.01404","date":"2023-02-02","proceeding":"NeurIPS 2023 11","authors":["Suhas Kotha","Christopher Brix","Zico Kolter","Krishnamurthy Dvijotham","huan zhang"],"abstract":"Most work on the formal verification of neural networks has focused on bounding the set of outputs that correspond to a given set of inputs (for example, bounded perturbations of a nominal input). However, many use cases of neural network verification require solving the inverse problem, or over-approximating the set of inputs that lead to certain outputs. We present the INVPROP algorithm for verifying properties over the preimage of a linearly constrained output set, which can be combined with branch-and-bound to increase precision. Contrary to other approaches, our efficient algorithm is GPU-accelerated and does not require a linear programming solver. We demonstrate our algorithm for identifying safe control regions for a dynamical system via backward reachability analysis, verifying adversarial robustness, and detecting out-of-distribution inputs to a neural network. Our results show that in certain settings, we find over-approximations over 2500x tighter than prior work while being 2.5x faster. By strengthening robustness verification with output constraints, we consistently verify more properties than the previous state-of-the-art on multiple benchmarks, including a large model with 167k neurons in VNN-COMP 2023. Our algorithm has been incorporated into the $\\alpha,\\!\\beta$-CROWN verifier, available at https://abcrown.org.","url_abs":"https://arxiv.org/abs/2302.01404v4","url_pdf":"https://arxiv.org/pdf/2302.01404v4.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":"provably-bounding-neural-network-preimages-1","repo_url":"https://github.com/kothasuhas/verify-input","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"provably-bounding-neural-network-preimages-1","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":"provably-bounding-neural-network-preimages-1","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":"provably-bounding-neural-network-preimages-1","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":"provably-bounding-neural-network-preimages-1","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-robustness","task_name":"Adversarial Robustness"},{"task_slug":null,"task_name":"GPU"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2302.01404","atlas_url":"https://app.syntology.ai/?focus=2302.01404","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2302.01404"}},"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. 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