{"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/improving-adversarial-robustness-of-deqs-with","title":"Improving Adversarial Robustness of DEQs with Explicit Regulations Along the Neural Dynamics","arxiv_id":"2306.01435","date":"2023-06-02","proceeding":null,"authors":["Zonghan Yang","Peng Li","Tianyu Pang","Yang Liu"],"abstract":"Deep equilibrium (DEQ) models replace the multiple-layer stacking of conventional deep networks with a fixed-point iteration of a single-layer transformation. Having been demonstrated to be competitive in a variety of real-world scenarios, the adversarial robustness of general DEQs becomes increasingly crucial for their reliable deployment. Existing works improve the robustness of general DEQ models with the widely-used adversarial training (AT) framework, but they fail to exploit the structural uniquenesses of DEQ models. To this end, we interpret DEQs through the lens of neural dynamics and find that AT under-regulates intermediate states. Besides, the intermediate states typically provide predictions with a high prediction entropy. Informed by the correlation between the entropy of dynamical systems and their stability properties, we propose reducing prediction entropy by progressively updating inputs along the neural dynamics. During AT, we also utilize random intermediate states to compute the loss function. Our methods regulate the neural dynamics of DEQ models in this manner. Extensive experiments demonstrate that our methods substantially increase the robustness of DEQ models and even outperform the strong deep network baselines.","url_abs":"https://arxiv.org/abs/2306.01435v1","url_pdf":"https://arxiv.org/pdf/2306.01435v1.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":"improving-adversarial-robustness-of-deqs-with","repo_url":"https://github.com/minicheshire/deq-regulating-neural-dynamics","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"adversarial-robustness","task_name":"Adversarial Robustness"}],"methods":[{"method_slug":"deq","method_name":"DEQ"},{"method_slug":"fail","method_name":"fail"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2306.01435","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2306.01435"}},"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/minicheshire/deq-regulating-neural-dynamics","reach":null}],"summary":{"ran_draft_wrong":1},"by_repo_kind":{"official":{"samples":1,"ran":1,"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":"304e362a32930910","entry":"pgd","repo":"minicheshire/deq-regulating-neural-dynamics","repo_kind":"official","path":"input-entropy-reduction/MDEQ-Vision/lib/core/cls_function.py","file_url":"https://github.com/minicheshire/deq-regulating-neural-dynamics/blob/HEAD/input-entropy-reduction/MDEQ-Vision/lib/core/cls_function.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"MISDECLARED","metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"304e362a32930910"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}