{"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/lyanet-a-lyapunov-framework-for-training","title":"LyaNet: A Lyapunov Framework for Training Neural ODEs","arxiv_id":"2202.02526","date":"2022-02-05","proceeding":null,"authors":["Ivan Dario Jimenez Rodriguez","Aaron D. Ames","Yisong Yue"],"abstract":"We propose a method for training ordinary differential equations by using a control-theoretic Lyapunov condition for stability. Our approach, called LyaNet, is based on a novel Lyapunov loss formulation that encourages the inference dynamics to converge quickly to the correct prediction. Theoretically, we show that minimizing Lyapunov loss guarantees exponential convergence to the correct solution and enables a novel robustness guarantee. We also provide practical algorithms, including one that avoids the cost of backpropagating through a solver or using the adjoint method. Relative to standard Neural ODE training, we empirically find that LyaNet can offer improved prediction performance, faster convergence of inference dynamics, and improved adversarial robustness. Our code available at https://github.com/ivandariojr/LyapunovLearning .","url_abs":"https://arxiv.org/abs/2202.02526v1","url_pdf":"https://arxiv.org/pdf/2202.02526v1.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":"lyanet-a-lyapunov-framework-for-training","repo_url":"https://github.com/ivandariojr/lyapunovlearning","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"adversarial-robustness","task_name":"Adversarial Robustness"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2202.02526","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2202.02526"}},"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/ivandariojr/lyapunovlearning","reach":null}],"summary":{"ran_draft_wrong":3},"by_repo_kind":{},"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":3,"samples":[{"code_sha256_prefix":"f3ee1c97f81b2274","entry":"get_arch_name","repo":null,"repo_kind":null,"path":null,"file_url":null,"link_basis":"identical_code_first_harvested_elsewhere","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":"deterministic","behaviour_fingerprint":false,"licence":null,"inline_ok":false,"mcp_get_code":{"code_sha256":"f3ee1c97f81b2274"}},{"code_sha256_prefix":"2f26b981f0269a1c","entry":"get_model_name","repo":null,"repo_kind":null,"path":null,"file_url":null,"link_basis":"identical_code_first_harvested_elsewhere","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":"deterministic","behaviour_fingerprint":false,"licence":null,"inline_ok":false,"mcp_get_code":{"code_sha256":"2f26b981f0269a1c"}},{"code_sha256_prefix":"9501e3c98d3be436","entry":"get_module_name","repo":null,"repo_kind":null,"path":null,"file_url":null,"link_basis":"identical_code_first_harvested_elsewhere","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":"deterministic","behaviour_fingerprint":false,"licence":null,"inline_ok":false,"mcp_get_code":{"code_sha256":"9501e3c98d3be436"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}