{"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/subhomogeneous-deep-equilibrium-models","title":"Subhomogeneous Deep Equilibrium Models","arxiv_id":"2403.00720","date":"2024-03-01","proceeding":null,"authors":["Pietro Sittoni","Francesco Tudisco"],"abstract":"Implicit-depth neural networks have grown as powerful alternatives to traditional networks in various applications in recent years. However, these models often lack guarantees of existence and uniqueness, raising stability, performance, and reproducibility issues. In this paper, we present a new analysis of the existence and uniqueness of fixed points for implicit-depth neural networks based on the concept of subhomogeneous operators and the nonlinear Perron-Frobenius theory. Compared to previous similar analyses, our theory allows for weaker assumptions on the parameter matrices, thus yielding a more flexible framework for well-defined implicit networks. We illustrate the performance of the resulting subhomogeneous networks on feedforward, convolutional, and graph neural network examples.","url_abs":"https://arxiv.org/abs/2403.00720v2","url_pdf":"https://arxiv.org/pdf/2403.00720v2.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":"subhomogeneous-deep-equilibrium-models","repo_url":"https://github.com/COMPiLELab/SubDEQ","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"graph-neural-network","task_name":"Graph Neural Network"}],"methods":[{"method_slug":"graph-neural-network","method_name":"Graph Neural Network"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2403.00720","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2403.00720"}},"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/COMPiLELab/SubDEQ","reach":{"status":"ok"}}],"summary":{"ran":6,"unverified":2},"by_repo_kind":{"official":{"samples":8,"ran":6,"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":8,"samples":[{"code_sha256_prefix":"65dac7423ad02a4f","entry":"anderson","repo":"COMPiLELab/SubDEQ","repo_kind":"official","path":"forward_backward.py","file_url":"https://github.com/COMPiLELab/SubDEQ/blob/HEAD/forward_backward.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"65dac7423ad02a4f"}},{"code_sha256_prefix":"25f0ff89fb595a24","entry":"cuda","repo":"COMPiLELab/SubDEQ","repo_kind":"official","path":"utils.py","file_url":"https://github.com/COMPiLELab/SubDEQ/blob/HEAD/utils.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"25f0ff89fb595a24"}},{"code_sha256_prefix":"c1a0e425aad156f4","entry":"epoch","repo":"COMPiLELab/SubDEQ","repo_kind":"official","path":"utils.py","file_url":"https://github.com/COMPiLELab/SubDEQ/blob/HEAD/utils.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"c1a0e425aad156f4"}},{"code_sha256_prefix":"8973427b406d8611","entry":"epoch_eval","repo":"COMPiLELab/SubDEQ","repo_kind":"official","path":"utils.py","file_url":"https://github.com/COMPiLELab/SubDEQ/blob/HEAD/utils.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"8973427b406d8611"}},{"code_sha256_prefix":"703555881b050a9c","entry":"generate_dataloader","repo":"COMPiLELab/SubDEQ","repo_kind":"official","path":"data_loader.py","file_url":"https://github.com/COMPiLELab/SubDEQ/blob/HEAD/data_loader.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"703555881b050a9c"}},{"code_sha256_prefix":"75e2303e4a3e5535","entry":"mnist_loaders","repo":"COMPiLELab/SubDEQ","repo_kind":"official","path":"data_loader.py","file_url":"https://github.com/COMPiLELab/SubDEQ/blob/HEAD/data_loader.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"75e2303e4a3e5535"}},{"code_sha256_prefix":"c1610bd44ddc501d","entry":"anderson_conv","repo":"COMPiLELab/SubDEQ","repo_kind":"official","path":"forward_backward.py","file_url":"https://github.com/COMPiLELab/SubDEQ/blob/HEAD/forward_backward.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"c1610bd44ddc501d"}},{"code_sha256_prefix":"e743e1407ddb74f9","entry":"mnist_loaders","repo":"COMPiLELab/SubDEQ","repo_kind":"official","path":"data_loader.py","file_url":"https://github.com/COMPiLELab/SubDEQ/blob/HEAD/data_loader.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"e743e1407ddb74f9"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}