{"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/invertible-monotone-operators-for-normalizing","title":"Invertible Monotone Operators for Normalizing Flows","arxiv_id":"2210.08176","date":"2022-10-15","proceeding":null,"authors":["Byeongkeun Ahn","Chiyoon Kim","Youngjoon Hong","Hyunwoo J. Kim"],"abstract":"Normalizing flows model probability distributions by learning invertible transformations that transfer a simple distribution into complex distributions. Since the architecture of ResNet-based normalizing flows is more flexible than that of coupling-based models, ResNet-based normalizing flows have been widely studied in recent years. Despite their architectural flexibility, it is well-known that the current ResNet-based models suffer from constrained Lipschitz constants. In this paper, we propose the monotone formulation to overcome the issue of the Lipschitz constants using monotone operators and provide an in-depth theoretical analysis. Furthermore, we construct an activation function called Concatenated Pila (CPila) to improve gradient flow. The resulting model, Monotone Flows, exhibits an excellent performance on multiple density estimation benchmarks (MNIST, CIFAR-10, ImageNet32, ImageNet64). Code is available at https://github.com/mlvlab/MonotoneFlows.","url_abs":"https://arxiv.org/abs/2210.08176v1","url_pdf":"https://arxiv.org/pdf/2210.08176v1.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":"invertible-monotone-operators-for-normalizing","repo_url":"https://github.com/mlvlab/monotoneflows","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"density-estimation","task_name":"Density Estimation"}],"methods":[{"method_slug":"normalizing-flows","method_name":"Normalizing Flows"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2210.08176","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2210.08176"}},"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":"deterministic:regex_extraction","url":"https://github.com/mlvlab/MonotoneFlows","reach":{"status":"ok","spdx":"MIT"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/mlvlab/monotoneflows","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"ran_draft_wrong":3,"ran_honours":1},"by_repo_kind":{"official":{"samples":3,"ran":3,"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":"3e0a8dc623475d8e","entry":"geometric_logprob","repo":"mlvlab/monotoneflows","repo_kind":"official","path":"train_img.py","file_url":"https://github.com/mlvlab/monotoneflows/blob/HEAD/train_img.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":2,"contract_check":"MISDECLARED","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"3e0a8dc623475d8e"}},{"code_sha256_prefix":"f6b944f50d3f15ae","entry":"count_parameters","repo":null,"repo_kind":null,"path":null,"file_url":null,"link_basis":"identical_code_first_harvested_elsewhere","language":"python","status":"ran_honours","verification_level":1,"contract_check":"HONOURS","metamorphic_tier":"well_formed","behaviour_fingerprint":false,"licence":null,"inline_ok":false,"mcp_get_code":{"code_sha256":"f6b944f50d3f15ae"}},{"code_sha256_prefix":"2dc23e3f121c6a38","entry":"standard_normal_logprob","repo":"mlvlab/monotoneflows","repo_kind":"official","path":"train_toy.py","file_url":"https://github.com/mlvlab/monotoneflows/blob/HEAD/train_toy.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"MISDECLARED","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"2dc23e3f121c6a38"}},{"code_sha256_prefix":"2168d015a2e457cb","entry":"standard_normal_sample","repo":"mlvlab/monotoneflows","repo_kind":"official","path":"train_toy.py","file_url":"https://github.com/mlvlab/monotoneflows/blob/HEAD/train_toy.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"MISDECLARED","metamorphic_tier":"well_formed","behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"2168d015a2e457cb"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}