{"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/hint-hierarchical-invertible-neural-transport","title":"HINT: Hierarchical Invertible Neural Transport for Density Estimation and Bayesian Inference","arxiv_id":"1905.10687","date":"2019-05-25","proceeding":null,"authors":["Jakob Kruse","Gianluca Detommaso","Ullrich Köthe","Robert Scheichl"],"abstract":"Many recent invertible neural architectures are based on coupling block designs where variables are divided in two subsets which serve as inputs of an easily invertible (usually affine) triangular transformation. While such a transformation is invertible, its Jacobian is very sparse and thus may lack expressiveness. This work presents a simple remedy by noting that subdivision and (affine) coupling can be repeated recursively within the resulting subsets, leading to an efficiently invertible block with dense, triangular Jacobian. By formulating our recursive coupling scheme via a hierarchical architecture, HINT allows sampling from a joint distribution p(y,x) and the corresponding posterior p(x|y) using a single invertible network. We evaluate our method on some standard data sets and benchmark its full power for density estimation and Bayesian inference on a novel data set of 2D shapes in Fourier parameterization, which enables consistent visualization of samples for different dimensionalities.","url_abs":"https://arxiv.org/abs/1905.10687v4","url_pdf":"https://arxiv.org/pdf/1905.10687v4.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":"hint-hierarchical-invertible-neural-transport","repo_url":"https://github.com/VLL-HD/HINT","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"bayesian-inference","task_name":"Bayesian Inference"},{"task_slug":"density-estimation","task_name":"Density Estimation"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1905.10687","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1905.10687"}},"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/VLL-HD/HINT","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"unverified":2},"by_repo_kind":{"official":{"samples":2,"ran":0,"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":0,"samples":[{"code_sha256_prefix":"dd292687da674cba","entry":"conv_subnet_constructor","repo":"VLL-HD/HINT","repo_kind":"official","path":"hint.py","file_url":"https://github.com/VLL-HD/HINT/blob/HEAD/hint.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"dd292687da674cba"}},{"code_sha256_prefix":"01c6a8f90f0524c0","entry":"linear_subnet_constructor","repo":"VLL-HD/HINT","repo_kind":"official","path":"hint.py","file_url":"https://github.com/VLL-HD/HINT/blob/HEAD/hint.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"01c6a8f90f0524c0"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}