{"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/rg-flow-a-hierarchical-and-explainable-flow","title":"RG-Flow: A hierarchical and explainable flow model based on renormalization group and sparse prior","arxiv_id":"2010.00029","date":"2020-09-30","proceeding":null,"authors":["Hong-Ye Hu","Dian Wu","Yi-Zhuang You","Bruno Olshausen","Yubei Chen"],"abstract":"Flow-based generative models have become an important class of unsupervised learning approaches. In this work, we incorporate the key ideas of renormalization group (RG) and sparse prior distribution to design a hierarchical flow-based generative model, RG-Flow, which can separate information at different scales of images and extract disentangled representations at each scale. We demonstrate our method on synthetic multi-scale image datasets and the CelebA dataset, showing that the disentangled representations enable semantic manipulation and style mixing of the images at different scales. To visualize the latent representations, we introduce receptive fields for flow-based models and show that the receptive fields of RG-Flow are similar to those of convolutional neural networks. In addition, we replace the widely adopted isotropic Gaussian prior distribution by the sparse Laplacian distribution to further enhance the disentanglement of representations. From a theoretical perspective, our proposed method has $O(\\log L)$ complexity for inpainting of an image with edge length $L$, compared to previous generative models with $O(L^2)$ complexity.","url_abs":"https://arxiv.org/abs/2010.00029v5","url_pdf":"https://arxiv.org/pdf/2010.00029v5.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":"rg-flow-a-hierarchical-and-explainable-flow","repo_url":"https://github.com/hongyehu/RG-Flow","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"disentanglement","task_name":"Disentanglement"},{"task_slug":"image-generation","task_name":"Image Generation"},{"task_slug":"image-inpainting","task_name":"Image Inpainting"},{"task_slug":"image-manipulation","task_name":"Image Manipulation"},{"task_slug":"style-transfer","task_name":"Style Transfer"}],"methods":[{"method_slug":"pixel-prediction","method_name":"Inpainting"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2010.00029","atlas_url":"https://app.syntology.ai/?focus=2010.00029","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2010.00029"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+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/hongyehu/RG-Flow","reach":null}],"summary":{"ran_honours":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":0,"samples":[{"code_sha256_prefix":"e3434205ac72f85a","entry":"str_to_int_list","repo":"hongyehu/RG-Flow","repo_kind":"official","path":"code/args.py","file_url":"https://github.com/hongyehu/RG-Flow/blob/HEAD/code/args.py","link_basis":"first_harvest_node","language":"python","status":"ran_honours","verification_level":1,"contract_check":"HONOURS","metamorphic_tier":"well_formed","behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"e3434205ac72f85a"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}