{"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/riemannian-generative-decoder","title":"Riemannian generative decoder","arxiv_id":"2506.19133","date":"2025-06-23","proceeding":null,"authors":["Andreas Bjerregaard","Søren Hauberg","Anders Krogh"],"abstract":"Riemannian representation learning typically relies on approximating densities on chosen manifolds. This involves optimizing difficult objectives, potentially harming models. To completely circumvent this issue, we introduce the Riemannian generative decoder which finds manifold-valued maximum likelihood latents with a Riemannian optimizer while training a decoder network. By discarding the encoder, we vastly simplify the manifold constraint compared to current approaches which often only handle few specific manifolds. We validate our approach on three case studies -- a synthetic branching diffusion process, human migrations inferred from mitochondrial DNA, and cells undergoing a cell division cycle -- each showing that learned representations respect the prescribed geometry and capture intrinsic non-Euclidean structure. Our method requires only a decoder, is compatible with existing architectures, and yields interpretable latent spaces aligned with data geometry.","url_abs":"https://arxiv.org/abs/2506.19133v1","url_pdf":"https://arxiv.org/pdf/2506.19133v1.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":"riemannian-generative-decoder","repo_url":"https://github.com/yhsure/riemannian-generative-decoder","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"decoder","task_name":"Decoder"},{"task_slug":"representation-learning","task_name":"Representation Learning"}],"methods":[{"method_slug":"diffusion","method_name":"Diffusion"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2506.19133","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2506.19133"}},"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/yhsure/riemannian-generative-decoder","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"unverified":5},"by_repo_kind":{"official":{"samples":5,"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":"7beb2ec5329af63b","entry":"add_noise","repo":"yhsure/riemannian-generative-decoder","repo_kind":"official","path":"_train.py","file_url":"https://github.com/yhsure/riemannian-generative-decoder/blob/HEAD/_train.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":"7beb2ec5329af63b"}},{"code_sha256_prefix":"a9a1e8e322962545","entry":"calculate_reconstruction_metrics","repo":"yhsure/riemannian-generative-decoder","repo_kind":"official","path":"_utils.py","file_url":"https://github.com/yhsure/riemannian-generative-decoder/blob/HEAD/_utils.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":"a9a1e8e322962545"}},{"code_sha256_prefix":"e46adcc62b462ff0","entry":"calculate_reconstruction_metrics_hmtDNA","repo":"yhsure/riemannian-generative-decoder","repo_kind":"official","path":"_utils.py","file_url":"https://github.com/yhsure/riemannian-generative-decoder/blob/HEAD/_utils.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":"e46adcc62b462ff0"}},{"code_sha256_prefix":"d2d1937bb7e812d0","entry":"set_all_seeds","repo":"yhsure/riemannian-generative-decoder","repo_kind":"official","path":"_utils.py","file_url":"https://github.com/yhsure/riemannian-generative-decoder/blob/HEAD/_utils.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":"d2d1937bb7e812d0"}},{"code_sha256_prefix":"2693320b6780295e","entry":"train_rgd","repo":"yhsure/riemannian-generative-decoder","repo_kind":"official","path":"_train.py","file_url":"https://github.com/yhsure/riemannian-generative-decoder/blob/HEAD/_train.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":"2693320b6780295e"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}