{"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/sampling-with-mollified-interaction-energy","title":"Sampling with Mollified Interaction Energy Descent","arxiv_id":"2210.13400","date":"2022-10-24","proceeding":null,"authors":["Lingxiao Li","Qiang Liu","Anna Korba","Mikhail Yurochkin","Justin Solomon"],"abstract":"Sampling from a target measure whose density is only known up to a normalization constant is a fundamental problem in computational statistics and machine learning. In this paper, we present a new optimization-based method for sampling called mollified interaction energy descent (MIED). MIED minimizes a new class of energies on probability measures called mollified interaction energies (MIEs). These energies rely on mollifier functions -- smooth approximations of the Dirac delta originated from PDE theory. We show that as the mollifier approaches the Dirac delta, the MIE converges to the chi-square divergence with respect to the target measure and the gradient flow of the MIE agrees with that of the chi-square divergence. Optimizing this energy with proper discretization yields a practical first-order particle-based algorithm for sampling in both unconstrained and constrained domains. We show experimentally that for unconstrained sampling problems our algorithm performs on par with existing particle-based algorithms like SVGD, while for constrained sampling problems our method readily incorporates constrained optimization techniques to handle more flexible constraints with strong performance compared to alternatives.","url_abs":"https://arxiv.org/abs/2210.13400v2","url_pdf":"https://arxiv.org/pdf/2210.13400v2.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":"sampling-with-mollified-interaction-energy","repo_url":"https://github.com/lingxiaoli94/mied","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"jax","reach":null},{"paper_slug":"sampling-with-mollified-interaction-energy","repo_url":"https://github.com/louissharrock/constrained-coin-sampling","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2210.13400","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2210.13400"}},"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/louissharrock/constrained-coin-sampling","reach":null},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/lingxiaoli94/mied","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":1,"samples":[{"code_sha256_prefix":"a0dc387cf916d926","entry":"log_exp_diff","repo":"lingxiaoli94/mied","repo_kind":"official","path":"mied/solvers/mied.py","file_url":"https://github.com/lingxiaoli94/mied/blob/HEAD/mied/solvers/mied.py","link_basis":"first_harvest_node","language":"python","status":"ran_honours","verification_level":1,"contract_check":"HONOURS","metamorphic_tier":"invariant","behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"a0dc387cf916d926"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}