{"paper":{"title":"The Joint Gromov Wasserstein Objective for Multiple Object Matching","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The Joint Gromov-Wasserstein objective extends pairwise matching to simultaneous matching of multiple objects while remaining non-negative and convergent under point sampling.","cross_cats":["q-bio.BM"],"primary_cat":"cs.CV","authors_text":"Aryan Tajmir Riahi, Khanh Dao Duc","submitted_at":"2025-11-21T00:31:21Z","abstract_excerpt":"The Gromov-Wasserstein (GW) distance serves as a powerful tool for matching objects in metric spaces. However, its traditional formulation is constrained to pairwise matching between single objects, limiting its utility in scenarios and applications requiring multiple-to-one or multiple-to-multiple object matching. In this paper, we introduce the Joint Gromov-Wasserstein (JGW) objective and extend the original framework of GW to enable simultaneous matching between collections of objects. Our formulation provides a non-negative dissimilarity measure that identifies partially isomorphic distrib"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Our formulation provides a non-negative dissimilarity measure that identifies partially isomorphic distributions of mm-spaces, with point sampling convergence.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That collections of objects can be jointly represented as metric measure spaces whose joint matching admits the same convergence and non-negativity properties as the classical pairwise case without additional regularity conditions.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The Joint Gromov-Wasserstein (JGW) objective extends GW to collections of metric measure spaces, yielding a non-negative dissimilarity that detects partial isomorphisms with point-sampling convergence and admits entropic solvers for point clouds.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The Joint Gromov-Wasserstein objective extends pairwise matching to simultaneous matching of multiple objects while remaining non-negative and convergent under point sampling.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"fe56aa27334cdcb287b34cc311c5d9db381511adbf7386a110f0096c9d4ebe54"},"source":{"id":"2511.16868","kind":"arxiv","version":2},"verdict":{"id":"11521ff9-2b60-4a16-b2d3-2001f27df2c9","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-17T21:09:27.664228Z","strongest_claim":"Our formulation provides a non-negative dissimilarity measure that identifies partially isomorphic distributions of mm-spaces, with point sampling convergence.","one_line_summary":"The Joint Gromov-Wasserstein (JGW) objective extends GW to collections of metric measure spaces, yielding a non-negative dissimilarity that detects partial isomorphisms with point-sampling convergence and admits entropic solvers for point clouds.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That collections of objects can be jointly represented as metric measure spaces whose joint matching admits the same convergence and non-negativity properties as the classical pairwise case without additional regularity conditions.","pith_extraction_headline":"The Joint Gromov-Wasserstein objective extends pairwise matching to simultaneous matching of multiple objects while remaining non-negative and convergent under point sampling."},"references":{"count":40,"sample":[{"doi":"","year":2020,"title":"Recent advances in shape correspondence","work_id":"6183f61d-b0f2-4133-83bd-aa6e60a872cd","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2015,"title":"Multiple anonymized social networks alignment","work_id":"9724d6fe-7aa1-4988-ba54-291a33355f24","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2023,"title":"AlignOT: An optimal transport based algorithm for fast 3D alignment with applications to cryogenic electron microscopy density maps","work_id":"cdc3052a-da83-484c-9142-2caa119e510d","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"Alignment of Partially Overlapping Cryo-EM Maps Using Unbalanced Gromov-Wasserstein Divergence","work_id":"cd1d1f6d-2c1e-40ab-87dd-d2db6a6cd022","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Spidermatch: 3D shape matching with global optimality and geometric consis- tency","work_id":"a29566d5-fe3b-4d47-8524-228cbba7ebf2","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":40,"snapshot_sha256":"a0485bcdd6d4611abc0d5f4e1d1a5b0196defec0c2cf3959f664ff4cd4741cb4","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}