{"paper":{"title":"Min Generalized Sliced Gromov Wasserstein: A Scalable Path to Gromov Wasserstein","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Min-GSGW learns coupled nonlinear slicers so that monotone 1D matching induces low-cost Gromov-Wasserstein transport plans in the original spaces.","cross_cats":["cs.CV"],"primary_cat":"cs.LG","authors_text":"Ashkan Shahbazi, Ping He, Soheil Kolouri, Xinran Liu","submitted_at":"2026-05-13T16:33:10Z","abstract_excerpt":"We propose min Generalized Sliced Gromov--Wasserstein (min-GSGW), a sliced formulation for the Gromov--Wasserstein (GW) problem using expressive generalized slicers. The key idea is to learn coupled nonlinear slicers that assign compatible push-forward values to both input measures, so that monotone coupling in the projected domain lifts to a transport plan evaluated against the GW objective in the original spaces. The resulting plan induces a GW objective value, and min-GSGW minimizes this cost directly in the original spaces. We further show that min-GSGW is rigid-motion invariant, a crucial"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"min-GSGW produces meaningful geometric correspondences and GW objective values at substantially lower computational cost than existing GW solvers while remaining rigid-motion invariant.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the learned coupled nonlinear slicers produce push-forward values whose monotone coupling in the projected domain lifts to a transport plan whose GW cost in the original spaces is close to the true optimum.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"min-GSGW learns coupled nonlinear slicers to produce a rigid-motion-invariant, scalable approximation to the Gromov-Wasserstein distance and its transport plans.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Min-GSGW learns coupled nonlinear slicers so that monotone 1D matching induces low-cost Gromov-Wasserstein transport plans in the original spaces.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"0732fa5d3f275fadf856b703fcbd90339e90bd8dc2fa269d948834e84c4b984e"},"source":{"id":"2605.13753","kind":"arxiv","version":1},"verdict":{"id":"5dbb16ab-c6c2-4df9-9d43-e1515c31f1ff","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T19:40:22.115458Z","strongest_claim":"min-GSGW produces meaningful geometric correspondences and GW objective values at substantially lower computational cost than existing GW solvers while remaining rigid-motion invariant.","one_line_summary":"min-GSGW learns coupled nonlinear slicers to produce a rigid-motion-invariant, scalable approximation to the Gromov-Wasserstein distance and its transport plans.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the learned coupled nonlinear slicers produce push-forward values whose monotone coupling in the projected domain lifts to a transport plan whose GW cost in the original spaces is close to the true optimum.","pith_extraction_headline":"Min-GSGW learns coupled nonlinear slicers so that monotone 1D matching induces low-cost Gromov-Wasserstein transport plans in the original spaces."},"references":{"count":26,"sample":[{"doi":"","year":2023,"title":"On assignment problems related to gromov–wasserstein distances on the real line.SIAM Journal on Imaging Sciences, 16(2):1028–1032, 2023","work_id":"d0706d48-5b3b-40b0-bafb-318296ceef88","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2015,"title":"ShapeNet: An Information-Rich 3D Model Repository","work_id":"b2ac5b60-daa9-435b-9369-12271e126edd","ref_index":2,"cited_arxiv_id":"1512.03012","is_internal_anchor":true},{"doi":"","year":2026,"title":"Differentiable generalized sliced wasserstein plans","work_id":"a3097df0-22ab-4853-97c9-6cb87ef1aca9","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"Semidefinite relaxations of the gromov- wasserstein distance","work_id":"494b95e8-bf24-46e8-a14e-046452fe7caa","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2021,"title":"Samir Chowdhury, David Miller, and Tom Needham. Quantized gromov-wasserstein, 2021","work_id":"3e37c2c1-f88d-424b-9714-ac7d01ceb31e","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":26,"snapshot_sha256":"2993a3893fddb7589339a3cced3fe34dc9fa6f9fccc36ff0b5b5634bf286d498","internal_anchors":1},"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"}