{"paper":{"title":"Function graph transformers universally approximate operators between function spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"David Mis, Ivan Dokmani\\'c, Maarten V. de Hoop, Matti Lassas, Takashi Furuya","submitted_at":"2026-05-18T07:25:14Z","abstract_excerpt":"We study the approximation of nonlinear operators between function spaces by transformers. Our approach is to lift functions to measures supported on their graphs and leverage a recently introduced measure-theoretic view of transformers. A function $h$ is represented by its graph measure $\\gamma_h$, with finite tokens $\\{(x_j,h(x_j))\\}_{j=1}^N$ being its empirical approximations. We show that this framework elegantly models discretization refinement via convergence of measures and provides a natural setting for operator learning. Within this framework, we introduce function graph transformers,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.17968","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.17968/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T23:33:35.578581Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"8c19e717ba1c74ec971f3ce48874ed3ea386229f99090879be448234b7b459aa"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","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"}