{"paper":{"title":"GRALIS: A Unified Canonical Framework for Linear Attribution Methods via Riesz Representation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Every additive linear continuous attribution method on square-integrable functions has a unique canonical form via the Riesz theorem.","cross_cats":["cs.AI","stat.ML"],"primary_cat":"cs.LG","authors_text":"Raimondo Fanale","submitted_at":"2026-05-06T22:01:28Z","abstract_excerpt":"The main XAI attribution methods for deep neural networks -- GradCAM, SHAP, LIME, Integrated Gradients -- operate on separate theoretical foundations and are not formally comparable. We present GRALIS (Gradient-Riesz Averaged Locally-Integrated Shapley), a mathematical framework establishing a representation theory for attributions: every additive, linear, and continuous attribution functional on L^2(Q,mu) admits a unique canonical representation (Q, w, Delta), proved necessary by the Riesz Representation Theorem. This class encompasses SHAP, IG, LIME and linearized GradCAM, but excludes nonli"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"every additive, linear, and continuous attribution functional on L^2(Q,mu) admits a unique canonical representation (Q, w, Delta), proved necessary by the Riesz Representation Theorem. This class encompasses SHAP, IG, LIME and linearized GradCAM.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the target attribution methods are additive, linear, and continuous functionals on the chosen L^2 space; if any method violates linearity or continuity the canonical representation and all seven theorems cease to apply.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"GRALIS supplies a canonical representation (Q, w, Delta) for every additive linear continuous attribution functional on L^2 via the Riesz Representation Theorem, unifying SHAP, IG, LIME and linearized GradCAM while proving seven simultaneous guarantees including completeness and interaction values.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Every additive linear continuous attribution method on square-integrable functions has a unique canonical form via the Riesz theorem.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"057c33db0252fdf314d50d18271e567a881b086e12d31c03e85a2b31103c8a20"},"source":{"id":"2605.05480","kind":"arxiv","version":2},"verdict":{"id":"bd29f95f-e24b-4258-ba7c-5416b6cb1df9","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-08T17:00:06.245084Z","strongest_claim":"every additive, linear, and continuous attribution functional on L^2(Q,mu) admits a unique canonical representation (Q, w, Delta), proved necessary by the Riesz Representation Theorem. This class encompasses SHAP, IG, LIME and linearized GradCAM.","one_line_summary":"GRALIS supplies a canonical representation (Q, w, Delta) for every additive linear continuous attribution functional on L^2 via the Riesz Representation Theorem, unifying SHAP, IG, LIME and linearized GradCAM while proving seven simultaneous guarantees including completeness and interaction values.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the target attribution methods are additive, linear, and continuous functionals on the chosen L^2 space; if any method violates linearity or continuity the canonical representation and all seven theorems cease to apply.","pith_extraction_headline":"Every additive linear continuous attribution method on square-integrable functions has a unique canonical form via the Riesz theorem."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.05480/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T20:31:19.608382Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T13:30:57.203547Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"ab8a2dbaade17afebda2dfd9d4978653831c4c896301f9ed3f41e9003f5148be"},"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"}