{"paper":{"title":"On Hallucinations in Inverse Problems: Fundamental Limits and Provable Assessment Methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Hallucinations in AI image reconstructions arise necessarily from the ill-posed inverse problem, with magnitude bounds set only by the forward model.","cross_cats":["cs.CV","cs.LG"],"primary_cat":"stat.ML","authors_text":"Anders C. Hansen, David Iagaru, Josselin Garnier, Nina M. Gottschling","submitted_at":"2026-05-13T08:11:43Z","abstract_excerpt":"Artificial intelligence (AI) has transformed imaging inverse problems, from medical diagnostics to Earth observation. Yet deep neural networks can produce hallucinations, realistic-looking but incorrect details, undermining their reliability, especially when ground truth data is unavailable. We develop a theoretical framework showing that such hallucinations are not merely artifacts of particular models, but can arise from the ill-posed nature of the inverse problem itself. We derive necessary and sufficient conditions for hallucinations, together with computable bounds on their magnitude that"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We derive necessary and sufficient conditions for hallucinations, together with computable bounds on their magnitude that depend only on the forward model.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The forward model is known exactly and the function spaces for signals allow derivation of necessary and sufficient conditions without additional data-dependent assumptions.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Hallucinations in inverse problem reconstructions are fundamental to ill-posedness, with necessary and sufficient conditions plus computable bounds depending only on the forward model.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Hallucinations in AI image reconstructions arise necessarily from the ill-posed inverse problem, with magnitude bounds set only by the forward model.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"6a9390388dbc8fd3e76cadb66f93628597b404d5deca4327ad85723d05d0e897"},"source":{"id":"2605.13146","kind":"arxiv","version":1},"verdict":{"id":"0f3751cd-f0db-4b03-9bbd-e6e78e234239","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T18:10:48.341846Z","strongest_claim":"We derive necessary and sufficient conditions for hallucinations, together with computable bounds on their magnitude that depend only on the forward model.","one_line_summary":"Hallucinations in inverse problem reconstructions are fundamental to ill-posedness, with necessary and sufficient conditions plus computable bounds depending only on the forward model.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The forward model is known exactly and the function spaces for signals allow derivation of necessary and sufficient conditions without additional data-dependent assumptions.","pith_extraction_headline":"Hallucinations in AI image reconstructions arise necessarily from the ill-posed inverse problem, with magnitude bounds set only by the forward model."},"references":{"count":65,"sample":[{"doi":"","year":2017,"title":"J. Adler and O. ¨Oktem. Solving ill-posed inverse problems using iterative deep neural networks. Inverse Problems, 33(12):124007, Nov. 2017","work_id":"600ea311-fdf0-429f-a3ce-7844dfe968e4","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"U. Akhaury, P. Jablonka, J.-L. Starck, and F. Courbin. Ground-based image deconvolution with swin transformer unet.Astronomy and Astrophysics, 688:A6, July 2024. 27","work_id":"83588586-b699-4e9c-acb2-25e138a1763b","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2020,"title":"V . Antun, F. Renna, C. Poon, B. Adcock, and A. C. Hansen. On instabilities of deep learning in image reconstruction and the potential costs of AI.Proc. Natl. Acad. Sci. USA, 117(48):30088– 30095, 202","work_id":"2f1c7413-a226-48fc-9233-f7fa997342ab","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2019,"title":"S. Arridge, P. Maass, O. ¨Oktem, and C.-B. Sch ¨onlieb. Solving inverse problems using data-driven models.Acta Numer., 28:1–174, 2019","work_id":"1587cd8a-97f9-4ccf-81d2-7134283f7594","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"C. Aybar, D. Montero, S. Donike, F. Kalaitzis, and L. G´omez-Chova. A comprehensive benchmark for optical remote sensing image super-resolution.IEEE Geoscience and Remote Sensing Letters, 21:1–5, 2024","work_id":"cc4f0f5d-8f4a-4b14-8939-1ab5f77cb534","ref_index":6,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":65,"snapshot_sha256":"498007f371fce1f05628c0fe8b2e4f992215e0c321436c638698ca439456db77","internal_anchors":1},"formal_canon":{"evidence_count":2,"snapshot_sha256":"87d28de37602da882a2652b48f7d051eee25a4d8e837d1404e6cc9a41ce99a7a"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}