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pith:JSVMMEKO

pith:2026:JSVMMEKOO6IXPBO42D55U373SC

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On Hallucinations in Inverse Problems: Fundamental Limits and Provable Assessment Methods

Anders C. Hansen, David Iagaru, Josselin Garnier, Nina M. Gottschling

Hallucinations in AI image reconstructions arise necessarily from the ill-posed inverse problem, with magnitude bounds set only by the forward model.

arxiv:2605.13146 v1 · 2026-05-13 · stat.ML · cs.CV · cs.LG

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Record completeness

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3 Author claim open · sign in to claim

4 Citations open

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Claims

C1strongest claim

We derive necessary and sufficient conditions for hallucinations, together with computable bounds on their magnitude that depend only on the forward model.

C2weakest 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.

C3one 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.

References

65 extracted · 65 resolved · 1 Pith anchors

[1] J. Adler and O. ¨Oktem. Solving ill-posed inverse problems using iterative deep neural networks. Inverse Problems, 33(12):124007, Nov. 2017 2017

[2] 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 2024

[3] 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 2020

[5] S. Arridge, P. Maass, O. ¨Oktem, and C.-B. Sch ¨onlieb. Solving inverse problems using data-driven models.Acta Numer., 28:1–174, 2019 2019

[6] 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 2024

Formal links

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Receipt and verification

First computed	2026-05-18T03:08:57.291485Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4caac6114e77917785dcd0fbda6ffb908db36c0548ac45dedf90f0d5888b20ce

Aliases

arxiv: 2605.13146 · arxiv_version: 2605.13146v1 · doi: 10.48550/arxiv.2605.13146 · pith_short_12: JSVMMEKOO6IX · pith_short_16: JSVMMEKOO6IXPBO4 · pith_short_8: JSVMMEKO

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/JSVMMEKOO6IXPBO42D55U373SC \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 4caac6114e77917785dcd0fbda6ffb908db36c0548ac45dedf90f0d5888b20ce

Canonical record JSON

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  "metadata": {
    "abstract_canon_sha256": "8b96d24ef09e76d7e5b381f8afac2cd3256d6892956eb1dbb510f001befbed91",
    "cross_cats_sorted": [
      "cs.CV",
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    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2026-05-13T08:11:43Z",
    "title_canon_sha256": "5740d4b353592b5881e7a7c3aea23c8fb199e01e8f70ccf5b6da21a3d74e5817"
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