Abstract: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 depend only on the forward model. Building on this theory, we introduce algorithms to: (1) estimate the minimum hallucination magnitude achievable by any reconstruction model for a given input; (2) assess the faithfulness of reconstructed details by a given reconstruction model. Experiments across three imaging tasks demonstrate that our approach applies broadly, including to modern generative models, and provides a principled way to quantify and evaluate AI hallucinations.
| Comments: | 31 pages, 11 figures; code available at this https URL |
| Subjects: | Machine Learning (stat.ML); Computer Vision and Pattern Recognition (cs.CV); Machine Learning (cs.LG) |
| Cite as: | arXiv:2605.13146 [stat.ML] |
| (or arXiv:2605.13146v1 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2605.13146 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: David Iagaru [view email]
[v1]
Wed, 13 May 2026 08:11:43 UTC (28,721 KB)