On Hallucinations in Inverse Problems: Fundamental Limits and Provable Assessment Methods
Authors: David Iagaru, Nina M. Gottschling, Anders C. Hansen et al.
Summary
arXiv:2605. 13146v1 Announce Type: new Abstract: Artificial intelligence (AI) has transformed imaging inverse problems, from medical diagnostics to Earth observation.
Relevance
Read next because On Hallucinations in Inverse Problems: Fundamental Limits and Provable Assessment Methods overlaps with clean result "Language-mismatch LoRA SFT on Qwen2.5-7B leaks the trained completion language into bystander directives the model was never trained on, absent under same-language SFT (LOW confidence)", clean result "Coupling evil personas with wrong answers fails to protect Qwen2.5-7B from EM-induced alignment collapse — and the apparent capability ordering across coupling conditions is mostly eval contamination (LOW confidence)", clean result "Only continuous soft prefixes hit both EM axes at once on Qwen-2.5-7B-Instruct: discrete prompt searches split between the alignment objective and the distributional objective, and both discretizations of the soft prefix collapse (MODERATE confidence)". Matching terms: rect, under, correct, eval, rate, model. Source: arxiv stat.ML (Machine Learning).
Abstract
arXiv:2605.13146v1 Announce Type: new 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.