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

2026-05-13

AI Summary

Deep neural networks are prone to generating plausible yet erroneous details—commonly referred to as hallucinations—when solving imaging inverse problems, thereby severely compromising result reliability. This work addresses this issue by rigorously deriving the necessary and sufficient conditions for hallucination emergence, grounded in the intrinsic ill-posedness of inverse problems. We propose a provable evaluation framework that requires no ground-truth data and relies solely on the forward model. By integrating functional analysis with computable boundary estimation, we establish theoretically sound upper and lower bounds on hallucination magnitude, along with a practical quantification algorithm applicable to diverse reconstruction models, including generative ones. Experiments across three imaging tasks demonstrate the universality and effectiveness of our approach, offering both theoretical guarantees and a practical tool for assessing the trustworthiness of AI-based reconstructions.

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.

Problem

• hallucinations
• inverse problems
• AI reliability
• ill-posedness
• imaging

Innovation

• hallucination
• inverse problems
• ill-posedness
• provable bounds
• faithfulness assessment