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

TL;DR

This paper presents a theoretical framework and algorithms to quantify and assess hallucinations in AI-based inverse problem solutions, highlighting their fundamental connection to the problem's ill-posedness.

Contribution

It introduces necessary and sufficient conditions for hallucinations, along with computable bounds, and algorithms to estimate and evaluate hallucination magnitudes in reconstructions.

Findings

Hallucinations can stem from the ill-posed nature of inverse problems.

Algorithms can estimate minimal hallucination levels for any model.

The approach applies broadly, including to modern generative models.

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.