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

2026-05-14 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics, Engineering & Applied Sciences · Depth: Expert, extended

Summary

This study introduces a theoretical and algorithmic framework to understand, detect, and quantify "hallucinations" in AI-driven solutions for imaging inverse problems, such as medical diagnostics and Earth observation. These hallucinations are realistic-looking but incorrect details generated by deep neural networks, often due to the ill-posed nature of the inverse problem itself. The framework provides necessary and sufficient conditions for hallucinations, along with computable bounds on their magnitude that depend solely on the forward model. The authors develop algorithms to estimate the minimum hallucination magnitude achievable by any reconstruction model and to assess the faithfulness of reconstructed details. Experiments across three imaging tasks—super-resolution of MNIST digits, sub-sampled MRI scans, and super-resolution of Sentinel-2 satellite data—demonstrate the broad applicability of this approach, including to modern generative models, offering a principled way to evaluate AI hallucinations.

Key takeaway

For Computer Vision Engineers developing AI solutions for inverse problems, understanding the fundamental limits of reconstruction accuracy is crucial. You should use the proposed framework to quantify the inherent ill-posedness of your problem via feasible-set diameters and worst-case kernel sizes. This will help you anticipate unavoidable hallucinations and assess the trustworthiness of reconstructed details, especially when ground truth is unavailable, guiding data curation and forward model refinement to mitigate risks.

Key insights

AI hallucinations in inverse problems are not just model artifacts but stem from the problem's inherent ill-posedness.

Principles

• Hallucination magnitude is bounded by feasible-set diameters.
• Too stable or consistent decoders inevitably hallucinate small details.
• Detail transfer occurs when details are almost invisible in measurement space.

Method

The proposed method involves approximating feasible set diameters using finite sample data and applying algorithms to compute necessary and sufficient conditions for detail transfer, enabling both decoder-agnostic and decoder-dependent hallucination assessment.

In practice

• Use region-of-interest metrics to quantify local hallucination severity.
• Apply patch-based splitting for high-dimensional data to enable feasible set computation.
• Manually paste details into reconstructions to test for hallucination susceptibility.

Topics

• AI Hallucinations
• Inverse Problems
• Generative Models
• Feasible Sets
• Worst-Case Kernel Size

Code references

• davidiagraid/AccuracyBounds_private

Best for: Computer Vision Engineer, AI Scientist, Machine Learning Engineer, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.