揭示图像逆问题中幻觉的根源并给出可计算的评估方法
On Hallucinations in Inverse Problems: Fundamental Limits and Provable Assessment Methods
- 从反问题病态性出发，理论证明幻觉是固有现象
- 给出幻觉最小幅度的可计算上界，仅依赖前向模型
- 适用于现代生成模型，适合可信度评估场景
人工智能已重塑成像逆问题，涵盖医学诊断到地球观测。然而深度神经网络可能产生幻觉——看似合理却错误的细节，尤其在缺乏真实标签时威胁可靠性。本文建立理论框架，表明此类幻觉并非特定模型的缺陷，而是逆问题本身病态性的结果。推导出幻觉存在的充要条件，并给出仅依赖前向模型的可计算幻觉幅度上界。基于此，提出算法：(1) 估计任意重建模型对给定输入能达到的最小幻觉幅度；(2) 评估特定重建模型生成细节的忠实度。三个成像任务的实验表明该方法具有广泛适用性，包括现代生成模型，为人工智能幻觉提供可量化的评估路径。
原文摘要 · Abstract (English)
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.
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