[2603.19562] Neural Uncertainty Principle: A Unified View of Adversarial Fragility and LLM Hallucination

Computer Science > Machine Learning arXiv:2603.19562 (cs) [Submitted on 20 Mar 2026] Title:Neural Uncertainty Principle: A Unified View of Adversarial Fragility and LLM Hallucination Authors:Dong-Xiao Zhang, Hu Lou, Jun-Jie Zhang, Jun Zhu, Deyu Meng View a PDF of the paper titled Neural Uncertainty Principle: A Unified View of Adversarial Fragility and LLM Hallucination, by Dong-Xiao Zhang and 4 other authors View PDF HTML (experimental) Abstract:Adversarial vulnerability in vision and hallucination in large language models are conventionally viewed as separate problems, each addressed with modality-specific patches. This study first reveals that they share a common geometric origin: the input and its loss gradient are conjugate observables subject to an irreducible uncertainty bound. Formalizing a Neural Uncertainty Principle (NUP) under a loss-induced state, we find that in near-bound regimes, further compression must be accompanied by increased sensitivity dispersion (adversarial fragility), while weak prompt-gradient coupling leaves generation under-constrained (hallucination). Crucially, this bound is modulated by an input-gradient correlation channel, captured by a specifically designed single-backward probe. In vision, masking highly coupled components improves robustness without costly adversarial training; in language, the same prefill-stage probe detects hallucination risk before generating any answer tokens. NUP thus turns two seemingly separate failure taxonomi...