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

• URL: http://arxiv.org/abs/2603.19562v3
• Date: Fri, 27 Mar 2026 04:47:21 GMT
• Title: Neural Uncertainty Principle: A Unified View of Adversarial Fragility and LLM Hallucination
• Abstract summary: Adversarial vulnerability in vision and hallucination in large language models are conventionally viewed as separate problems.<n>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.<n>In vision, masking highly coupled components improves robustness without costly adversarial training.<n>In language, the same prefill-stage probe detects hallucination risk before generating any answer tokens.
• Score: 60.197429875410286
• License: http://creativecommons.org/publicdomain/zero/1.0/
• 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 taxonomies into a shared uncertainty-budget view and provides a principled lens for reliability analysis. Guided by this NUP theory, we propose ConjMask (masking high-contribution input components) and LogitReg (logit-side regularization) to improve robustness without adversarial training, and use the probe as a decoding-free risk signal for LLMs, enabling hallucination detection and prompt selection. NUP thus provides a unified, practical framework for diagnosing and mitigating boundary anomalies across perception and generation tasks.

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