Detecting Adversarial Data via Provable Adversarial Noise Amplification

The nonuniform and growing impact of adversarial noise across the layers of deep neural networks has been used in the literature, without a formal mathematical justification, to detect adversarial inputs and improve robustness. In this work, we study this phenomenon in detail and present a formal adversarial noise amplification theorem. We specify a set of sufficient conditions under which the adversarial noise amplification is mathematically guaranteed. Based on theoretical observations, we propose a novel training methodology with a custom spectral loss function and a specific architectural design to enhance the amplification signal for detecting adversarial data. Finally, we introduce a new, lightweight detection mechanism that leverages the enhanced amplification signal and operates entirely at inference time. To validate our approach, we demonstrate the detector's efficacy against both state-of-the-art attacks and a purpose-built adaptive attack, confirming that enhanced amplification can serve as a robust and reliable signal for adversarial defense.