Title: Assessing Model Resilience Through Fisher Information: Spectral Limits, Theoretical Proof, and Efficient Computation

Abstract:

Ensuring the reliability of deep neural networks is paramount for applications where safety is critical. However, current assessment techniques frequently suffer from a reliance on specific attack vectors and limited interpretability. To address these limitations, we introduce a rigorous, attack-independent robustness metric rooted in the spectral norm of the Fisher Information Matrix (FIM). This metric effectively captures the maximum sensitivity of a model’s output distribution against input disturbances.

From a theoretical standpoint, we demonstrate that the FIM is equivalent to the variance of the input Jacobian. Furthermore, we derive closed-form spectral bounds for widely used architectures, such as VGG, ResNet, DenseNet, and Transformers. This work provides the first theoretical framework for ranking model robustness. To facilitate large-scale assessment, we have engineered efficient computational methods, leveraging power iteration and Hutchinson-based estimation, which are applicable in both white-box and black-box scenarios.

Our empirical studies, conducted across diverse datasets—including CIFAR, ImageNet, and medical imaging data—and various architectural designs, reveal a strong alignment between our proposed metric and adversarial vulnerability. Consequently, this framework acts as an interpretable diagnostic instrument that augments traditional attack-based evaluations. It offers valuable insights into architectural sensitivity and aids in the development of more resilient models. The source code is accessible at: https://github.com/franz-chang/SRP/.

Source: arXiv Generated at: 2026-06-04 00:00:00 UTC