The robustness of deep neural networks is crucial for safety-critical deployments, yet existing evaluation methods are often attack-dependent and lack interpretability. We propose a principled, attack-agnostic robustness metric based on the spectral norm of the Fisher Information Matrix (FIM), which quantifies the worst-case sensitivity of the model's output distribution to input perturbations. Theoretically, we establish that the FIM equals the variance of the input Jacobian and derive closed-form spectral bounds for common architectures, including VGG, ResNet, DenseNet, and Transformer, providing the first theoretical robustness ranking. To enable scalable evaluation, we develop efficient algorithms, including power iteration and Hutchinson-based estimation, that support both white-box and black-box settings. Extensive experiments across multiple datasets, including CIFAR, ImageNet, and medical images, and across multiple architectures show a strong correlation between our metric and adversarial vulnerability. Our framework serves as an interpretable diagnostic tool that complements attack-based evaluations, offering insights into architectural sensitivity and guiding the design of more robust models. Code is available at: https://github.com/franz-chang/SRP/.
The hubness problem, in which hub embeddings are close to many unrelated examples, occurs often in high-dimensional embedding spaces and may pose a practical threat for purposes such as information retrieval and automatic evaluation metrics. In particular, since cross-modal similarity between text and images cannot be calculated by direct comparisons, such as string matching, cross-modal encoders that project different modalities into a shared space are helpful for various cross-modal applications, and thus, the existence of hubs may pose practical threats. To reveal the vulnerabilities of cross-modal encoders, we propose a method for identifying the hub embedding and its corresponding hub text. Experiments on image captioning evaluation in MSCOCO and nocaps along with image-to-text retrieval tasks in MSCOCO and Flickr30k showed that our method can identify a single hub text that unreasonably achieves comparable or higher similarity scores than human-written reference captions in many images, thereby revealing the vulnerabilities in cross-modal encoders.