Perturbation Effects on Robustness and Individual Fairness

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/.

Deep neural networks (DNNs) are suffering from ethical issues such as individual discrimination. In response, extensive NN repair techniques have been developed to adjust models and mitigate such undesired behaviors. However, existing fairness repair methods are typically data-centric, which often lack provable guarantees and generalization to unseen samples. To overcome these limitations, we propose ProF, a novel fairness repair framework with provable guarantees. The key intuition of ProF is to leverage interval bound propagation (a widely used NN verification technique) to soundly capture model outputs over the whole set $S(\mathbf{x})$ around a biased sample $\mathbf{x}$. The derived bounds are utilized to guide fairness repair which encourages the model to produce consistent outputs on $S(\mathbf{x})$. Specifically, we integrate fairness constraints and model modifications into a unified constraint-solving formulation, which can be transformed to a Mixed-Integer Linear Programming (MILP) problem solvable by off-the-shelf solvers. The solution to the MILP problem effectively induces a repaired model with guaranteed fairness over the whole set $S(\mathbf{x})$. We evaluate ProF on four widely used benchmark datasets and demonstrate that it achieves provable fairness repair, with generalization of up to 95.93% on full datasets and 93.16% on the entire input space. Notably, ProF can be easily configured to support multiple sensitive attributes and more practical fairness definitions, while providing provable repair guarantees and delivering around 90% fairness improvement. Our code is available at https://github.com/nninjn/ProF.

Differentiable optimization layers are traditionally integrated in predict-then-optimize frameworks where a neural model estimates parameters that subsequently serve as fixed inputs to downstream decision-making optimization problems. In this work, we introduce the concept of a "fairness layer": a differentiable optimization layer appended to a model's output layer that guarantees a chosen notion of output parity is satisfied when integrated into a neural network. Additionally, we introduce an online primal-dual inference algorithm that provides provable aggregate fairness guarantees for streaming predictions with arbitrarily small batch sizes, where traditional per-batch constraints become overly restrictive. Numerical experiments demonstrate the effectiveness of the fairness layer and associated algorithm, and theoretical analysis characterizes the layer's differentiability and stability properties during model training and backpropagation. Our code for these experiments is publicly available on GitHub (https://github.com/dtroxell19/FairDL-ICML-2026.git) and our public Python package documentation can be found online: https://dtroxell19.github.io/fairness_training/.