Abdul-Rauf Nuhu

Abdul-Rauf Nuhu, Kishor Datta Gupta, Wendwosen Bellete Bedada et al.

Generating unsafe sub-requirements from a partitioned input space to support verification-guided test cases for formal verification of black-box models is a challenging problem for researchers. The size of the search space makes exhaustive search computationally impractical. This paper investigates a meta-heuristic approach to search for unsafe candidate sub-requirements in partitioned input space. We present a Negative Selection Algorithm (NSA) for identifying the candidates' unsafe regions within given safety properties. The Meta-heuristic capability of the NSA algorithm made it possible to estimate vast unsafe regions while validating a subset of these regions. We utilize a parallel execution of partitioned input space to produce safe areas. The NSA based on the prior knowledge of the safe regions is used to identify candidate unsafe region areas and the Marabou framework is then used to validate the NSA results. Our preliminary experimentation and evaluation show that the procedure finds candidate unsafe sub-requirements when validated with the Marabou framework with high precision.

Vahid Hemmati, Ahmad Mohammadi, Abdul-Rauf Nuhu et al.

Adversarial robustness remains a critical challenge in deploying neural network classifiers, particularly in real-time systems where ground-truth labels are unavailable during inference. This paper investigates \textit{Volatility in Certainty} (VC), a recently proposed, label-free metric that quantifies irregularities in model confidence by measuring the dispersion of sorted softmax outputs. Specifically, VC is defined as the average squared log-ratio of adjacent certainty values, capturing local fluctuations in model output smoothness. We evaluate VC as a proxy for classification accuracy and as an indicator of adversarial drift. Experiments are conducted on artificial neural networks (ANNs) and convolutional neural networks (CNNs) trained on MNIST, as well as a regularized VGG-like model trained on CIFAR-10. Adversarial examples are generated using the Fast Gradient Sign Method (FGSM) across varying perturbation magnitudes. In addition, mixed test sets are created by gradually introducing adversarial contamination to assess VC's sensitivity under incremental distribution shifts. Our results reveal a strong negative correlation between classification accuracy and log(VC) (correlation rho < -0.90 in most cases), suggesting that VC effectively reflects performance degradation without requiring labeled data. These findings position VC as a scalable, architecture-agnostic, and real-time performance metric suitable for early-warning systems in safety-critical applications.

Abdul-Rauf Nuhu, Parham M. Kebria, Vahid Hemmati et al.

Generalization is a critical property of data-driven models, particularly deep learning models deployed in safety-critical applications. Robustness-based generalization bounds have gained attention as a principled way to link robustness properties to generalization performance, often in a data-dependent manner. However, most existing bounds suffer from vacuousness in practical settings, yielding loose upper bounds that greatly exceed the actual error rates and limiting their usefulness for real-world evaluation. While this issue is often attributed to the uncertainty term, a substantial part of the problem originates from the robustness term itself, particularly for the 0-1 loss. Existing approaches typically treat the robustness term as a global measure, ignoring its variation across different sub-regions of the input space. In this work, we propose a generalization bound that addresses this limitation by scaling the robustness term according to the number of stable and unstable samples within each sub-region. Our bounds incorporate both data- and model-dependent factors while maintaining practical relevance (yielding tighter upper bounds on true error). Experiments on models trained on the ImageNet dataset show that our bounds remain consistently non-vacuous and achieve the tightest estimates among existing methods, closely aligning with empirical performance across a range of robust deep neural networks.

Abdul-Rauf Nuhu, Parham Kebria, Vahid Hemmati et al.

Data-driven models, especially deep learning classifiers often demonstrate great success on clean datasets. Yet, they remain vulnerable to common data distortions such as adversarial and common corruption perturbations. These perturbations can significantly degrade performance, thereby challenging the overall reliability of the models. Traditional robustness validation typically relies on perturbed test datasets to assess and improve model performance. In our framework, however, we propose a validation approach that extracts "weak robust" samples directly from the training dataset via local robustness analysis. These samples, being the most susceptible to perturbations, serve as an early and sensitive indicator of the model's vulnerabilities. By evaluating models on these challenging training instances, we gain a more nuanced understanding of its robustness, which informs targeted performance enhancement. We demonstrate the effectiveness of our approach on models trained with CIFAR-10, CIFAR-100, and ImageNet, highlighting how robustness validation guided by weak robust samples can drive meaningful improvements in model reliability under adversarial and common corruption scenarios.