Volatility in Certainty (VC): A Metric for Detecting Adversarial Perturbations During Inference in Neural Network Classifiers

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.

Negative Selection Approach to support Formal Verification and Validation of BlackBox Models' Input Constraints

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.