Eda Yilmaz

Eda Yilmaz, Georgii Oblapenko, Manuel Torrilhon

In the present work, an approach to the moment closure problem on the basis of orthogonal polynomials derived from Gram matrices is proposed. Its properties are studied in the context of the moment closure problem arising in gas kinetic theory, for which the proposed approach is proven to have multiple attractive mathematical properties. Numerical studies are carried out for model gas particle distributions and the approach is compared to other moment closure methods, such as Grad's closure and the maximum-entropy method. The proposed ``Gramian'' closure is shown to provide very accurate results for a wide range of distribution functions.

Eda Yilmaz, Hacer Yalim Keles

We introduce Adversarial Sparse Teacher (AST), a robust defense method against distillation-based model stealing attacks. Our approach trains a teacher model using adversarial examples to produce sparse logit responses and increase the entropy of the output distribution. Typically, a model generates a peak in its output corresponding to its prediction. By leveraging adversarial examples, AST modifies the teacher model's original response, embedding a few altered logits into the output while keeping the primary response slightly higher. Concurrently, all remaining logits are elevated to further increase the output distribution's entropy. All these complex manipulations are performed using an optimization function with our proposed Exponential Predictive Divergence (EPD) loss function. EPD allows us to maintain higher entropy levels compared to traditional KL divergence, effectively confusing attackers. Experiments on CIFAR-10 and CIFAR-100 datasets demonstrate that AST outperforms state-of-the-art methods, providing effective defense against model stealing while preserving high accuracy. The source codes will be made publicly available here soon.