arXiv subjects

Eda Yilmaz

Publications and source records attributed to Eda Yilmaz.

3 recordsLinked to original sources

arXiv2024

On Nonlinear Closures for Moment Equations Based on Orthogonal Polynomials

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.

math.NA↗

arXiv2024

Adversarial Sparse Teacher: Defense Against Distillation-Based Model Stealing Attacks Using Adversarial Examples

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.

cs.LG↗

arXiv2016

Knapsack Problems: A Parameterized Point of View

The knapsack problem (KP) is a very famous NP-hard problem in combinatorial optimization. Also its generalization to multiple dimensions named d-dimensional knapsack problem (d-KP) and to multiple knapsacks named multiple knapsack problem (MKP) are well known problems. Since KP, d-KP, and MKP are integer-valued problems defined on inputs of various informations, we study the fixed-parameter tractability of these problems. The idea behind fixed-parameter tractability is to split the complexity into two parts - one part that depends purely on the size of the input, and one part that depends on some parameter of the problem that tends to be small in practice. Further we consider the closely related question, whether the sizes and the values can be reduced, such that their bit-length is bounded polynomially or even constantly in a given parameter, i.e. the existence of kernelizations is studied. We discuss the following parameters: the number of items, the threshold value for the profit, the sizes, the profits, the number d of dimensions, and the number m of knapsacks. We also consider the connection of parameterized knapsack problems to linear programming, approximation, and pseudo-polynomial algorithms.

cs.CC↗