# Students Projects

**Adversarial Attacks and Robustness of DNN**(Julien Béguinot & Léo Monbroussou 2022) This is a presentation of techniques to ensure the robustness of Deep Neural Network against Data Poisoning and Adversarial Attacks. It is mainly based on the articles “Deep partition aggregation : Provable defense against general poisoning attacks, Alexander Levine and Soheil Feizi, 2021” and “Robustness against adversarial attacks in neural networks using incremental dissipativity, Bernardo Aquino, Arash Rahnama, Peter Seiler, Lizhen Lin, and Vijay Gupta, 2021.”. We presented this as a part of the final project of the “Mathematical Foundation of Deep Learning” lecture of the M2 MICAS. Full Text PDF**Presentation : A Coordinated Uplink Scheduling and Power Control Algorithm for Multicell Networks**(Julien Béguinot 2022) This is a presentation of the article of the same name by Kaiming Shen and Wei Yu (2015). I presented this as a final project for the “Multi-User Communications” lecture of the M2 MICAS. It is a distributed algorithm for power allocations and scheduling between base stations. It involves optimization techniques and mainly fractional programming. Full Text PDF**Presentation: High-Order Lifting**(Julien Béguinot 2022) This is a presentation of the article of the same name by Arne Storjohan (2002). I presented this as a final project for the “Efficient Algorithms in Computer Algebra” lecture of the M2 MPRI. This presents Las Vegas probabilitic algorithms for fast system solving of polynomial matrices. Full Text PDF**Les Tectoèdres**(Julien Béguinot & Mathieu Da Silva, 2017)*In French*This report presents an exploration of some scientific results concerning ’tectohedrons’, a family of polyhedrons discovered and studied by Roger Iss in his article*Des tas de sable aux graphes*. Our work aims to show a mathematical transport which can be a transport of properties. A study of the tectohedrons’ family can be done by making bijections between the tectohedron’s set and other sets. These bijections, that is to say these ’transports’, enable to tranform a pro blem which seems geometric into a numerical issue. Finally, with these transports of properties, we succeeded in simulating tectohedrons in 3D and we demonstrated a formula which gives the number of tectohedrons. Full Text PDF**Weighted Adaptive Importante Sampling Schemes**(Julien Béguinot & Mathis Fitoussi, 2021)*In French*In this repport we investigate weigthed schemes for Adaptive Important Sampling in the context of Monte Carlo Estimators. Using martingales we show that even though a deterministic weigthed scheme speed up the convergence of a Monte Carlo estimators in the first itterations it is asymptotycaly equivalent to the classical AIS Monte Carlo. It suggests to rejects Owen’s “square root rule”. Full Text PDF**IDS versus GANs**(Julien Béguinot, Arthur Biapo, Victor Masiak, Zirui Peng, Quentin Sopheap, Huidi Zhu, encadrés par Thomas Robert, Juillet 2020)*In French*This is a repport about a one week long investigation about IDS (Intrusion Detection System) and GANs (Generative Adversarial Networks). It investigates machine learning techniques to detect intrusion on a network. Then we study some countermeasures due to GANs. Full Text PDF

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