LOS Seminar

Horațiu Cheval (LOS)
The Tikhonov-Mann iteration for families of mappings

Abstract: We present recent results from [3] in which we generalize the strongly convergent Krasnoselskii-Mann-type iteration defined by Boț and Meier in [1] from Hilbert spaces to the abstract setting of W-hyperbolic spaces and we compute effective rates of asymptotic regularity for our generalization. This extends at the same time results by Leuştean and the author on the Tikhonov-Mann [2] iteration from single mappings to families of mappings, providing similar computational results as for the former.

References:
[1] R.I. Boț, D. Meier. A strongly convergent Krasnosel’skii–Mann-type algorithm for finding a common fixed point of a countably infinite family of nonexpansive operators in Hilbert spaces. Journal of Computational and Applied Mathematics, 395:113589, 2021
[2] H. Cheval, L. Leuștean. Quadratic rates of asymptotic regularity for the Tikhonov-Mann iteration. Optimization Methods and Software, 37(6):2225–2240, 2022
[3] H. Cheval. Rates of asymptotic regularity of the Tikhonov-Mann iteration for families of mappings. arXiv:2304.11366 [math.OC], 2023

Andrei Sipoş (LOS)
An example-based proof mining tutorial

Abstract: I will present the workings of proof mining through three case studies: Ulrich Berger's didactic example for the classical Herbrand theorem, Terence Tao's finite monotone convergence principle and my own analysis of a convergence theorem on the unit interval due to D. Borwein and J. Borwein.

Andrei Pătraşcu (LOS)
Discussions on the applications of optimization over metric spaces in sparse representations problems

Abstract: In this seminar we will discuss several papers on optimization algorithms over various spaces and sparse representations.

Paul Irofti (LOS)
Dictionary Learning with Uniform Sparse Representations for Anomaly Detection

Abstract: Many applications like audio and image processing show that sparse representations are a powerful and efficient signal modeling technique. Finding an optimal dictionary that generates at the same time the sparsest representations of data and the smallest approximation error is a hard problem approached by dictionary learning (DL). We study how DL performs in detecting abnormal samples in a dataset of signals. In this paper we use a particular DL formulation that seeks uniform sparse representations model to detect the underlying subspace of the majority of samples in a dataset, using a K-SVD-type algorithm. Numerical simulations show that one can efficiently use this resulted subspace to discriminate the anomalies over the regular data points.
This is joint work with Cristian Rusu and Andrei Pătrașcu.

Dongwon Lee (Pennsylvania State University)
Generative Language Model, Deepfake, and Fake News 2.0: Scenarios and Implications

Abstract: The recent explosive advancements in both generative language models in NLP and deepfake-enabling methods in Computer Vision have greatly helped trigger a new surge in AI research and introduced a myriad of novel AI applications. However, at the same time, these new AI technologies can be used by adversaries for malicious usages, opening a window of opportunity for fake news creators and state-sponsored hackers. In this talk, I will present three plausible scenarios where adversaries could exploit these cutting-edge AI techniques to their advantage, producing more sophisticated fake news by synthesizing realistic artifacts or evading detection of fake news from state-of-the-art detectors. I will conclude the talk by discussing the important implications of the new type of fake news (i.e., Fake News 2.0) and some future research directions.

• LOS Seminar in 2021/2022
• LOS Seminar in 2020/2021