09/08/2026
CHUỖI SEMINAR: CÁC HỆ THỐNG PHỨC TẠP VÀ ỨNG DỤNG
Mời các bạn đến nghe chuỗi seminar do các diễn giả từ Mỹ, Pháp và Việt Nam trình bày. Các seminar về các chủ đề độc lập. có thể tham dự một số buổi. Mở cửa tự do.
Đơn vị tổ chức: Trung tâm Toán Unesco - Viện toán học - VAST và CIMPA.
Chủ trì: Phan Thị Hà Dương
Địa điểm: Hội trường 301, nhà A5, Viện Toán học 18 Hoàng Quốc Việt.
Thời gian: 10-13/08/2026
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10 August, 2026
9:00-10:00 Lecture 1: Privacy Preservation in Large Language Models (LLMs)
Prof. Thái Trà My, University of Florida, USA
10:30-11:00 Lecture 2: Algorithmic Metatheorems: Upper and Lower Bounds for Graphs of Bounded Clique-width
Assoc. Prof. Kevin Perrot, Aix Marseille University, France
14:30-16:00 Lecture 3: Community Detection in Scholarly Networks: When It’s Softer but Harder!
Dr. Vũ Thị Hướng, Zuse Institute Berlin, Germany and Institute of Mathematics, VAST, Vietnam
11 August, 2026
9:30-11:00 Lecture 4: From Graph Structure to Argumentation Semantics: A Dynamics-Based Analysis of Abstract Argumentation Frameworks
Dr. Trịnh Văn Giang, Vietnam National University Ho Chi Minh City, Vietnam
14:30-15:15 Lecture 5: Introduction to the Algebra of Finite Dynamical Systems
Dr. Marius Roland, Aix Marseille University, France
15:45-16:30 Lecture 6: Interpretable Black-Box Adversarial Attacks through Regional Confidence
Ms. Hồ Thùy Trâm, University of Science, VNU-HCM, Vietnam
12 August, 2026
9:30-11:00 Lecture 7: Tensor Products of Functional Graphs: Factorization and Root-Finding on Cycles by using multivariate polynomials
Assoc. Prof. Phan Thị Hà Dương, ICRTM, IM, VAST, Vietnam
14:30-16:00 Lecture 8: A Fast Binary Splitting Approach for Non-Adaptive Learning of Erdős–Rényi Graphs
Dr. Tạ Duy Hoàng, Hanoi University of Science and Technology, Vietnam
13 August, 2026
9:30-11:00 Lecture 9: TBA
Prof. Christophe Crespelle, Université Côte d'Azur, France
Abstract
Lecture 1: Large Language Models (LLMs) have revolutionized artificial intelligence but introduced profound privacy vulnerabilities, including data leakage, model inversion, and the inadvertent exposure of sensitive information. As LLMs integrate into high-stakes applications, mitigating these risks is \linebreak paramount. This talk explores the fundamental privacy challenges inherent in LLM operations and introduces NOIR, the first privacy-preserving LLM model. To prevent prompting contents exposure to honest-but-curious cloud service providers, NOIR utilizes a secure, distributed architecture that transmits only encoded embeddings. By employing local differential privacy at the token embedding level alongside a data-independent, randomized tokenizer, NOIR effectively shields both proprietary prompts and resultant answers. The talk will demonstrate how NOIR achieves an optimal balance, providing rigorous privacy guarantees without compromising computational efficiency or downstream model performance.
Lecture 2: At the crossroad of finite model theory, graphs decompositions and computational complexity, I will survey the tools required to state and prove that any graph question expressible in monadic second order logic is tractable on bounded clique-width graphs (Courcelle's theorem). These tools also allow to prove a hardness metatheorem when the graph is succinctly represented by a Boolean circuit, which is a newly explored research track.
Lecture 3: Community detection is one of the central tools for analyzing scholarly citation networks. Existing methods, such as the Leiden algorithm, produce {\bf hard} partitions, assigning each publication to a single community. But research itself is rarely that simple: interdisciplinary papers often belong to several research areas simultaneously. Allowing {\bf soft memberships} naturally leads to {\bf overlapping
communities}, providing a more realistic representation of science - but also a much harder problem. Using large real-world citation networks from the Web of Science with up to billions of citation links, this talk discusses the transition from hard graph partitioning to a continuous optimization formulation and highlights some of the mathematical and computational challenges that arise in practice.
The talk is based on recent and ongoing research of the project Fully Algorithmic Librarian (https://fan.zib.de/).
Lecture 4: Abstract argumentation frameworks represent conflicts between arguments as directed graphs, but the relationship between graph structure and semantic behavior is often difficult to identify directly. This talk presents a dynamics-based approach to the graphical analysis of abstract argumentation frameworks. By interpreting an argumentation framework through an associated discrete dynamical system, particularly a Boolean network, semantic objects can be studied using notions such as fixed points, attractors, and invariant regions.
After introducing formal argumentation and the foundational framework proposed by Phan Minh Dung, I will formulate the general problem of graphical analysis: determining how structural properties of a graphical representation constrain or explain the possible semantic outcomes. I will then present the main correspondence underlying our approach, selected theoretical results, illustrative examples, and directions currently being developed toward a more systematic framework.
Lecture 5: A finite, deterministic, discrete-time {\it dynamical system} consists of a pair $(A, f_A)$ where $A$ is a finite set of states and $f_A : A \to A$ is a total function from $A$ to itself, called the {\it transition function}. The latter defines the evolution of the system over time. These dynamics are described explicitly by its transition graph, whose vertices are the states of the system and which contains, for each state $a \in A$, an arc $(a, f_A(a))$ linking it to the next state. The general form of the dynamics of such a system consists of one or more {\it limit cycles} of periodic states (for example, $(a,f_A(a), f_A^2(a), \dots , f_a^n(a) = a)$ is a limit cycle of period $n$), together with a transient regime of non-periodic states arranged in tree, whose root belongs to one of the states of a limit cycle.
These systems, considered up to isomorphism, are called FDDSs and are particularly well suited to the scientific approach. Indeed, they are not only widely used to verify that a specification satisfies certain expected or required properties, but also to model and analyze natural phenomena, notably in physics and biology. It is also possible to describe standard deterministic models of computation in computer science, such as cellular automata or bounded-tape Turing machines, in the form of these systems.
In the literature, it is known that FDDSs, equipped with sum (disjoint union) and product (direct product) operations, form a commutative semiring. We can therefore define a semiring of polynomials, as well as polynomial equations whose coefficients and variables are FDDSs. This type of equation is undecidable in the general case, but belongs to the class $\mathsf{NP}$ when one side of the equation is constant. Solving equations of the form $P(X_1,\dots, X_n) = B$ then makes it possible to determine whether $B$ satisfies certain structural constraints, but also to exhibit an underlying dynamics.
In this talk, we will provide an introduction to the algebra underlying these systems and the complexity of solving equation $AX=B$.
Lecture 6: Black-box adversarial attacks study how to generate adversarial examples when only the outputs of a machine learning model are accessible. Such attacks provide a practical framework for evaluating the robustness of real-world AI systems, where gradients and model parameters are unavailable. Recent score-based black-box attacks against image classification models have significantly improved query efficiency through randomized search strategies. However, they typically perturb pixels or frequency coefficients directly, making the resulting adversarial perturbations difficult to interpret. This talk reviews the principles of score-based black-box adversarial attacks, with an emphasis on query-efficient optimization. I will then present SPARC ({\it Superpixel-based Black-Box Adversarial Attack with Regional Confidence}), which exploits image structure through superpixel segmentation and confidence-guided perturbation allocation to generate adversarial examples that are both query-efficient and visually interpretable.
Lecture 7: Functional graphs are directed graphs in which every vertex has out-degree one, providing a natural representation of discrete dynamical systems. We study the tensor product of functional graphs, with a particular focus on graphs consisting of disjoint directed cycles. For this class, the tensor product is characterized by the greatest common divisors and least common multiples of cycle lengths, leading to an algebraic representation by multivariate polynomials with nonnegative integer coefficients. We develop algorithms for factorization and root-finding problems on these graphs, including logarithmic-time algorithms for roots of powers and polynomials restricted to the cycle part.
Lecture 8: We study non-adaptive learning of Erdős–Rényi random graphs using edge-detecting group queries, where each test asks whether a chosen set of vertices contains at least one edge. Although learning arbitrary graphs non-adaptively is costly, the random structure of Erdős–Rényi graphs allows more efficient recovery. Previous methods either required slow decoding or used extra logarithmic factors in the number of tests. We extend binary splitting to the graph setting and show that the edge set can be recovered with high probability using the optimal order of tests while achieving significantly faster decoding time.
Lecture 9: TBA
