Keynote Speakers

Lev Kazakovtsev. Accelerating Nearest Neighbor Search in Vector Databases

Zhengtai Xie. Synchronous Learning and Planning Strategies for Robots with Optimization Algorithms

Ratikanta Behera. Tensors generalized inverses under M - product and applications

Jajati Keshari Sahoo. Parameterized iterative methods for solving tensor equations based on generalized Hadamard product

Xinwei Cao. Selecting Portfolio Using Neural Dynamics with Online Computation

Yuriy Skobtsov. Evolutionary Quantum Algorithms

Accelerating Nearest Neighbor Search in Vector Databases

Nowadays, data collection tools accumulate large volumes of multidimensional information on various objects of study. Such databases are a valuable source of knowledge for methods of intelligent data analysis. One of the most important problems in machine learning is search for similar objects. Nearest neighbor search (NNS) is an optimization problem that involves finding the data vector most similar (closest) to a given vector (query) in the dataset. To accelerate the search, supplementary data structures (indices) are usually built. In vector databases, the most popular of index structures is the inverted file index (IVF) based on the k-means problem solution: each of the data vectors is assigned to the closest centroid. The set of centroids is determined by a clustering algorithm. 

In this talk, the author summarizes recent results of Krasnoyarsk research team in this field: new specialized clustering algorithms based on simplified greedy agglomerative search, new adaptive IVF search procedure which estimates the query complexity on the first search steps and enables us to speed-up the search by a factor of 10-35%, new initialization procedures for clustering algorithms, new clustering models and corresponding algorithms.

Synchronous Learning and Planning Strategies for Robots with Optimization Algorithms

Robot learning and control problems can be formulated as optimization problems, thereby motivating the development of diverse optimization algorithms that drive the error to zero. This talk focuses on a variety of complex robotic systems and devises structural-learning techniques for multi-robot systems, robotic visual servoing platforms, mobile robots, and robot motion/force-control systems. Several synchronous learning-and-planning strategies together with their intelligent algorithms are proposed. By integrating neural dynamics, data-driven methodologies, Kalman-filtering algorithms, and model-free control techniques, the research generates virtual data to assist the training process and establishes a unified learning-and-control framework for robotic systems. The framework enables autonomous motion control even when the structural information of the robot is unknown.

Tensors generalized inverses under M -product and applications

Tensor generalized inverses have emerged as fundamental tools in numerical multilinear algebra, particularly foraddressing the challenges posed by large-scale multidimensional data processing. The theory of the generalized inverses of tensors has become increasingly pivotal in computational mathematics and numerical analysis, warranting systematic theoretical development and refinement.This presentation advances the theoretical foundations of tensor generalized inverses via M-product by establishing novel characterizations of various classes of generalized inverses. The theoretical framework is substantiated by carefully selected numerical examples that illustrate the applicability and efficacy of the proposed results. Additionally, we introduce computationally efficient algorithms for computing the Moore-Penrose inverse of tensors, addressing both theoretical rigor and practical implementation considerations. The practical significance of these theoretical contributions is demonstrated through an application to image deblurring problems, where the proposed methodologies exhibit considerable effectiveness in restoration tasks.

Parameterized iterative methods for solving tensor equations based on generalized Hadamard product

Iterative methods based on tensors have emerged as powerful tools for solving tensor equations and have significantly advanced across multiple disciplines. In this talk, we will discuss two-step tensor-based iterative methods to solve the tensor equations by incorporating a generalized Hadamard product. Preconditioning techniques and parametric optimization will be discussed, to enhance convergence properties. Theoretical justifications along with comprehensive numerical experiments will demonstrate the computational efficiency of the proposed two-step parametrized iterative methods. In addition, we discuss the solution of the Sylvester equations and a regularized least-squares solution for image deblurring problems.

Selecting Portfolio Using Neural Dynamics with Online Computation

In this talk, we explore the use of neural dynamics for portfolio selection, integrating online computation techniques to optimize investment strategies. Traditional portfolio optimization often struggles with dynamic market changes and real-time data. By leveraging neural networks, we propose a novel approach where the model adapts to market conditions continuously, updating portfolio weights online without retraining from scratch. This method enables efficient, real-time decision-making while minimizing risk and maximizing returns. We will discuss the underlying mathematical framework, key algorithms, and the advantages of this approach for modern financial markets and adaptive risk management.

Evolutionary Quantum Algorithms

New evolutionary algorithms based on quantum computing models are presented. Qubits are used to encode a potential solution. In the evolution of solutions, quantum gates are used instead of traditional genetic crossover and mutation operators. Two main types of quantum genetic algorithms are considered: 1) with binary observation, where after measuring the quantum representation, binary chromosomes are formed and processed; 2) with real observation, where after measuring the quantum representation, vectors of real numbers are formed and processed. Through  observation of a quantum (qubit) representation, binary (or real) chromosomes are formed and processed, which are used in a classical genetic algorithm. Pseudocodes of evolutionary quantum algorithms with observation and modification procedures are given. Quantum evolutionary operators of rotation (interference), mutation (inversion) and crossover are considered. A comparison of traditional and quantum evolutionary algorithms has been made. New swarm algorithms based on quantum computing models are presented. The advantages and disadvantages of the above models and their areas of application are noted.