The use of multimodal data in emotion recognition systems has great potential for applications in various fields: healthcare, human-machine interfaces, operator monitoring, and marketing. Until recently, the development of emotion recognition systems based on multimodal data was constrained by insufficient computing power. However, with the advent of high-performance GPU-based systems and the development of efficient deep neural network architectures, there has been a surge of research aimed at using multiple modalities such as audio, video, and physiological signals to accurately detect human emotions. In addition, physiological data from wearable devices has become important due to the relative ease of its collection and the accuracy it enables. This paper discusses architectures and methods for applying deep neural networks to analyse multimodal data to improve the accuracy and reliability of emotion recognition systems, presenting current approaches to implementing such algorithms and existing open multimodal datasets.

The article addresses the development of a methodology for hierarchical multi-task learning of neural networks, inspired by the ERNIE 3 architecture, and its experimental validation using the FRED-T5 model for Russian-language text analysis and generation tasks. Hierarchical multi-task learning represents a promising approach for creating universal language models capable of efficiently solving a variety of natural language processing (NLP) tasks. The proposed methodology integrates specialized encoder blocks for natural language understanding (NLU) tasks with a shared decoder for natural language generation (NLG) tasks, thus improving model performance and reducing computational costs. This paper presents a comparative analysis of the developed methodology’s performance using the open Russian SuperGLUE benchmark and the pre-trained Russian-language model FRED-T5-1.7B. Experimental results confirm a significant improvement in model quality in both zero-shot and few-shot scenarios compared to the baseline configuration. Additionally, the paper explores practical applications of the developed approach in real NLP tasks and provides recommendations for further advancement of the methodology and its integration into applied systems for processing Russian-language texts.

The development of high-quality tools for automatic determination of text levels according to the CEFR scale allows creating educational and testing materials more quickly and objectively. In this paper, the authors examine two types of modern text models: linguistic characteristics and embeddings of large language models for the task of classifying Russian-language texts by six CEFR levels: A1-C2 and three broader categories A, B, C. The two types of models explicitly represent the text as a vector of numerical characteristics. In this case, dividing the text into levels is considered as a common classification task in the field of computational linguistics. The experiments were conducted with our own corpus of 1904 texts. The best quality is achieved by rubert-base-cased-conversational without additional adaptation when determining both six and three text categories. The maximum F-measure value for levels A, B, C is 0.77. The maximum F-measure value for predicting six text categories is 0.67. The quality of text level determination depends more on the model than on the machine learning classification algorithm. The results differ from each other by no more than 0.01-0.02, especially for ensemble methods.

The study of various processes leads to the need to clarify (expand) the boundaries of the applicability of computational structures and modeling tools. The purpose of this article is to develop the Taylor expansion for functions of several variables based on the concept of $S$-differentiability. A function $f$ from $L_1[Q_0]$, where $Q_0$ is an $m$-dimensional cube, is called $S$-differentiable at an interior point $x_0$ of this cube, if there exists an algebraic if there exists an analgebraic polynomial $P(x)$ of degree not greater than first for which it is uniform over all vectors $v$ of the unit sphere ${\mathbb R}^m$ the integral of $t$ within $0$ and $h$ from the expression $f(x_0 + t \cdot v)-P(t \cdot v)$ is $o(h^2)$ for $h \to 0{+}$. It is shown that with this definition, differentiation of a composite function with a linear interior component is valid, and the vector-gradient principle holds. The following result is proved. Let the function $f$ have continuous partial derivatives up to order $n$ inclusive in some neighborhood of the interior point $x_0 \in Q_0$ that are $S$-differentiable at the point $x_0$, then the Taylor expansion the function $f$ with accuracy $o\big(\Vert x - x_0\Vert^{n + 1}\big)$ holds in this neighborhood.

The logistic equation with delay and diffusion, which is important in mathematical ecology, is considered. It is assumed that the boundary conditions at one end of the interval [0,1] contain a parameter. The question of local — in the neighborhood of the equilibrium state — dynamics of the corresponding boundary value problem for all values of the boundary condition parameters is investigated. Critical cases in the problem of stability of the equilibrium state are identified and normal forms — scalar complex ordinary differential equations of the first order — are constructed. Their nonlocal dynamics determine the behavior of solutions of the original problem in a small neighborhood of the equilibrium state.