Bulletin of L.N. Gumilyov Eurasian National University. Mathematics, computer science, mechanics series

Identification of the spoken language using the Wav2Vec2 model for the Kazakh language

Zh. Kozhirbayev — 2025-03-30

This study presents the development and fine-tuning of an oral language identification model using the XLSR (Cross-Lingual Speech Recognition) Wav2Vec2 variant. Trained on a rich and diverse dataset spanning six languages, with a particular focus on low-resource languages such as Kazakh, the model demonstrates remarkable capabilities in multilingual speech recognition. Thanks to extensive evaluation, the finely tuned model not only surpasses existing benchmarks, but also surpasses other modern models, including Whisper variants. Having achieved an impressive F1 score of 92.9% and an accuracy of 93%, the model demonstrates its performance in real multilingual and low-resource scenarios. This work makes a significant contribution to the development of speech recognition technologies by providing a reliable solution for language identification in various language environments, especially in underrepresented language settings. Its success highlights the potential of Wav2Vec2-based models in improving speech processing systems in low-resource multilingual contexts. The results of this analysis can contribute to the development of reliable and effective automatic speech recognition systems optimized for the Kazakh language. Such technologies will find applications in various fields, including speech-to-text conversion, voice assistants and voice communication tools.

Average Square Errors by Banach Measure of Recovery of Functions by Finite Sums of Terms of Their Trigonometric Fourier Series

Nurlan Nauryzbayev — 2025-03-31

The paper considers the problem of recovering functions using finite sums of terms of their trigonometric Fourier series with respect to probability measures on function classes characterized by the inability to determine a "spectrum of large coefficients". This difficulty motivates the consideration of arbitrary "finite sums of terms from the Fourier series".

The problem of defining probability measures on classes with individual estimates for trigonometric Fourier coefficients was resolved based on the fundamental nature of the property "A function can be defined in two ways: either by a rule or by the complete set of its trigonometric Fourier coefficients", as discussed in the monograph by V.M. Tikhomirov, The remaining steps were largely a matter of technical execution.

The transition to sequences of Fourier coefficients, using A.N. Kolmogorov’s extension theorem (on the extension of measures from finite-dimensional to infinite-dimensional spaces), allowed the introduction of a probability measure on classes with weighted Fourier coefficients, ultimately leading to the Banach measure – first constructed by Stefan Banach in the appendix to Stanisław Saks' book "Theory of the Integral". This paper also proposes some constructive details of the process of probabilistic measure