## 2 State of the Art  
Modern developments aim to increase accuracy and resistance to external factors. Researchers test the proposed methods using voice archives with different recording lengths, noise levels, and the number and age of subjects. One of the key metrics in this area is considered to be the Equal Error Rate (EER). EER is an important indicator because it allows one to quantify the balance between the False Rejection Rate (FRR) and the False Acceptance Rate (FAR). Authentication systems are divided into text-dependent and text-independent ones, that does not allow for a direct comparison of their accuracy. There are several known basic approaches to extracting features from voice images, in particular, i-vector and x-vector. The first is based on a Gaussian mixture (EER = 9.23% [2]). X-vector is based on the use of neural networks (NNs) and usually shows higher performance (EER = 5.21% [2]). Experiments comparing these methods were conducted on voice archives, such as NIST SRE 2016, VoxCeleb 2017 and SWBD. Short-Time Fourier Transform (STFT) is also often used to analyze speech signal features. The paper [3] presents a model for speaker recognition based on short speech segments lasting less than one second. The experiments used their own dataset, including recordings of pronunciations of numbers in English collected from six students. A total of 3000 audio files were recorded in WAV format. The authors proposed an improved multi-frequency cepstral coefficient (MFCC) algorithm that uses both low-frequency and mid- and high-frequency components. These features were used in a two-dimensional convolutional neural network (2D-CNN), which built a three-dimensional tensor for processing acoustic data. The accuracy of the model on the test dataset was 99.6%, measured using the F1-score metric, which considered both the precision and recall of the model. The authors of the ResNet architecture made a fundamental contribution to the development of deep learning and speaker recognition. This architecture uses \"residual blocks\" with skip connections between layers, which solves the gradient decay problem and simplifies the training of deep neural networks. This concept [4] was successfully tested on two models based on a 34-layer architecture with AM-Softmax and AAM-Softmax loss functions. The results showed a significant reduction in errors compared to most of the works presented at Interspeech 2020, reaching EER = 5.19% on the VoxSRC 2020 set. The paper [5] presents an improved Res2 Net architecture that can recognize more complex patterns by implementing a multi-scale approach in the \"residual blocks\" and dividing the feature map into smaller segments. The best model consisted of a 50-layer Res2 Net network with the AM-SoftMax loss function and achieved an EER of 0.83% on the VoxCeleb dataset. One problem is the lack of phonetic information in speech segments when authenticating with a voice password or short speech fragments. In such cases, the authors of the study [6] recommended extracting vector representations using x-vector from deep NN layers, which resulted in a 14% decrease in EER to 13.35%. It was also determined that training the PLDA (Probabilistic Linear Discriminant Analysis) model, which is used at the speaker classification stage, on short speech segments contributes to an additional reduction in the equiprobable error by 5% (x-vector extraction occurring on the seventh layer with a dimension of 150). The RecXi model [7] was proposed in the study [7]. It includes three Gaussian inference layers, each of which extracts individual speech components. The test resulted in a 9.56% reduction in the EER value compared to the base SOTA model. The experiment was conducted using VoxCeleb and SITW. One of the most recently proposed approaches to improve the information content of speech data is the multimodal Vision-Guided Speaker Recognition (VGSR) training [8], in which the face recognition system acts as a teacher, passing on knowledge useful for distinguishing faces to speaker recognition models.