Andrey Gorshenin

This paper presents several contributions to the field of informed machine learning. First, a Deep Gaussian Mixture Informed method for pseudo-labeling in

In the paper, the capabilities of the Kolmogorov–Arnold neural network family in applications to the analysis of complex structured data from the field of space physics and astrophysics have been explored. The main objective of the study is to demonstrate empirically the effectiveness of such architectures, including their hybrid modifications, in comparison with traditional recurrent and transformer models for these problems. Open data, such as time series of interplanetary magnetic field induction and data from stellar spectra, have been used for the experiments. The novelty of the study has been determined by the first effective testing of Kolmogorov–Arnold neural networks in relation to these data. Furthermore, in the paper, an approach to identifying anomalous values in data using a special verification procedure for statistical hypotheses has been tested. According to the obtained results, the considered hybrid architectures demonstrate superiority over classical models in terms of the mean square error metric by up to 18.75% for short-term forecasting (up to 10 min) and up to 10.2% for a horizon of up to 50 min. High accuracy was achieved in filling missing values (the root mean square error is in the range of 0.11–0.13), which confirms their effectiveness under high volatility conditions of space signals. The use of a variant of Kolmogorov–Arnold networks based on the Fourier transform for redshift estimation made it possible to reduce the verification error to 0.024 while ensuring a 1.5–3.6-fold acceleration of the training process convergence relative to transformers and standard Kolmogorov–Arnold architectures. In each of the problem, the use of KAN layers and the choice of an appropriate functional basis made it possible to outperform classical solutions. The proposed statistical approach has proven its effectiveness both in identifying global extremes and in detecting local outliers, which are critical for analyzing the stability of physical systems in quasi-stationary modes.

This paper presents a new multiagent architecture with probabilistic data aggregation for detecting fake messages in text, images, and audio sources. The development of such approaches is increasingly in demand for a variety of information systems due to the growing volume of heterogeneous content, the limitations of single models in credibility assessment, and the lack of sufficiently large labeled datasets in real-world conditions that would allow the effective detection of unreliable content, which leads to the need to use probabilistic approaches. The fundamental novelty of the solution presented in this work lies in the probabilistic aggregation of agent inferences with confidence calibration and interpretable justifications. The architecture includes an intelligent router, modality-specific agents, and a context-weighted aggregation module. To evaluate the quality of the proposed architecture and compare it with various large language models, a custom graph dataset of real and synthetic messages with various combinations of modalities was created. In the experimental series, the aggregator outperformed single text (Mistral-7B-Instruct-v0.3, Phi-4, etc.) and vision language models (for example, LLaVa‑v1.5‑7B and Qwen2‑vl‑2B‑Instruct, etc.): the values of the accuracy metrics (Accuracy) and F₁-score of the proposed architecture are 10–17% higher; the Weighted F₁‑score values improved by 16%; the values of the Brier score and log loss metrics, reflecting the calibration of probabilistic predictions and the severity of penalty for overconfident errors, were reduced by 13–30%. The system operates in zero-shot mode based on open pretrained models, including YandexGPT‑5‑Lite‑8B‑Instruct, Qwen3‑8B and those vision language models mentioned above, and supports fast domain adaptation using system prompts and standardized output formats. The results demonstrate the effectiveness of the multiagent approach for reliable assessment of the credibility of multimodal messages and its applicability to intelligent content quality control tools in modern general-purpose information systems, including social networks.

An Erratum to this paper has been published: https://doi.org/10.1134/S1064562425330038

The article is devoted to the development of methods for probability informing of machine learning models and deep neural networks in the problem of time series forecasting. In continuation of previous studies that used moments of finite mixtures of normal distributions and connected mixture components, this paper proposes a new joint approach to this type of informing: using the connected components with simultaneous modifications of the standard loss function. Weighted loss functions are considered, including approximation of the data distribution density using kernel estimators and finite normal mixtures. The experiments conducted using real datasets (geophysical and electric time series) demonstrate the possibility of significant improvement of forecasting metrics (root mean square errors, mean absolute error in percent) compared to baseline models that do not use informed models. Thus, on geophysical data, the reduction in the mean square error in short-term forecasting problems only from the modification of the loss function amounted to 15.7%, and the greatest improvement within informing was 31.8% compared to the basic methods. For the characteristics of electrical circuit elements, the improvement of metrics in the medium-term forecasting problem with modification of only the loss function amounted to 12.5%, and the combined approach increased the values by 13.6%. A reduction in the number of training epochs required to achieve similar or higher accuracy was demonstrated with a moderate change in the duration of the epoch itself—on average, no more than 3.7%. It is noted that in all cases the results of informed models exceed classical versions of algorithms.

The article presents a new methodology for solving problems of self-supervised and semisupervised learning using deep Gaussian mixture models for the case of small datasets for which only a limited set of training data is typically available. On the basis of a mathematical model implemented in the layers of a neural network, a method is proposed for forming pseudolabels of data, which are subsequently used to train a classifier or regressor, for which various machine learning methods and neural network architectures are used in the research. The deep Gaussian mixture models allows us to form an enriched feature space for describing data, expanding the approach of probability-informed machine learning developed by the authors. To test the method, 19 open tabular datasets from the University of California Irvine repository, designed to solve various machine learning problems, as well as time series describing the change in the radiation flux of type Ia supernovae (binary stars), were used. It has been established that, in the case where the labeled data constitutes less than half of the set, the methodology proposed in the article allows using more complex and deep architectures (for example, transformer ones) for processing and obtaining results with better accuracy with their help. With a large proportion of labeled data, the use of deep Gaussian mixture models allows us to increase the accuracy of simpler algorithms to the level of more complex ones (in terms of the number of trainable parameters and architecture) without using additional observations. An increase in the accuracy of solving supervised learning problems using pseudolabels generated by deep Gaussian mixture models is demonstrated, compared to traditionally used labeling approaches, such as classical Gaussian mixture models and k-means. Thus, the average increase in the F1-score in the classification task amounted to as much as 19.26%, and the average relative decrease in the mean square error in the regression problem reached 36.74% on test datasets.