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Recently, saddle point problems have received much attention due to their powerful modeling capability for a lot of problems from diverse domains. Applications of these problems occur in many applied areas, such as robust optimization, distributed optimization, game theory, and many applications in machine learning such as empirical risk minimization and generative adversarial networks training. Therefore, many researchers have actively worked on developing numerical methods for solving saddle point problems in many different settings. This paper is devoted to developing a numerical method for solving saddle point problems in the nonconvex uniformly-concave setting. We study a general class of saddle point problems with composite structure and H\"older-continuous higher-order derivatives. To solve the problem under consideration, we propose an approach in which we reduce the problem to a combination of two auxiliary optimization problems separately for each group of variables, the outer minimization problem w.r.t. primal variables, and the inner maximization problem w.r.t the dual variables. For solving the outer minimization problem, we use the Adaptive Gradient Method, which is applicable for nonconvex problems and also works with an inexact oracle that is generated by approximately solving the inner problem. For solving the inner maximization problem, we use the Restarted Unified Acceleration Framework, which is a framework that unifies the high-order acceleration methods for minimizing a convex function that has H\"older-continuous higher-order derivatives. Separate complexity bounds are provided for the number of calls to the first-order oracles for the outer minimization problem and higher-order oracles for the inner maximization problem. Moreover, the complexity of the whole proposed approach is then estimated.

Interpretability in recent deep learning models has become an epicenter of research particularly in sensitive domains such as healthcare, and finance. Concept bottleneck models have emerged as a promising approach for achieving transparency and interpretability by leveraging a set of humanunderstandable concepts as an intermediate representation before the prediction layer. However, manual concept annotation is discouraged due to the time and effort involved. Our work explores the potential of large language models (LLMs) for generating high-quality concept banks and proposes a multimodal evaluation metric to assess the quality of generated concepts. We investigate three key research questions: the ability of LLMs to generate concept banks comparable to existing knowledge bases like ConceptNet, the sufficiency of unimodal text-based semantic similarity for evaluating concept-class label associations, and the effectiveness of multimodal information in quantifying concept generation quality compared to unimodal concept-label semantic similarity. Our findings reveal that multimodal models outperform unimodal approaches in capturing concept-class label similarity. Furthermore, our generated concepts for the CIFAR-10 and CIFAR-100 datasets surpass those obtained from ConceptNet and the baseline comparison, demonstrating the standalone capability of LLMs in generating highquality concepts. Being able to automatically generate and evaluate high-quality concepts will enable researchers to quickly adapt and iterate to a newer dataset with little to no effort before they can feed that into concept bottleneck models.

In this paper the problem of automated building of a citation graph from a collection of scientific documents is considered as a sequence of machine learning tasks. The overall data processing technology is described which consists of six stages: preprocessing, metainformation extraction, bibliography lists extraction, splitting bibliography lists into separate bibliography records, standardization of each bibliography record, and record linkage. The goal of this paper is to provide a survey of approaches and algorithms suitable for each stage, motivate the choice of the best combination of algorithms, and adapt some of them for multilingual bibliographies processing. For some of the tasks new algorithms and heuristics are proposed and evaluated on the mixed English and Russian documents corpora.

We investigate machine learning methods with a certain kind of decision rule. In particular, inverse-distance method of interpolation, method of interpolation by radial basis functions, the method of multidimensional interpolation and approximation, based on the theory of random functions, the last method of interpolation is kriging. This paper shows a method of rapid retraining “model” when adding new data to the existing ones. The term “model” means interpolating or approximating function constructed from the training data. This approach reduces the computational complexity of constructing an updated “model” from $O(n^3)$ to $O(n^2)$. We also investigate the possibility of a rapid assessment of generalizing opportunities “model” on the training set using the method of cross-validation leave-one-out cross-validation, eliminating the major drawback of this approach — the necessity to build a new “model” for each element which is removed from the training set.

This article explores a method of machine learning based on the theory of random functions. One of the main problems of this method is that decision rule of a model becomes more complicated as the number of training dataset examples increases. The decision rule of the model is the most probable realization of a random function and it's represented as a polynomial with the number of terms equal to the number of training examples. In this article we will show the quick way of the number of training dataset examples reduction and, accordingly, the complexity of the decision rule. Reducing the number of examples of training dataset is due to the search and removal of weak elements that have little effect on the final form of the decision function, and noise sampling elements. For each $(x_i,y_i)$-th element sample was introduced the concept of value, which is expressed by the deviation of the estimated value of the decision function of the model at the point $x_i$, built without the $i$-th element, from the true value $y_i$. Also we show the possibility of indirect using weak elements in the process of training model without increasing the number of terms in the decision function. At the experimental part of the article, we show how changed amount of data affects to the ability of the method of generalizing in the classification task.

Correct modeling of complex dynamics of urban transportation flows requires the collection of large volumes of empirical data to specify types of the modes and their identification. At the same time, setting a large number of observation posts is expensive and technically not always feasible. All this results in insufficient factographic support for the traffic control systems as well as for urban planners with the obvious consequences for the quality of their decisions. As one of the means to provide large-scale data collection at least for the qualitative situation analysis, the wide-area video cameras are used in different situation centers. There they are analyzed by human operators who are responsible for observation and control. Some video cameras provided their videos for common access, which makes them a valuable resource for transportation studies. However, there are significant problems with getting qualitative data from such cameras, which relate to the theory and practice of image processing. This study is devoted to the practical application of certain mainstream neuro-networking technologies for the estimation of essential characteristics of actual transportation flows. The problems arising in processing these data are analyzed, and their solutions are suggested. The convolution neural networks are used for tracking, and the methods for obtaining basic parameters of transportation flows from these observations are studied. The simplified neural networks are used for the preparation of training sets for the deep learning neural network YOLOv4 which is later used for the estimation of speed and density of automobile flows.

The article considers minimization of the expectation of convex function. Problems of this type often arise in machine learning and a variety of other applications. In practice, stochastic gradient descent (SGD) and similar procedures are usually used to solve such problems. We propose to use the ellipsoid method with mini-batching, which converges linearly and can be more efficient than SGD for a class of problems. This is verified by our experiments, which are publicly available. The algorithm does not require neither smoothness nor strong convexity of the objective to achieve linear convergence. Thus, its complexity does not depend on the conditional number of the problem. We prove that the method arrives at an approximate solution with given probability when using mini-batches of size proportional to the desired accuracy to the power −2. This enables efficient parallel execution of the algorithm, whereas possibilities for batch parallelization of SGD are rather limited. Despite fast convergence, ellipsoid method can result in a greater total number of calls to oracle than SGD, which works decently with small batches. Complexity is quadratic in dimension of the problem, hence the method is suitable for relatively small dimensionalities.

Gradient-free optimization methods or zeroth-order methods are widely used in training neural networks, reinforcement learning, as well as in industrial tasks where only the values of a function at a point are available (working with non-analytical functions). In particular, the method of error back propagation in PyTorch works exactly on this principle. There is a well-known fact that computer calculations use heuristics of floating-point numbers, and because of this, the problem of finiteness of the mantissa arises.

In this paper, firstly, we reviewed the most popular methods of gradient approximation: Finite forward/central difference (FFD/FCD), Forward/Central wise component (FWC/CWC), Forward/Central randomization on $l_2$ sphere (FSSG2/CFFG2); secondly, we described current theoretical representations of the noise introduced by the inaccuracy of calculating the function at a point: adversarial noise, random noise; thirdly, we conducted a series of experiments on frequently encountered classes of problems, such as quadratic problem, logistic regression, SVM, to try to determine whether the real nature of machine noise corresponds to the existing theory. It turned out that in reality (at least for those classes of problems that were considered in this paper), machine noise turned out to be something between adversarial noise and random, and therefore the current theory about the influence of the mantissa limb on the search for the optimum in gradient-free optimization problems requires some adjustment.

At present, the accelerator complex NICA is being built at JINR (Dubna). It is intended for performing experiments to study interactions of relativistic nuclei and polarized particles (protons and deuterons). One of the experimental facilitues MPD (MultiPurpose Detector) was designed to investigate nucleus-nucleus, protonnucleus and proton-proton interactions. The existing plans of future MPD upgrade consider a possibility to install an inner tracker made of the new generation silicon pixel sensors. It is expected that such a detector will considerably enhance the research capability of the experiment both for nucleus-nucleus interactions (due to a high spatial resolution near the collision region) and proton-proton ones (due to a fast detector response).

This paper presents main characteristics of such a tracker, obtained using a Monte-Carlo simulation of the detector for proton-proton collisions. In particular, the detector ability to reconstruct decay vertices of short-lived particles and perform a selection of rare events of such decays from much more frequent “common” interactions are evaluated. Also, the problem of a separation of multiple collisions during the high luminosity accelerator running and the task of detector triggering on rare events are addressed. The results obtained can be used to justify the necessity to build such a detector and to develop a high-level trigger system, possibly based on machine learning techniques.