Missing data represent one of the most frequent difficulties encountered in data science. A wide range of effective techniques for dealing with missing values has been developed to date. One commonly adopted approach relies on nearest neighbor methods, which perform imputation by leveraging information from the most similar observations. Such techniques are particularly prevalent in big data analysis, where datasets can comprise billions of instances. Under these conditions, improving the efficiency of \(k\)-Nearest Neighbors (KNN) algorithms becomes crucial, as their computational cost can be substantial. In this study, we investigate approaches for accelerating missing value imputation based on KNN. We introduce a novel algorithm that employs approximate nearest neighbor (ANN) techniques and examine the relationship between computational efficiency and imputation accuracy. The experimental results demonstrate that widely used ANN algorithms are capable of significantly reducing runtime while preserving a high level of imputation quality.

The article is devoted to the validation of a short version of the questionnaire "Types of orientations in difficult situations" (TODS-36) as a tool for classifying types of perception of difficult situations and evaluating the role of text description analysis involving large language models in determining these types. The following tasks are being solved: development and validation of an algorithm for classifying types of perception of difficult life situations based on the TODS-36 profile using large language models to analyze text descriptions; comparison of the results of algorithmic classification with expert assessment; comparison of the effectiveness of various algorithm modifications. The study sample included 200 text descriptions of difficult situations received from 200 respondents (131 women, 69 men) aged 14 to 54 years. The reference classification was performed by expert psychologists based on a joint analysis of the quantitative indicators of the TODS-36 questionnaire scales and qualitative data (text descriptions of difficult situations). A series of six experiments was conducted. In experiments 1–4, the role of quantitative data and formal classification rules gradually increased. In experiment 5, classification accuracy was assessed when qualitative data were coded by a large language model; in experiment 6, it was assessed when the coding was performed by expert psychologists. The most effective among the algorithms using a large language model was the hybrid one, in which threshold rules are applied to quantitative indicators and the large language model analyzes qualitative data. Its accuracy was 85% on the full sample. At the same time, the highest accuracy in the series of experiments – 85.5% – was obtained using the same algorithm with expert coding of qualitative data. The results obtained confirm the possibility of using the TODS-36 questionnaire as a tool for classifying types of perception of difficult situations and allow us to consider large language models as a means of supporting an expert in classifying types of perception of difficult situations.

This paper presents a review of the current state of research on theoretical approaches to complexity in deep learning and their relation to generalization. Methodologically, the review is structured as a scoping review: it documents bibliographic sources, deduplication and semi-automated corpus narrowing, expert screening, and the composition of a final analytical publication set. The central question is why classical complexity measures, despite their foundational role in statistical learning theory, are insufficient for explaining the behavior of modern overparameterized neural networks. VC dimension, Rademacher complexity, PAC-Bayesian bounds, and information-theoretic approaches remain indispensable as a baseline analytical language, yet they mainly characterize worst-case hypothesis-class capacity and only partially reflect the geometry of the learned solution, the optimization trajectory, and architectural inductive biases. The main focus is therefore placed on contemporary approaches based on the loss landscape, Hessian spectra, optimization methods, and empirical scaling laws. The review develops a synthetic interpretation of the field according to which a useful theory of complexity for deep learning should describe not only the expressive capacity of a class, but also the effective complexity of the solutions actually reached by concrete algorithms on concrete data.

Neural architecture search is a method for automatic selection of an optimal neural network architecture for a given task based on a provided dataset. One of the approaches to neural architecture search is Differentiable architecture search (DARTS). DARTS transforms the discrete search space into a continuous one, enabling the use of gradient-based optimization to learn the architectural parameters of the network. In this paper, we investigate the applicability of DARTS for selecting quantization schemes and bit-widths for different components of generative language models, and present the results of the conducted experiments. The code for training and evaluation of the quantized model is available at: https://github.com/daria1d/Darts-QAT.

The method of constructing convex linear hulls of a finite set of points is often used in recognition problems. In an \(n\)-dimensional space, \(n\)-element subsets of points are considered for this purpose. If the remaining points lie on the same side of the hyperplane containing the selected points, then this hyperplane is called a face. Checking whether a new point belongs to the convex linear hull is reduced to verifying a system of linear inequalities determined by the faces.

We propose considering a coarse-grained problem in which the coordinates of the points take three values, \(0,1,-1\), interpreted as elements of a field with three elements. In this setting, the linear form is equal to zero at points lying on the hyperplane, equal to \(1\) on one side of it, and equal to \(-1\) on the other side. Checking whether a point belongs to the convex linear hull is reduced to verifying the conditions \(S_a(x)\in \{0,\lambda _a\}\) for all faces \(S_a\) of the convex linear hull, where the value \(0\) corresponds to the point lying on the hyperplane \(S_a\), while \(\lambda _a\) is the common value of the linear form at the points of the set that do not belong to \(S_a\). Thus, whether a new point belongs to the convex linear hull is determined by its position relative to all faces of the hull.

The paper continues the investigation into the complexity of automata implementation via state encoding. Previous research was focused on the identification of “simple implementations” of automata and mappings on a finite set. This paper is devoted to mappings with “complex implementations”, i.e., mappings for which any irredundant encoding yields a Boolean operator of maximum complexity in terms of the Zhegalkin polynomial degree. It is proved that for any set cardinality \(n=2^k\) such mappings exist. These mappings can be used in future research to prove that automata admitting only “complex implementations” also exist.

For systems of automaton functions that form a closed class, it is important to determine the basis from the minimal number of variables from which they can be obtained by superposition operations. Of particular interest are classes in which the ’proper’ automata from the basis have a single input variable; this restriction does not apply to Boolean functions from the basis, which are automata with a single state. An example of such a class is the class of all automata. The author studies subclasses of automata whose transition and output functions belong to a certain Post class.

We consider one-dimensional cellular automata with locators for which the semigroup defined on the broadcast alphabet is an idempotent monoid. It has previously been shown that complex cellular automata problems such as the firing squad synchronization problem or the problem of controlling the motion of a point on a line are solved quite simply in idempotent cellular automata with locators, and the problems essentially degenerate. In this paper, we show that for problems that require distance comparison, idempotent cellular automata with locators provide no asymptotic advantage over conventional cellular automata. However, the use of non-idempotent cellular automata provides a significant time advantage.

The \(K\)-completeness problem in the class of linear \(p\)-adic automata is studied for an odd prime \(p\). Completeness criteria are obtained for homogeneous and inhomogeneous linear \(p\)-adic functions. The results generalize known results for linear \(2\)-adic automata to arbitrary odd prime bases. In addition, a strictly increasing chain of \(K\)-closed classes \(I_\alpha\), \(\alpha \in (0,1]\), of continuum cardinality is constructed.

This paper considers Tanner codes constructed on the incidence graph of points and hyperplanes of a projective space, with projective Reed–Muller codes as component codes. The assignment of symbols of local codes to edges is performed so that the resulting Tanner code inherits the symmetry of the projective space. Lower bounds on the minimum distance and dimension of such codes are obtained. In particular, it is shown that, for certain parameter values, these codes are asymptotically good.