arXiv subjects

Dmitry I. Ignatov

Publications and source records attributed to Dmitry I. Ignatov.

At least 19 recordsLinked to original sources

arXiv2026

LANTERN: Illuminating Hidden Mathematical Knowledge in Language Models

Language models can now prove theorems, but people still decide which problems to pursue. We ask whether a model's internal representations can help identify promising mathematical connections. We develop LANTERN, a fast, cost-efficient pipeline that uses a classifier over pretrained-model activations to rank candidate relations, followed by staged filtering, hypothesis generation, executable verification, and analytical checking. Applied to the On-Line Encyclopedia of Integer Sequences (OEIS), LANTERN ranked 50 million pairs among 10,000 frequently referenced sequences and produced 62 verified relations between pairs without an existing OEIS cross-reference. A content screen retained 13 relations worth presenting; nine of these are informative or insightful, including four which are entirely novel to the best of our knowledge: none appears in the OEIS or in our targeted literature search. The entire end-to-end process including classifier training, candidate ranking, filtering and verification took under 8 hours.

cs.CL↗

arXiv2026

Time Series Forecasting based on Solana Digital Asset Dataset

Accurate analysis and forecasting of Solana digital assets require data that captures both token-level behavior and ecosystem-level DEX activity. This paper introduces, to the best of our knowledge, the first Solana digital asset time series dataset designed for forecasting and market-structure analysis. The dataset contains 1,584 tokens observed at daily resolution from March 24, 2024 to March 16, 2025, with 27 variables combining token transactions, prices, liquidity-pool balances, trader activity, Solana DEX volume, DEX trader counts, newly created pairs, and SOL price indicators. Rather than treating the dataset only as input for model comparison, we use it to characterize the DEX-driven token market during a period of rapid ecosystem growth. The analysis identifies synchronized market-wide activity peaks in mid-November 2024 and mid-January 2025 across DEX volume, token trading volume, active wallets, buyers, sellers, new traders, liquidity-pool balances, and SOL price. The January 2025 peak coincides with the 'Trump' token event and is accompanied by a visible transition from liquidity accumulation to withdrawals, suggesting that individual token dynamics are strongly coupled to broader Solana market sentiment and DEX activity. Forecasting experiments are then used as an empirical validation of the dataset's signal content. In three-day-ahead market-capitalization prediction, PatchTST achieves the best overall rank, fine-tuned Chronos follows closely, and statistical baselines remain competitive for trend-dominated tokens. Feature-importance analysis further shows that SOL price, SOL moving averages, total DEX volume, DEX trader counts, and newly created pairs are among the most informative covariates. The main contribution is therefore a curated Solana forecasting dataset and a data-driven analysis of the ecosystem-level factors that shape token volatility.

cs.CE↗

arXiv2026

Exploring the Relationship between Brain Hemisphere States and Frequency Bands through Classical Machine Learning and Deep Learning Optimization Techniques with Neurofeedback

This study investigates the performance of classifiers across EEG frequency bands, evaluating efficient class prediction for the left and right hemispheres using various optimisers. Three neural network architectures a deep dense network, a shallow three-layer network, and a convolutional neural network (CNN) are implemented and compared using the TensorFlow and PyTorch frameworks. Adagrad and RMSprop optimisers consistently outperformed others across frequency bands, with Adagrad excelling in the beta band and RMSprop achieving superior performance in the gamma band. Classical machine learning methods (Linear SVM and Random Forest) achieved perfect classification with 50--100 times faster training times than deep learning models. However, in neurofeedback simulations with real-time performance requirements, the deep neural network demonstrated superior feedback-signal generation (a 44.7% regulation rate versus 0% for classical methods). SHAP analysis reveals the nuanced contributions of EEG frequency bands to model decisions. Overall, the study highlights the importance of selecting a model dependent on the task: classical methods for efficient offline classification and deep learning for adaptive, real-time neurofeedback applications.

cs.LG↗

arXiv2023

Transformer-based classification of user queries for medical consultancy with respect to expert specialization

The need for skilled medical support is growing in the era of digital healthcare. This research presents an innovative strategy, utilizing the RuBERT model, for categorizing user inquiries in the field of medical consultation with a focus on expert specialization. By harnessing the capabilities of transformers, we fine-tuned the pre-trained RuBERT model on a varied dataset, which facilitates precise correspondence between queries and particular medical specialisms. Using a comprehensive dataset, we have demonstrated our approach's superior performance with an F1-score of over 92%, calculated through both cross-validation and the traditional split of test and train datasets. Our approach has shown excellent generalization across medical domains such as cardiology, neurology and dermatology. This methodology provides practical benefits by directing users to appropriate specialists for prompt and targeted medical advice. It also enhances healthcare system efficiency, reduces practitioner burden, and improves patient care quality. In summary, our suggested strategy facilitates the attainment of specific medical knowledge, offering prompt and precise advice within the digital healthcare field.

cs.LG↗

arXiv2022

On the Cryptomorphism between Davis' Subset Lattices, Atomic Lattices, and Closure Systems under T1 Separation Axiom

In this paper we count set closure systems (also known as Moore families) for the case when all single element sets are closed. In particular, we give the numbers of such strict (empty set included) and non-strict families for the base set of size $n=6$. We also provide the number of such inequivalent Moore families with respect to all permutations of the base set up to $n=6$. The search in OEIS and existing literature revealed the coincidence of the found numbers with the entry for D.\ M.~Davis' set union lattice (\seqnum{A235604}, up to $n=5$) and $|\mathcal L_n|$, the number of atomic lattices on $n$ atoms, obtained by S.\ Mapes (up to $n=6$), respectively. Thus we study all those cases, establish one-to-one correspondences between them via Galois adjunctions and Formal Concept Analysis, and provide the reader with two of our enumerative algorithms as well as with the results of these algorithms used for additional tests. Other results include the largest size of intersection free families for $n=6$ plus our conjecture for $n=7$, an upper bound for the number of atomic lattices $\mathcal L_n$, and some structural properties of $\mathcal L_n$ based on the theory of extremal lattices.

cs.DM↗

arXiv2021

On Interpretability and Similarity in Concept-Based Machine Learning

Machine Learning (ML) provides important techniques for classification and predictions. Most of these are black-box models for users and do not provide decision-makers with an explanation. For the sake of transparency or more validity of decisions, the need to develop explainable/interpretable ML-methods is gaining more and more importance. Certain questions need to be addressed: How does an ML procedure derive the class for a particular entity? Why does a particular clustering emerge from a particular unsupervised ML procedure? What can we do if the number of attributes is very large? What are the possible reasons for the mistakes for concrete cases and models? For binary attributes, Formal Concept Analysis (FCA) offers techniques in terms of intents of formal concepts, and thus provides plausible reasons for model prediction. However, from the interpretable machine learning viewpoint, we still need to provide decision-makers with the importance of individual attributes to the classification of a particular object, which may facilitate explanations by experts in various domains with high-cost errors like medicine or finance. We discuss how notions from cooperative game theory can be used to assess the contribution of individual attributes in classification and clustering processes in concept-based machine learning. To address the 3rd question, we present some ideas on how to reduce the number of attributes using similarities in large contexts.

cs.LG↗

arXiv2020

Object-Attribute Biclustering for Elimination of Missing Genotypes in Ischemic Stroke Genome-Wide Data

Missing genotypes can affect the efficacy of machine learning approaches to identify the risk genetic variants of common diseases and traits. The problem occurs when genotypic data are collected from different experiments with different DNA microarrays, each being characterised by its pattern of uncalled (missing) genotypes. This can prevent the machine learning classifier from assigning the classes correctly. To tackle this issue, we used well-developed notions of object-attribute biclusters and formal concepts that correspond to dense subrelations in the binary relation $\textit{patients} \times \textit{SNPs}$. The paper contains experimental results on applying a biclustering algorithm to a large real-world dataset collected for studying the genetic bases of ischemic stroke. The algorithm could identify large dense biclusters in the genotypic matrix for further processing, which in return significantly improved the quality of machine learning classifiers. The proposed algorithm was also able to generate biclusters for the whole dataset without size constraints in comparison to the In-Close4 algorithm for generation of formal concepts.

q-bio.GN↗

arXiv2020

Triclustering in Big Data Setting

In this paper, we describe versions of triclustering algorithms adapted for efficient calculations in distributed environments with MapReduce model or parallelisation mechanism provided by modern programming languages. OAC-family of triclustering algorithms shows good parallelisation capabilities due to the independent processing of triples of a triadic formal context. We provide the time and space complexity of the algorithms and justify their relevance. We also compare performance gain from using a distributed system and scalability.

cs.DC↗

arXiv2020

DaNetQA: a yes/no Question Answering Dataset for the Russian Language

DaNetQA, a new question-answering corpus, follows (Clark et. al, 2019) design: it comprises natural yes/no questions. Each question is paired with a paragraph from Wikipedia and an answer, derived from the paragraph. The task is to take both the question and a paragraph as input and come up with a yes/no answer, i.e. to produce a binary output. In this paper, we present a reproducible approach to DaNetQA creation and investigate transfer learning methods for task and language transferring. For task transferring we leverage three similar sentence modelling tasks: 1) a corpus of paraphrases, Paraphraser, 2) an NLI task, for which we use the Russian part of XNLI, 3) another question answering task, SberQUAD. For language transferring we use English to Russian translation together with multilingual language fine-tuning.

cs.CL↗

arXiv2020

Mixed Integer Programming for Searching Maximum Quasi-Bicliques

This paper is related to the problem of finding the maximal quasi-bicliques in a bipartite graph (bigraph). A quasi-biclique in the bigraph is its "almost" complete subgraph. The relaxation of completeness can be understood variously; here, we assume that the subgraph is a $γ$-quasi-biclique if it lacks a certain number of edges to form a biclique such that its density is at least $γ\in (0,1]$. For a bigraph and fixed $γ$, the problem of searching for the maximal quasi-biclique consists of finding a subset of vertices of the bigraph such that the induced subgraph is a quasi-biclique and its size is maximal for a given graph. Several models based on Mixed Integer Programming (MIP) to search for a quasi-biclique are proposed and tested for working efficiency. An alternative model inspired by biclustering is formulated and tested; this model simultaneously maximizes both the size of the quasi-biclique and its density, using the least-square criterion similar to the one exploited by triclustering \textsc{TriBox}.

cs.DS↗

arXiv2019

Compression of Recurrent Neural Networks for Efficient Language Modeling

Recurrent neural networks have proved to be an effective method for statistical language modeling. However, in practice their memory and run-time complexity are usually too large to be implemented in real-time offline mobile applications. In this paper we consider several compression techniques for recurrent neural networks including Long-Short Term Memory models. We make particular attention to the high-dimensional output problem caused by the very large vocabulary size. We focus on effective compression methods in the context of their exploitation on devices: pruning, quantization, and matrix decomposition approaches (low-rank factorization and tensor train decomposition, in particular). For each model we investigate the trade-off between its size, suitability for fast inference and perplexity. We propose a general pipeline for applying the most suitable methods to compress recurrent neural networks for language modeling. It has been shown in the experimental study with the Penn Treebank (PTB) dataset that the most efficient results in terms of speed and compression-perplexity balance are obtained by matrix decomposition techniques.

cs.CL↗

arXiv2017

Neural Networks Compression for Language Modeling

In this paper, we consider several compression techniques for the language modeling problem based on recurrent neural networks (RNNs). It is known that conventional RNNs, e.g, LSTM-based networks in language modeling, are characterized with either high space complexity or substantial inference time. This problem is especially crucial for mobile applications, in which the constant interaction with the remote server is inappropriate. By using the Penn Treebank (PTB) dataset we compare pruning, quantization, low-rank factorization, tensor train decomposition for LSTM networks in terms of model size and suitability for fast inference.

stat.ML↗

arXiv2017

Introduction to Formal Concept Analysis and Its Applications in Information Retrieval and Related Fields

This paper is a tutorial on Formal Concept Analysis (FCA) and its applications. FCA is an applied branch of Lattice Theory, a mathematical discipline which enables formalisation of concepts as basic units of human thinking and analysing data in the object-attribute form. Originated in early 80s, during the last three decades, it became a popular human-centred tool for knowledge representation and data analysis with numerous applications. Since the tutorial was specially prepared for RuSSIR 2014, the covered FCA topics include Information Retrieval with a focus on visualisation aspects, Machine Learning, Data Mining and Knowledge Discovery, Text Mining and several others.

cs.IR↗

arXiv2017

Multimodal Clustering for Community Detection

Multimodal clustering is an unsupervised technique for mining interesting patterns in $n$-adic binary relations or $n$-mode networks. Among different types of such generalized patterns one can find biclusters and formal concepts (maximal bicliques) for 2-mode case, triclusters and triconcepts for 3-mode case, closed $n$-sets for $n$-mode case, etc. Object-attribute biclustering (OA-biclustering) for mining large binary datatables (formal contexts or 2-mode networks) arose by the end of the last decade due to intractability of computation problems related to formal concepts; this type of patterns was proposed as a meaningful and scalable approximation of formal concepts. In this paper, our aim is to present recent advance in OA-biclustering and its extensions to mining multi-mode communities in SNA setting. We also discuss connection between clustering coefficients known in SNA community for 1-mode and 2-mode networks and OA-bicluster density, the main quality measure of an OA-bicluster. Our experiments with 2-, 3-, and 4-mode large real-world networks show that this type of patterns is suitable for community detection in multi-mode cases within reasonable time even though the number of corresponding $n$-cliques is still unknown due to computation difficulties. An interpretation of OA-biclusters for 1-mode networks is provided as well.

cs.SI↗

arXiv2017

On closure operators related to maximal tricliques in tripartite hypergraphs

Triadic Formal Concept Analysis (3FCA) was introduced by Lehman and Wille almost two decades ago. And many researchers work in Data Mining and Formal Concept Analysis using the notions of closed sets, Galois and closure operators, closure systems, but up-to-date even though that different researchers actively work on mining triadic and n-ary relations, a proper closure operator for enumeration of triconcepts, i.e. maximal triadic cliques of tripartite hypergaphs, was not introduced. In this paper we show that the previously introduced operators for obtaining triconcepts and maximal connected and complete sets (MCCSs) are not always consistent and provide the reader with a definition of valid closure operator and associated set system. Moreover, we study the difficulties of related problems from order-theoretic and combinatorial point view as well as provide the reader with justifications of the complexity classes of these problems.

cs.DM↗

arXiv2017

Towards a Unified Taxonomy of Biclustering Methods

Being an unsupervised machine learning and data mining technique, biclustering and its multimodal extensions are becoming popular tools for analysing object-attribute data in different domains. Apart from conventional clustering techniques, biclustering is searching for homogeneous groups of objects while keeping their common description, e.g., in binary setting, their shared attributes. In bioinformatics, biclustering is used to find genes, which are active in a subset of situations, thus being candidates for biomarkers. However, the authors of those biclustering techniques that are popular in gene expression analysis, may overlook the existing methods. For instance, BiMax algorithm is aimed at finding biclusters, which are well-known for decades as formal concepts. Moreover, even if bioinformatics classify the biclustering methods according to reasonable domain-driven criteria, their classification taxonomies may be different from survey to survey and not full as well. So, in this paper we propose to use concept lattices as a tool for taxonomy building (in the biclustering domain) and attribute exploration as means for cross-domain taxonomy completion.

cs.AI↗

arXiv2017

Bayesian Learning of Consumer Preferences for Residential Demand Response

In coming years residential consumers will face real-time electricity tariffs with energy prices varying day to day, and effective energy saving will require automation - a recommender system, which learns consumer's preferences from her actions. A consumer chooses a scenario of home appliance use to balance her comfort level and the energy bill. We propose a Bayesian learning algorithm to estimate the comfort level function from the history of appliance use. In numeric experiments with datasets generated from a simulation model of a consumer interacting with small home appliances the algorithm outperforms popular regression analysis tools. Our approach can be extended to control an air heating and conditioning system, which is responsible for up to half of a household's energy bill.

cs.LG↗

arXiv2016

Concept Stability for Constructing Taxonomies of Web-site Users

Owners of a web-site are often interested in analysis of groups of users of their site. Information on these groups can help optimizing the structure and contents of the site. In this paper we use an approach based on formal concepts for constructing taxonomies of user groups. For decreasing the huge amount of concepts that arise in applications, we employ stability index of a concept, which describes how a group given by a concept extent differs from other such groups. We analyze resulting taxonomies of user groups for three target websites.

cs.CY↗