Search results for “natural logarithm”

Reference table of indefinite integrals of expressions containing the natural logarithm.

Modern natural language processing models such as transformers operate multimodal data. In the present paper, multimodal data is explored using multimodal topic modeling on transactional data of bank corporate clients. A definition of the importance of modality for the model is proposed on the basis of which improvements are considered for two modeling scenarios: preserving the maximum amount of information by balancing modalities and automatic selection of modality weights to optimize auxiliary criteria based on topic representations of documents. A model is proposed for adding numerical data to topic models in the form of modalities: each topic is assigned a normal distribution with learning parameters. Significant improvements are demonstrated in comparison with standard topic models on the problem of modeling bank corporate clients. Based on the topic representations of the bank’s customers, a 90-day delay on the loan is predicted.

Machine translation is a natural language text processing task that aims to automatically translate input text from one language into another language. The currently known machine translation models show a fairly high quality of translation between large languages, but for smaller language areas, represented by less data, the problem is still not solved. Different methods are used to deal with various errors in automatic translation systems. This paper discusses approaches that use translation models of reverse language directions and improve consistency between translations of the same text using direct and reverse translation models. The paper presents a general theoretical justification for such methods in terms of solving the likelihood maximization problem and also proposes a method for stable training of modern models using cyclic translations.

A wide class of natural language processing tasks is solved using markup.At the moment, the vast majority of models and datasets rely on a simple markup structure containing only fragments and labels.Moreover, simple classification metrics such as F1, Precision, Recall are used to evaluate the model's accuracy.The problem with such metrics is that they do not take into account all aspects of the markup structure and that they are applicable only under the assumption of the existence of an ideal markup.This paper proposes a more general and universal markup structure that allows solving complex problems and builds a methodology for multi-criteria evaluation of text markup models based on inconsistent expert markup.After that, the application of the constructed method is considered to assess the quality of the model obtained within the winning algorithm of the "READ//ABLE" competition, which focused on building an effective essay markup system.The results demonstrate that the new markup structure and evaluation approach provides a more comprehensive and accurate assessment of model performance, addressing the limitations of traditional metrics by accounting for complex markup scenarios and expert inconsistencies.

Topic modelling is an area of text mining that has been actively developed in the last 15 years. A probabilistic topic model extracts a set of hidden topics from a collection of text documents. It defines each topic by a probability distribution over words and describes each document with a probability distribution over topics. In applications, there are often many requirements, such as, for example, problem-specific knowledge and additional data, to be taken into account. Therefore, it is natural for topic modelling to be considered a multiobjective optimization problem. However, historically, Bayesian learning became the most popular approach for topic modelling. In the Bayesian paradigm, all requirements are formalized in terms of a probabilistic generative process. This approach is not always convenient due to some limitations and technical difficulties. In this work, we develop a non-Bayesian multiobjective approach called the Additive Regularization of Topic Models (ARTM). It is based on regularized Maximum Likelihood Estimation (MLE), and we show that many of the well-known Bayesian topic models can be re-formulated in a much simpler way using the regularization point of view. We review some of the most important types of topic models: multimodal, multilingual, temporal, hierarchical, graph-based, and short-text. The ARTM framework enables easy combination of different types of models to create new models with the desired properties for applications. This modular “lego-style” technology for topic modelling is implemented in the open-source library BigARTM.

In the exploratory search paradigm of information retrieval, the user has a complicated search demand that can not be formulated in a short query. The user collects thematically relevant information iteratively in a “query-browse-refine” process being motivated by learning, understanding, and knowledge acquisition purposes. We consider an elementary step of this scenario in which the search intent can be expressed by a long text query. For this case, we develop an exploratory search engine based on probabilistic topic modeling. Topic model gives a low-dimensional sparse interpretable vector representation (topical embedding) of a text. The search engine uses these embeddings for ranking documents by their similarity to the query. We show that performing only one query, the topic-based search engine achieves better precision and recall that human assessors do spending up to one hour in a conventional browse-refine loop. We use additive regularization for topic modeling (ARTM) to make the model simultaneously sparse, decorrelated, n-gram, multimodal and hierarchical. We show experimentally that each of these features of the model is important to achieve precision and recall higher than 90

Topic modelling is fundamentally a soft clustering problem (of known objects -- documents, over unknown clusters -- topics). That is, the task is incorrectly posed. In particular, the topic models are unstable and incomplete. All this leads to the fact that the process of finding a good topic model (repeated hyperparameter selection, model training, and topic quality assessment) can be particularly long and labor-intensive. We aim to simplify the process, to make it more deterministic and provable. To this end, we present a method for iterative training of a topic model. The essence of the method is that a series of related topic models are trained so that each subsequent model is at least as good as the previous one, i.e., that it retains all the good topics found earlier. The connection between the models is achieved by additive regularization. The result of this iterative training is the last topic model in the series, which we call the iteratively updated additively regularized topic model (ITAR). Experiments conducted on several collections of natural language texts show that the proposed ITAR model performs better than other popular topic models (LDA, ARTM, BERTopic), its topics are diverse, and its perplexity (ability to "explain" the underlying data) is moderate.

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.

A complete local ring with a finitely generated maximal ideal is Noetherian. Drop completeness and it fails: an ultraproduct construction gives a non-Noetherian local ring whose maximal ideal is principal.

Why the definition of a filtered category insists on non-emptiness: the empty colimit fails to commute with the empty limit, and that is the only failure.

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.