Doklady Mathematics最新文献

Depth estimation is a crucial task across various domains, but the high cost of collecting labeled depth data has led to growing interest in self-supervised monocular depth estimation methods. In this paper, we introduce SwiftDepth++, a lightweight depth estimation model that delivers competitive results while maintaining a low computational budget. The core innovation of SwiftDepth++ lies in its novel depth decoder, which enhances efficiency by rapidly compressing features while preserving essential information. Additionally, we incorporate a teacher-student knowledge distillation framework that guides the student model in refining its predictions. We evaluate SwiftDepth++ on the KITTI and NYU datasets, where it achieves an absolute relative error (Abs_rel) of 10.2% on the KITTI dataset and 22% on the NYU dataset without fine-tuning, all with approximately 6 million parameters. These results demonstrate that SwiftDepth++ not only meets the demands of modern depth estimation tasks but also significantly reduces computational complexity, making it a practical choice for real-world applications.

There is an increasing interest in developing new models for graph classification problem that serves as a common benchmark for evaluation and comparison of GNNs and graph kernels. To ensure a fair comparison of the models several commonly used datasets exist and current assessments and conclusions rely on the validity of these datasets. However, as we show in this paper majority of these datasets contain isomorphic copies of the data points, which can lead to misleading conclusions. For example, the relative ranking of the graph models can change substantially if we remove isomorphic graphs in the test set.

To mitigate this we present several results. We show that explicitly incorporating the knowledge of isomorphism in the datasets can significantly boost the performance of any graph model. Finally, we re-evaluate commonly used graph models on refined graph datasets and provide recommendations for designing new datasets and metrics for graph classification problem.

Sharing scientific knowledge in the community is an important endeavor. However, most papers are written in English, which makes dissemination of knowledge in countries where English is not spoken by the majority of people harder. Nowadays, machine translation and language models may help to solve this problem, but it is still complicated to train and evaluate models in languages other than English with no or little data in the required language. To address this, we propose the first benchmark for evaluating models on scientific texts in Russian. It consists of papers from Russian electronic library of scientific publications. We also present a set of tasks which can be used to fine-tune various models on our data and provide a detailed comparison between state-of-the-art models on our benchmark.

Deep learning’s emerging role in the financial sector’s decision-making introduces risks of adversarial attacks. A specific threat is a poisoning attack that modifies the training sample to develop a backdoor that persists during model usage. However, data cleaning procedures and routine model checks are easy-to-implement actions that prevent the usage of poisoning attacks. The problem is even more challenging for event sequence models, for which it is hard to design an attack due to the discrete nature of the data. We start with a general investigation of the possibility of poisoning for event sequence models. Then, we propose a concealed poisoning attack that can bypass natural banks’ defences. The empirical investigation shows that the developed poisoned model trained on contaminated data passes the check procedure, being similar to a clean model, and simultaneously contains a simple to-implement backdoor.

A method is presented that allows to reduce a problem described by differential equations with initial and boundary conditions to a problem described only by differential equations which encapsulate initial and boundary conditions. It becomes possible to represent the loss function for physics-informed neural networks (PINNs) methodology in the form of a single term associated with modified differential equations. Thus eliminating the need to tune the scaling coefficients for the terms of loss function related to boundary and initial conditions. The weighted loss functions respecting causality were modified and new weighted loss functions, based on generalized functions, are derived. Numerical experiments have been carried out for a number of problems, demonstrating the accuracy of the proposed approaches. The neural network architecture was proposed for the Korteweg–De Vries equation, which is more relevant for this problem under consideration, and it demonstrates superior extrapolation of the solution in the space-time domain where training was not performed.

Methods for constructing multimodal 3D maps are becoming increasingly important for robot navigation systems. In such maps, each 3D point or object contains, in addition to color and semantic category information, compressed vector representations of a text description or sound. This allows solving problems of moving to objects based on natural language queries, even those that do not explicitly mention the object. This article proposes an original taxonomy of methods that allow constructing multimodal 3D maps using neural network methods. It is shown that sparse methods that use a scene representation in the form of an object graph and large language models to find an answer to spatial and semantic queries demonstrate the most promising results on existing open benchmarks. Based on the analysis, recommendations are formulated for choosing certain methods for solving practical problems of intelligent robotics.

The accuracy of solving partial differential equations using physics-informed neural networks (PINNs) significantly depends on their architecture and the choice of hyperparameters. However, manually searching for the optimal configuration can be difficult due to the high computational complexity. In this paper, we propose an approach for optimizing the PINN architecture using a differential evolution algorithm. We focus on optimizing over a small number of training epochs, which allows us to consider a wider range of configurations while reducing the computational cost. The number of epochs is chosen such that the accuracy of the model at the initial stage correlates with its accuracy after full training, which significantly speeds up the optimization process. To improve efficiency, we also apply a surrogate model based on a Gaussian process, which reduces the number of required PINN trainings. The paper presents the results of optimizing PINN architectures for solving various partial differential equations and offers recommendations for improving their performance.

The problem of searching for a mathematical expression is formulated. Classes of mathematical problems where this problem is in demand are presented. A general approach to solving this problem based on machine learning using symbolic regression methods is given. This approach allows finding not only the parameters of the desired mathematical expression, but also its structure. The general problem of machine learning by methods of symbolic regression is described and a unified approach to overcoming it based on the application of the principle of small variations of the basis solution is given.

The development of large language models (LLMs) is currently receiving a great amount of interest, but an update of text generation methods should entail a continuous update of methods for detecting machine-generated texts. Earlier, it has been highlighted that values of perplexity and log-probability are able to capture a measure of the difference between artificial and human-written texts. Using this observation, we define a new criterion based on these two values to judge whether a passage is generated from a given LLM. In this paper, we propose a novel efficient method that enables the detection of machine-generated fragments using an approximation of the LLM perplexity value based on pre-collected statistical language models. Approximation lends a hand in achieving high performance and quality metrics also on fragments from weights-closed LLMs. A large number of pre-collected statistical dictionaries results in an increased generalisation ability and the possibility to cover text sequences from the wild. Such approach is easy to update by only adding a new dictionary with latest model text outputs. The presented method has a high performance and achieves quality with an average of 94% recall in detecting generated fragments among texts from various open-source LLMs. In addition, the method is able to perform in milliseconds, which outperforms state-of-the-art models by a factor of thousands.

Clustering has always been in great demand by scientific and industrial communities. However, due to the lack of ground truth, interpreting its obtained results can be debatable. The current research provides an empirical benchmark on the efficiency of three popular and one recently proposed crisp clustering methods. To this end, we extensively analyzed these (four) methods by applying them to nine real-world and 420 synthetic datasets using four different values of p in Minkowski distance. Furthermore, we validated a previously proposed yet not well-known straightforward rule to interpret the recovered clusters. Our computations showed (i) Nesterov gradient descent clustering is the most effective clustering method using our real-world data, while K-Means had edge over it using our synthetic data; (ii) Minkowski distance with p = 1 is the most effective distance function, (iii) the investigated cluster interpretation rule is intuitive and valid.