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Species Distribution Models (SDMs) often suffer from spatial autocorrelation (SAC), leading to biased performance estimates. We tested cross-validation (CV) strategies - random splits, spatial blocking with varied distances, environmental (ENV) clustering, and a novel spatio-temporal method - under two proposed training schemes: LAST FOLD, widely used in spatial CV at the cost of data loss, and RETRAIN, which maximizes data usage but risks reintroducing SAC. LAST FOLD consistently yielded lower errors and stronger correlations. Spatial blocking at an optimal distance (SP 422) and ENV performed best, achieving Spearman and Pearson correlations of 0.485 and 0.548, respectively, although ENV may be unsuitable for long-term forecasts involving major environmental shifts. A spatio-temporal approach yielded modest benefits in our moderately variable dataset, but may excel with stronger temporal changes. These findings highlight the need to align CV approaches with the spatial and temporal structure of SDM data, ensuring rigorous validation and reliable predictive outcomes.

Change point detection (CPD) methods aim to identify abrupt shifts in the distribution of input data streams. Accurate estimators for this task are crucial across various real-world scenarios. Yet, traditional unsupervised CPD techniques face significant limitations, often relying on strong assumptions or suffering from low expressive power due to inherent model simplicity. In contrast, representation learning methods overcome these drawbacks by offering flexibility and the ability to capture the full complexity of the data without imposing restrictive assumptions. However, these approaches are still emerging in the CPD field and lack robust theoretical foundations to ensure their reliability. Our work addresses this gap by integrating the expressive power of representation learning with the groundedness of traditional CPD techniques. We adopt spectral normalization (SN) for deep representation learning in CPD tasks and prove that the embeddings after SN are highly informative for CPD. Our method significantly outperforms current state-of-the-art methods during the comprehensive evaluation via three standard CPD datasets.

Collusion is a complex phenomenon in which companies secretly collaborate to engage in fraudulent practices. This paper presents an innovative methodology for detecting and predicting collusion patterns in different national markets using neural networks (NNs) and graph neural networks (GNNs). GNNs are particularly well suited to this task because they can exploit the inherent network structures present in collusion and many other economic problems. Our approach consists of two phases: In Phase I, we develop and train models on individual market datasets from Japan, the United States, two regions in Switzerland, Italy, and Brazil, focusing on predicting collusion in single markets. In Phase II, we extend the models' applicability through zero-shot learning, employing a transfer learning approach that can detect collusion in markets in which training data is unavailable. This phase also incorporates out-of-distribution (OOD) generalization to evaluate the models' performance on unseen datasets from other countries and regions. In our empirical study, we show that GNNs outperform NNs in detecting complex collusive patterns. This research contributes to the ongoing discourse on preventing collusion and optimizing detection methodologies, providing valuable guidance on the use of NNs and GNNs in economic applications to enhance market fairness and economic welfare.

We give new formulas for reconstructions from band-limited Hankel transform of integer or half-integer order. Our formulas rely on the PSWF-Radon approach to super-resolution in multidimensional Fourier analysis. This approach consists of combining the theory of classical one-dimensional prolate spheroidal wave functions with the Radon transform theory. We also use the relation between Fourier and Hankel transforms and Cormack-type inversion of the Radon transform. Finally, we investigate numerically the capabilities of our approach to super-resolution for band-limited Hankel inversion in relation to varying levels of noise.

Self-energy and vacuum polarization effects in quantum electrodynamics (QED) are calculated for the supercritical Coulomb field, where Dirac energy levels become embedded in the negative-energy continuum. In this regime, the quantum vacuum becomes unstable, resulting in spontaneous electron-positron pair creation. By calculating the imaginary part of the QED correction, we gain access to an unexplored channel of vacuum instability: radiative spontaneous pair creation. Our results show that this radiative channel is greatly enhanced in the vicinity of the threshold of the supercritical regime, providing evidence for nonperturbative effects with respect to the fine-structure constant $\alpha$. We therefore conjecture that the total probability of spontaneous pair creation could differ significantly from the predictions of Dirac theory, especially near the supercritical threshold., Comment: 6 pages, 3 figures

Accurately estimating image quality and model robustness improvement are critical challenges in unconstrained face recognition, which can be addressed through uncertainty estimation via probabilistic face embeddings. Previous research mainly focused on uncertainty estimation in face verification, leaving the open-set face recognition task underexplored. In open-set face recognition, one seeks to classify an image, which could also be unknown. Here, the low variance of probabilistic embedding does not imply a low error probability: an image embedding could be close to several classes in a gallery, thus yielding high uncertainty. We propose a method aware of two sources of ambiguity in the open-set recognition system: (1) the gallery uncertainty caused by overlapping classes and (2) the uncertainty of the face embeddings. To detect both types, we use a Bayesian probabilistic model of embedding distribution, which provides a principled uncertainty estimate. Challenging open-set face recognition datasets, such as IJB-C, serve as a testbed for our method. We also propose a new open-set recognition protocol for whale and dolphin identification. The proposed approach better identifies recognition errors than uncertainty estimation methods based solely on image quality.

High-quality representation of transactional sequences is vital for modern banking applications, including risk management, churn prediction, and personalized customer offers. Different tasks require distinct representation properties: local tasks benefit from capturing the client's current state, while global tasks rely on general behavioral patterns. Previous research has demonstrated that various self-supervised approaches yield representations that better capture either global or local qualities. This study investigates the integration of two self-supervised learning techniques - instance-wise contrastive learning and a generative approach based on restoring masked events in latent space. The combined approach creates representations that balance local and global transactional data characteristics. Experiments conducted on several public datasets, focusing on sequence classification and next-event type prediction, show that the integrated method achieves superior performance compared to individual approaches and demonstrates synergistic effects. These findings suggest that the proposed approach offers a robust framework for advancing event sequences representation learning in the financial sector.

Observation of the underlying actors that generate event sequences reveals that they often evolve continuously. Most modern methods, however, tend to model such processes through at most piecewise-continuous trajectories. To address this, we adopt a way of viewing events not as standalone phenomena but instead as observations of a Gaussian Process, which in turn governs the actor's dynamics. We propose integrating these obtained dynamics, resulting in a continuous-trajectory modification of the widely successful Neural ODE model. Through Gaussian Process theory, we were able to evaluate the uncertainty in an actor's representation, which arises from not observing them between events. This estimate led us to develop a novel, theoretically backed negative feedback mechanism. Empirical studies indicate that our model with Gaussian process interpolation and negative feedback achieves state-of-the-art performance, with improvements up to 20% AUROC against similar architectures.

Knowledge Graph Embedding (KGE) is a popular approach, which aims to represent entities and relations of a knowledge graph in latent spaces. Their representations are known as embeddings. To measure the plausibility of triplets, score functions are defined over embedding spaces. Despite wide dissemination of KGE in various tasks, KGE methods have limitations in reasoning abilities. In this paper we propose a mathematical framework to compare reasoning abilities of KGE methods. We show that STransE has a higher capability than TransComplEx, and then present new STransCoRe method, which improves the STransE by combining it with the TransCoRe insights, which can reduce the STransE space complexity., Comment: This paper may involve data that is not readily available to the public

This article presents constraints on dark-matter-electron interactions obtained from the first underground data-taking campaign with multiple SuperCDMS HVeV detectors operated in the same housing. An exposure of 7.63 g-days is used to set upper limits on the dark-matter-electron scattering cross section for dark matter masses between 0.5 and 1000 MeV/$c^2$, as well as upper limits on dark photon kinetic mixing and axion-like particle axioelectric coupling for masses between 1.2 and 23.3 eV/$c^2$. Compared to an earlier HVeV search, sensitivity was improved as a result of an increased overburden of 225 meters of water equivalent, an anticoincidence event selection, and better pile-up rejection. In the case of dark-matter-electron scattering via a heavy mediator, an improvement by up to a factor of 25 in cross-section sensitivity was achieved., Comment: 7 pages + title and references, 4 figures, and 1 table

This paper presents a solution for the Multilingual Text Detoxification task in the PAN-2024 competition of the SmurfCat team. Using data augmentation through machine translation and a special filtering procedure, we collected an additional multilingual parallel dataset for text detoxification. Using the obtained data, we fine-tuned several multilingual sequence-to-sequence models, such as mT0 and Aya, on a text detoxification task. We applied the ORPO alignment technique to the final model. Our final model has only 3.7 billion parameters and achieves state-of-the-art results for the Ukrainian language and near state-of-the-art results for other languages. In the competition, our team achieved first place in the automated evaluation with a score of 0.52 and second place in the final human evaluation with a score of 0.74.

The problem of using structured methods to represent knowledge is well-known in conceptual modeling and has been studied for many years. It has been proven that adopting modeling patterns represents an effective structural method. Patterns are, indeed, generalizable recurrent structures that can be exploited as solutions to design problems. They aid in understanding and improving the process of creating models. The undeniable value of using patterns in conceptual modeling was demonstrated in several experimental studies. However, discovering patterns in conceptual models is widely recognized as a highly complex task and a systematic solution to pattern identification is currently lacking. In this paper, we propose a general approach to the problem of discovering frequent structures, as they occur in conceptual modeling languages. As proof of concept, we implement our approach by focusing on two widely-used conceptual modeling languages. This implementation includes an exploratory tool that integrates a frequent subgraph mining algorithm with graph manipulation techniques. The tool processes multiple conceptual models and identifies recurrent structures based on various criteria. We validate the tool using two state-of-the-art curated datasets: one consisting of models encoded in OntoUML and the other in ArchiMate. The primary objective of our approach is to provide a support tool for language engineers. This tool can be used to identify both effective and ineffective modeling practices, enabling the refinement and evolution of conceptual modeling languages. Furthermore, it facilitates the reuse of accumulated expertise, ultimately supporting the creation of higher-quality models in a given language.

Hydrodynamic discontinuities in an external potential and incompressible flow are investigated. Using the reaction front as an example in a 2D stream, an overdetermined system of equations is obtained that describes its motion in terms of the surface itself. Assuming that the harmonic flux approaching discontinuity is additional smooth, these equations can be used to determine the motion of this discontinuity without taking into account the influence of the flow behind the front, as well as the entire external flow. It is well known that for vanishingly low viscosity, the integral relation on the boundary (Dirichlet, Neumann problems) connects the tangential and normal components of the velocity. Knowing one of them along the boundary of the discontinuity, one can determine the entire external flow. However, assuming the external flow is smooth, this will also be the case for all derivatives of velocity with respect to coordinates and time. Then a paradox arises, knowing the position of the discontinuity and the velocity data at a point on its surface, it is possible to determine the motion of this discontinuity without taking into account the influence of the flow behind the front, as well as the entire external flow. There is no physical explanation for this mechanism. It is possible that a boundary layer is formed in front of the front, where viscosity plays a significant role and Euler equations are violated. It is argued that the classical idea of the motion of hydrodynamic discontinuities in the smooth, potential and incompressible flow in the external region should be supplemented in this case., Comment: 19 pages, 2 figures

In today's world, banks use artificial intelligence to optimize diverse business processes, aiming to improve customer experience. Most of the customer-related tasks can be categorized into two groups: 1) local ones, which focus on a client's current state, such as transaction forecasting, and 2) global ones, which consider the general customer behaviour, e.g., predicting successful loan repayment. Unfortunately, maintaining separate models for each task is costly. Therefore, to better facilitate information management, we compared eight state-of-the-art unsupervised methods on 11 tasks in search for a one-size-fits-all solution. Contrastive self-supervised learning methods were demonstrated to excel at global problems, while generative techniques were superior at local tasks. We also introduced a novel approach, which enriches the client's representation by incorporating external information gathered from other clients. Our method outperforms classical models, boosting accuracy by up to 20\%.

Various dark matter search experiments employ phonon-based crystal detectors operated at cryogenic temperatures. Some of these detectors, including certain silicon detectors used by the SuperCDMS Collaboration, are able to achieve single-charge sensitivity when a voltage bias is applied across the detector. The total amount of phonon energy measured by such a detector is proportional to the number of electron-hole pairs created by the interaction. However, crystal impurities and surface effects can cause propagating charges to either become trapped inside the crystal or create additional unpaired charges, producing non-quantized measured energy as a result. A new analytical model for describing these detector response effects in phonon-based crystal detectors is presented. This model improves upon previous versions by demonstrating how the detector response, and thus the measured energy spectrum, is expected to differ depending on the source of events. We use this model to extract detector response parameters for SuperCDMS HVeV detectors, and illustrate how this robust modelling can help statistically discriminate between sources of events in order to improve the sensitivity of dark matter search experiments., Comment: 19 pages, 7 figures

In machine learning, ensembles are important tools for improving the model performance. In natural language processing specifically, ensembles boost the performance of a method due to multiple large models available in open source. However, existing approaches mostly rely on simple averaging of predictions by ensembles with equal weights for each model, ignoring differences in the quality and conformity of models. We propose to estimate weights for ensembles of NLP models using not only knowledge of their individual performance but also their similarity to each other. By adopting distance measures based on Topological Data Analysis (TDA), we improve our ensemble. The quality improves for both text classification accuracy and relevant uncertainty estimation.

In the rapidly evolving domain of Recommender Systems (RecSys), new algorithms frequently claim state-of-the-art performance based on evaluations over a limited set of arbitrarily selected datasets. However, this approach may fail to holistically reflect their effectiveness due to the significant impact of dataset characteristics on algorithm performance. Addressing this deficiency, this paper introduces a novel benchmarking methodology to facilitate a fair and robust comparison of RecSys algorithms, thereby advancing evaluation practices. By utilizing a diverse set of $30$ open datasets, including two introduced in this work, and evaluating $11$ collaborative filtering algorithms across $9$ metrics, we critically examine the influence of dataset characteristics on algorithm performance. We further investigate the feasibility of aggregating outcomes from multiple datasets into a unified ranking. Through rigorous experimental analysis, we validate the reliability of our methodology under the variability of datasets, offering a benchmarking strategy that balances quality and computational demands. This methodology enables a fair yet effective means of evaluating RecSys algorithms, providing valuable guidance for future research endeavors., Comment: 8 pages with 11 figures

With the rise of electronic data, particularly Earth observation data, data-based geospatial modelling using machine learning (ML) has gained popularity in environmental research. Accurate geospatial predictions are vital for domain research based on ecosystem monitoring and quality assessment and for policy-making and action planning, considering effective management of natural resources. The accuracy and computation speed of ML has generally proved efficient. However, many questions have yet to be addressed to obtain precise and reproducible results suitable for further use in both research and practice. A better understanding of the ML concepts applicable to geospatial problems enhances the development of data science tools providing transparent information crucial for making decisions on global challenges such as biosphere degradation and climate change. This survey reviews common nuances in geospatial modelling, such as imbalanced data, spatial autocorrelation, prediction errors, model generalisation, domain specificity, and uncertainty estimation. We provide an overview of techniques and popular programming tools to overcome or account for the challenges. We also discuss prospects for geospatial Artificial Intelligence in environmental applications.

Existing neural networks are memory-consuming and computationally intensive, making deploying them challenging in resource-constrained environments. However, there are various methods to improve their efficiency. Two such methods are quantization, a well-known approach for network compression, and re-parametrization, an emerging technique designed to improve model performance. Although both techniques have been studied individually, there has been limited research on their simultaneous application. To address this gap, we propose a novel approach called RepQ, which applies quantization to re-parametrized networks. Our method is based on the insight that the test stage weights of an arbitrary re-parametrized layer can be presented as a differentiable function of trainable parameters. We enable quantization-aware training by applying quantization on top of this function. RepQ generalizes well to various re-parametrized models and outperforms the baseline method LSQ quantization scheme in all experiments., Comment: BMVC 2023 (Oral)

In a recent paper "Solvability of equations in elementary functions" [arXiv:1911.10409] the insolvability in elementary functions of equation $\tan(x) - x = a$ was proved. This work applies the same topological method to prove the insolvability of equation $x^x = a$., Comment: 6 pages

Global warming accelerates permafrost degradation, impacting the reliability of critical infrastructure used by more than five million people daily. Furthermore, permafrost thaw produces substantial methane emissions, further accelerating global warming and climate change and putting more than eight billion people at additional risk. To mitigate the upcoming risk, policymakers and stakeholders must be given an accurate prediction of the thaw development. Unfortunately, comprehensive physics-based permafrost models require location-specific fine-tuning that is challenging in practice. Models of intermediate complexity require few input parameters but have relatively low accuracy. The performance of pure data-driven models is low as well as the observational data is sparse and limited. In this work, we designed a physics-informed machine-learning approach for permafrost thaw prediction. The method uses a heat equation to regularize data-driven approach trained over permafrost monitoring data and climate projections. The latter leads to higher precision and better numerical stability allowing for reliable decision-making or construction and maintenance in the areas endangered by permafrost thaw with a time horizon of decades., Comment: 30 pages, 24 figures

The problem of high-quality drought forecasting up to a year in advance is critical for agriculture planning and insurance. Yet, it is still unsolved with reasonable accuracy due to data complexity and aridity stochasticity. We tackle drought data by introducing an end-to-end approach that adopts a spatio-temporal neural network model with accessible open monthly climate data as the input. Our systematic research employs diverse proposed models and five distinct environmental regions as a testbed to evaluate the efficacy of the Palmer Drought Severity Index (PDSI) prediction. Key aggregated findings are the exceptional performance of a Transformer model, EarthFormer, in making accurate short-term (up to six months) forecasts. At the same time, the Convolutional LSTM excels in longer-term forecasting.

Adversarial attacks expose vulnerabilities of deep learning models by introducing minor perturbations to the input, which lead to substantial alterations in the output. Our research focuses on the impact of such adversarial attacks on sequence-to-sequence (seq2seq) models, specifically machine translation models. We introduce algorithms that incorporate basic text perturbation heuristics and more advanced strategies, such as the gradient-based attack, which utilizes a differentiable approximation of the inherently non-differentiable translation metric. Through our investigation, we provide evidence that machine translation models display robustness displayed robustness against best performed known adversarial attacks, as the degree of perturbation in the output is directly proportional to the perturbation in the input. However, among underdogs, our attacks outperform alternatives, providing the best relative performance. Another strong candidate is an attack based on mixing of individual characters.

In machine learning models, the estimation of errors is often complex due to distribution bias, particularly in spatial data such as those found in environmental studies. We introduce an approach based on the ideas of importance sampling to obtain an unbiased estimate of the target error. By taking into account difference between desirable error and available data, our method reweights errors at each sample point and neutralizes the shift. Importance sampling technique and kernel density estimation were used for reweighteing. We validate the effectiveness of our approach using artificial data that resemble real-world spatial datasets. Our findings demonstrate advantages of the proposed approach for the estimation of the target error, offering a solution to a distribution shift problem. Overall error of predictions dropped from 7% to just 2% and it gets smaller for larger samples.

Banks routinely use neural networks to make decisions. While these models offer higher accuracy, they are susceptible to adversarial attacks, a risk often overlooked in the context of event sequences, particularly sequences of financial transactions, as most works consider computer vision and NLP modalities. We propose a thorough approach to studying these risks: a novel type of competition that allows a realistic and detailed investigation of problems in financial transaction data. The participants directly oppose each other, proposing attacks and defenses -- so they are examined in close-to-real-life conditions. The paper outlines our unique competition structure with direct opposition of participants, presents results for several different top submissions, and analyzes the competition results. We also introduce a new open dataset featuring financial transactions with credit default labels, enhancing the scope for practical research and development.

Transformer-based language models have set new benchmarks across a wide range of NLP tasks, yet reliably estimating the uncertainty of their predictions remains a significant challenge. Existing uncertainty estimation (UE) techniques often fall short in classification tasks, either offering minimal improvements over basic heuristics or relying on costly ensemble models. Moreover, attempts to leverage common embeddings for UE in linear probing scenarios have yielded only modest gains, indicating that alternative model components should be explored. We tackle these limitations by harnessing the geometry of attention maps across multiple heads and layers to assess model confidence. Our approach extracts topological features from attention matrices, providing a low-dimensional, interpretable representation of the model's internal dynamics. Additionally, we introduce topological features to compare attention patterns across heads and layers. Our method significantly outperforms existing UE techniques on benchmarks for acceptability judgments and artificial text detection, offering a more efficient and interpretable solution for uncertainty estimation in large-scale language models.

The financial industry relies on deep learning models for making important decisions. This adoption brings new danger, as deep black-box models are known to be vulnerable to adversarial attacks. In computer vision, one can shape the output during inference by performing an adversarial attack called poisoning via introducing a backdoor into the model during training. For sequences of financial transactions of a customer, insertion of a backdoor is harder to perform, as models operate over a more complex discrete space of sequences, and systematic checks for insecurities occur. We provide a method to introduce concealed backdoors, creating vulnerabilities without altering their functionality for uncontaminated data. To achieve this, we replace a clean model with a poisoned one that is aware of the availability of a backdoor and utilize this knowledge. Our most difficult for uncovering attacks include either additional supervised detection step of poisoned data activated during the test or well-hidden model weight modifications. The experimental study provides insights into how these effects vary across different datasets, architectures, and model components. Alternative methods and baselines, such as distillation-type regularization, are also explored but found to be less efficient. Conducted on three open transaction datasets and architectures, including LSTM, CNN, and Transformer, our findings not only illuminate the vulnerabilities in contemporary models but also can drive the construction of more robust systems.

Portfolio management is an essential part of investment decision-making. However, traditional methods often fail to deliver reasonable performance. This problem stems from the inability of these methods to account for the unique characteristics of multivariate time series data from stock markets. We present a two-stage method for constructing an investment portfolio of common stocks. The method involves the generation of time series representations followed by their subsequent clustering. Our approach utilizes features based on Topological Data Analysis (TDA) for the generation of representations, allowing us to elucidate the topological structure within the data. Experimental results show that our proposed system outperforms other methods. This superior performance is consistent over different time frames, suggesting the viability of TDA as a powerful tool for portfolio selection.

We measured the nuclear--recoil ionization yield in silicon with a cryogenic phonon-sensitive gram-scale detector. Neutrons from a mono-energetic beam scatter off of the silicon nuclei at angles corresponding to energy depositions from 4\,keV down to 100\,eV, the lowest energy probed so far. The results show no sign of an ionization production threshold above 100\,eV. These results call for further investigation of the ionization yield theory and a comprehensive determination of the detector response function at energies below the keV scale.

Most user-related data can be represented as a sequence of events associated with a timestamp and a collection of categorical labels. For example, the purchased basket of goods and the time of buying fully characterize the event of the store visit. Anticipation of the label set for the future event called the problem of temporal sets prediction, holds significant value, especially in such high-stakes industries as finance and e-commerce. A fundamental challenge of this task is the joint consideration of the temporal nature of events and label relations within sets. The existing models fail to capture complex time and label dependencies due to ineffective representation of historical information initially. We aim to address this shortcoming by presenting the framework with a specific way to aggregate the observed information into time- and set structure-aware views prior to transferring it into main architecture blocks. Our strong emphasis on input arrangement facilitates the subsequent efficient learning of label interactions. The proposed model is called Label-Attention NETwork, or LANET. We conducted experiments on four different datasets and made a comparison with four established models, including SOTA, in this area. The experimental results suggest that LANET provides significantly better quality than any other model, achieving an improvement up to $65 \%$ in terms of weighted F1 metric compared to the closest competitor. Moreover, we contemplate causal relationships between labels in our work, as well as a thorough study of LANET components' influence on performance. We provide an implementation of LANET to encourage its wider usage.

We present a new analysis of previously published of SuperCDMS data using a profile likelihood framework to search for sub-GeV dark matter (DM) particles through two inelastic scattering channels: bremsstrahlung radiation and the Migdal effect. By considering these possible inelastic scattering channels, experimental sensitivity can be extended to DM masses that are undetectable through the DM-nucleon elastic scattering channel, given the energy threshold of current experiments. We exclude DM masses down to $220~\textrm{MeV}/c^2$ at $2.7 \times 10^{-30}~\textrm{cm}^2$ via the bremsstrahlung channel. The Migdal channel search provides overall considerably more stringent limits and excludes DM masses down to $30~\textrm{MeV}/c^2$ at $5.0 \times 10^{-30}~\textrm{cm}^2$., Comment: Submitted to PRD

Event sequences often emerge in data mining. Modeling these sequences presents two main challenges: methodological and computational. Methodologically, event sequences are non-uniform and sparse, making traditional models unsuitable. Computationally, the vast amount of data and the significant length of each sequence necessitate complex and efficient models. Existing solutions, such as recurrent and transformer neural networks, rely on parametric intensity functions defined at each moment. These functions are either limited in their ability to represent complex event sequences or notably inefficient. We propose COTIC, a method based on an efficient convolution neural network designed to handle the non-uniform occurrence of events over time. Our paper introduces a continuous convolution layer, allowing a model to capture complex dependencies, including, e.g., the self-excitement effect, with little computational expense. COTIC outperforms existing models in predicting the next event time and type, achieving an average rank of 1.5 compared to 3.714 for the nearest competitor. Furthermore, COTIC`s ability to produce effective embeddings demonstrates its potential for various downstream tasks. Our code is open and available at: https://github.com/VladislavZh/COTIC., Comment: 29 pages, 4 figures