arXiv subjects

Ivan Oseledets

Publications and source records attributed to Ivan Oseledets.

At least 127 records · Page 7Linked to original sources

arXiv2023

Unsupervised evaluation of GAN sample quality: Introducing the TTJac Score

Evaluation metrics are essential for assessing the performance of generative models in image synthesis. However, existing metrics often involve high memory and time consumption as they compute the distance between generated samples and real data points. In our study, the new evaluation metric called the "TTJac score" is proposed to measure the fidelity of individual synthesized images in a data-free manner. The study first establishes a theoretical approach to directly evaluate the generated sample density. Then, a method incorporating feature extractors and discrete function approximation through tensor train is introduced to effectively assess the quality of generated samples. Furthermore, the study demonstrates that this new metric can be used to improve the fidelity-variability trade-off when applying the truncation trick. The experimental results of applying the proposed metric to StyleGAN 2 and StyleGAN 2 ADA models on FFHQ, AFHQ-Wild, LSUN-Cars, and LSUN-Horse datasets are presented. The code used in this research will be made publicly available online for the research community to access and utilize.

cs.CV↗

arXiv2023

Quantization Aware Factorization for Deep Neural Network Compression

Tensor decomposition of convolutional and fully-connected layers is an effective way to reduce parameters and FLOP in neural networks. Due to memory and power consumption limitations of mobile or embedded devices, the quantization step is usually necessary when pre-trained models are deployed. A conventional post-training quantization approach applied to networks with decomposed weights yields a drop in accuracy. This motivated us to develop an algorithm that finds tensor approximation directly with quantized factors and thus benefit from both compression techniques while keeping the prediction quality of the model. Namely, we propose to use Alternating Direction Method of Multipliers (ADMM) for Canonical Polyadic (CP) decomposition with factors whose elements lie on a specified quantization grid. We compress neural network weights with a devised algorithm and evaluate it's prediction quality and performance. We compare our approach to state-of-the-art post-training quantization methods and demonstrate competitive results and high flexibility in achiving a desirable quality-performance tradeoff.

cs.LG↗

arXiv2023

Efficient GPT Model Pre-training using Tensor Train Matrix Representation

Large-scale transformer models have shown remarkable performance in language modelling tasks. However, such models feature billions of parameters, leading to difficulties in their deployment and prohibitive training costs from scratch. To reduce the number of the parameters in the GPT-2 architecture, we replace the matrices of fully-connected layers with the corresponding Tensor Train Matrix~(TTM) structure. Finally, we customize forward and backward operations through the TTM-based layer for simplicity and the stableness of further training. % The resulting GPT-2-based model stores up to 40% fewer parameters, showing the perplexity comparable to the original model. On the downstream tasks, including language understanding and text summarization, the model performs similarly to the original GPT-2 model. The proposed tensorized layers could be used to efficiently pre-training other Transformer models.

cs.AI↗

arXiv2023

General Covariance Data Augmentation for Neural PDE Solvers

The growing body of research shows how to replace classical partial differential equation (PDE) integrators with neural networks. The popular strategy is to generate the input-output pairs with a PDE solver, train the neural network in the regression setting, and use the trained model as a cheap surrogate for the solver. The bottleneck in this scheme is the number of expensive queries of a PDE solver needed to generate the dataset. To alleviate the problem, we propose a computationally cheap augmentation strategy based on general covariance and simple random coordinate transformations. Our approach relies on the fact that physical laws are independent of the coordinate choice, so the change in the coordinate system preserves the type of a parametric PDE and only changes PDE's data (e.g., initial conditions, diffusion coefficient). For tried neural networks and partial differential equations, proposed augmentation improves test error by 23% on average. The worst observed result is a 17% increase in test error for multilayer perceptron, and the best case is a 80% decrease for dilated residual network.

math.NA↗

arXiv2023

Translate your gibberish: black-box adversarial attack on machine translation systems

Neural networks are deployed widely in natural language processing tasks on the industrial scale, and perhaps the most often they are used as compounds of automatic machine translation systems. In this work, we present a simple approach to fool state-of-the-art machine translation tools in the task of translation from Russian to English and vice versa. Using a novel black-box gradient-free tensor-based optimizer, we show that many online translation tools, such as Google, DeepL, and Yandex, may both produce wrong or offensive translations for nonsensical adversarial input queries and refuse to translate seemingly benign input phrases. This vulnerability may interfere with understanding a new language and simply worsen the user's experience while using machine translation systems, and, hence, additional improvements of these tools are required to establish better translation.

cs.CL↗

arXiv2023

PROTES: Probabilistic Optimization with Tensor Sampling

We developed a new method PROTES for black-box optimization, which is based on the probabilistic sampling from a probability density function given in the low-parametric tensor train format. We tested it on complex multidimensional arrays and discretized multivariable functions taken, among others, from real-world applications, including unconstrained binary optimization and optimal control problems, for which the possible number of elements is up to $2^{100}$. In numerical experiments, both on analytic model functions and on complex problems, PROTES outperforms existing popular discrete optimization methods (Particle Swarm Optimization, Covariance Matrix Adaptation, Differential Evolution, and others).

math.NA↗

arXiv2023

Adaptive Cross Tubal Tensor Approximation

In this paper, we propose a new adaptive cross algorithm for computing a low tubal rank approximation of third-order tensors, with less memory and lower computational complexity than the truncated tensor SVD (t-SVD). This makes it applicable for decomposing large-scale tensors. We conduct numerical experiments on synthetic and real-world datasets to confirm the efficiency and feasibility of the proposed algorithm. The simulation results show more than one order of magnitude acceleration in the computation of low tubal rank (t-SVD) for large-scale tensors. An application to pedestrian attribute recognition is also presented.

math.NA↗

arXiv2023

TT-SDF2PC: Registration of Point Cloud and Compressed SDF Directly in the Memory-Efficient Tensor Train Domain

This paper addresses the following research question: ``can one compress a detailed 3D representation and use it directly for point cloud registration?''. Map compression of the scene can be achieved by the tensor train (TT) decomposition of the signed distance function (SDF) representation. It regulates the amount of data reduced by the so-called TT-ranks. Using this representation we have proposed an algorithm, the TT-SDF2PC, that is capable of directly registering a PC to the compressed SDF by making use of efficient calculations of its derivatives in the TT domain, saving computations and memory. We compare TT-SDF2PC with SOTA local and global registration methods in a synthetic dataset and a real dataset and show on par performance while requiring significantly less resources.

cs.RO↗

arXiv2023

Multiparticle Kalman filter for object localization in symmetric environments

This study considers the object localization problem and proposes a novel multiparticle Kalman filter to solve it in complex and symmetric environments. Two well-known classes of filtering algorithms to solve the localization problem are Kalman filter-based methods and particle filter-based methods. We consider these classes, demonstrate their complementary properties, and propose a novel filtering algorithm that takes the best from two classes. We evaluate the multiparticle Kalman filter in symmetric and noisy environments. Such environments are especially challenging for both classes of classical methods. We compare the proposed approach with the particle filter since only this method is feasible if the initial state is unknown. In the considered challenging environments, our method outperforms the particle filter in terms of both localization error and runtime.

cs.RO↗

arXiv2023

Federated Privacy-preserving Collaborative Filtering for On-Device Next App Prediction

In this study, we propose a novel SeqMF model to solve the problem of predicting the next app launch during mobile device usage. Although this problem can be represented as a classical collaborative filtering problem, it requires proper modification since the data are sequential, the user feedback is distributed among devices and the transmission of users' data to aggregate common patterns must be protected against leakage. According to such requirements, we modify the structure of the classical matrix factorization model and update the training procedure to sequential learning. Since the data about user experience are distributed among devices, the federated learning setup is used to train the proposed sequential matrix factorization model. One more ingredient of the proposed approach is a new privacy mechanism that guarantees the protection of the sent data from the users to the remote server. To demonstrate the efficiency of the proposed model we use publicly available mobile user behavior data. We compare our model with sequential rules and models based on the frequency of app launches. The comparison is conducted in static and dynamic environments. The static environment evaluates how our model processes sequential data compared to competitors. Therefore, the standard train-validation-test evaluation procedure is used. The dynamic environment emulates the real-world scenario, where users generate new data by running apps on devices, and evaluates our model in this case. Our experiments show that the proposed model provides comparable quality with other methods in the static environment. However, more importantly, our method achieves a better privacy-utility trade-off than competitors in the dynamic environment, which provides more accurate simulations of real-world usage.

cs.IR↗

arXiv2023

Machine learning methods for prediction of breakthrough curves in reactive porous media

Reactive flows in porous media play an important role in our life and are crucial for many industrial, environmental and biomedical applications. Very often the concentration of the species at the inlet is known, and the so-called breakthrough curves, measured at the outlet, are the quantities which could be measured or computed numerically. The measurements and the simulations could be time-consuming and expensive, and machine learning and Big Data approaches can help to predict breakthrough curves at lower costs. Machine learning (ML) methods, such as Gaussian processes and fully-connected neural networks, and a tensor method, cross approximation, are well suited for predicting breakthrough curves. In this paper, we demonstrate their performance in the case of pore scale reactive flow in catalytic filters.

physics.flu-dyn↗

arXiv2023

Cross Tensor Approximation for Image and Video Completion

This paper proposes a general framework to use the cross tensor approximation or tensor ColUmn-Row (CUR) approximation for reconstructing incomplete images and videos. The key importance of the new algorithms is their simplicity and ease of implementation with low computational complexity. For the case of data tensors with 1) structural missing components or 2) a high missing rate, we propose an efficient smooth tensor CUR algorithms which first make the sampled fibers smooth and then apply the proposed CUR algorithms. The numerical experiments show the significant benefit of this smoothing procedure. The main contribution of this paper is to develop/investigate improved multistage CUR algorithms with filtering (smoothing ) preprocessing for tensor completion. The second contribution is a detailed comparison of the performance of image recovery for four different CUR strategies via extensive computer simulations. Our simulations clearly indicated that the proposed algorithms are much faster than most of the existing state-of-the-art algorithms developed for tensor completion, while performance is comparable and often even better. Furthermore, we will provide in GitHub the MATLAB codes which can be used for various applications. Moreover, to our best knowledge, the CUR (cross approximation) algorithms have not been investigated nor compared till now for image and video completion.

math.NA↗

arXiv2023

Mitigating Human and Computer Opinion Fraud via Contrastive Learning

We introduce the novel approach towards fake text reviews detection in collaborative filtering recommender systems. The existing algorithms concentrate on detecting the fake reviews, generated by language models and ignore the texts, written by dishonest users, mostly for monetary gains. We propose the contrastive learning-based architecture, which utilizes the user demographic characteristics, along with the text reviews, as the additional evidence against fakes. This way, we are able to account for two different types of fake reviews spamming and make the recommendation system more robust to biased reviews.

cs.AI↗

arXiv2023

FREDE: Anytime Graph Embeddings

Low-dimensional representations, or embeddings, of a graph's nodes facilitate several practical data science and data engineering tasks. As such embeddings rely, explicitly or implicitly, on a similarity measure among nodes, they require the computation of a quadratic similarity matrix, inducing a tradeoff between space complexity and embedding quality. To date, no graph embedding work combines (i) linear space complexity, (ii) a nonlinear transform as its basis, and (iii) nontrivial quality guarantees. In this paper we introduce FREDE (FREquent Directions Embedding), a graph embedding based on matrix sketching that combines those three desiderata. Starting out from the observation that embedding methods aim to preserve the covariance among the rows of a similarity matrix}, FREDE iteratively improves on quality while individually processing rows of a nonlinearly transformed PPR similarity matrix derived from a state-of-the-art graph embedding method} and provides, at any iteration, column-covariance approximation guarantees in due course almost indistinguishable from those of the optimal approximation by SVD. Our experimental evaluation on variably sized networks shows that FREDE performs almost as well as SVD and competitively against state-of-the-art embedding methods in diverse data science tasks, even when it is based on as little as 10% of node similarities.

cs.LG↗

arXiv2022

FMM-Net: neural network architecture based on the Fast Multipole Method

In this paper, we propose a new neural network architecture based on the H2 matrix. Even though networks with H2-inspired architecture already exist, and our approach is designed to reduce memory costs and improve performance by taking into account the sparsity template of the H2 matrix. In numerical comparison with alternative neural networks, including the known H2-based ones, our architecture showed itself as beneficial in terms of performance, memory, and scalability.

math.NA↗

arXiv2022

Tensor-based Sequential Learning via Hankel Matrix Representation for Next Item Recommendations

Self-attentive transformer models have recently been shown to solve the next item recommendation task very efficiently. The learned attention weights capture sequential dynamics in user behavior and generalize well. Motivated by the special structure of learned parameter space, we question if it is possible to mimic it with an alternative and more lightweight approach. We develop a new tensor factorization-based model that ingrains the structural knowledge about sequential data within the learning process. We demonstrate how certain properties of a self-attention network can be reproduced with our approach based on special Hankel matrix representation. The resulting model has a shallow linear architecture and compares competitively to its neural counterpart.

cs.LG↗

arXiv2022

Understanding DDPM Latent Codes Through Optimal Transport

Diffusion models have recently outperformed alternative approaches to model the distribution of natural images, such as GANs. Such diffusion models allow for deterministic sampling via the probability flow ODE, giving rise to a latent space and an encoder map. While having important practical applications, such as estimation of the likelihood, the theoretical properties of this map are not yet fully understood. In the present work, we partially address this question for the popular case of the VP SDE (DDPM) approach. We show that, perhaps surprisingly, the DDPM encoder map coincides with the optimal transport map for common distributions; we support this claim theoretically and by extensive numerical experiments.

stat.ML↗

arXiv2022

Object-Based Augmentation Improves Quality of Remote Sensing Semantic Segmentation

Today deep convolutional neural networks (CNNs) push the limits for most computer vision problems, define trends, and set state-of-the-art results. In remote sensing tasks such as object detection and semantic segmentation, CNNs reach the SotA performance. However, for precise performance, CNNs require much high-quality training data. Rare objects and the variability of environmental conditions strongly affect prediction stability and accuracy. To overcome these data restrictions, it is common to consider various approaches including data augmentation techniques. This study focuses on the development and testing of object-based augmentation. The practical usefulness of the developed augmentation technique is shown in the remote sensing domain, being one of the most demanded ineffective augmentation techniques. We propose a novel pipeline for georeferenced image augmentation that enables a significant increase in the number of training samples. The presented pipeline is called object-based augmentation (OBA) and exploits objects' segmentation masks to produce new realistic training scenes using target objects and various label-free backgrounds. We test the approach on the buildings segmentation dataset with six different CNN architectures and show that the proposed method benefits for all the tested models. We also show that further augmentation strategy optimization can improve the results. The proposed method leads to the meaningful improvement of U-Net model predictions from 0.78 to 0.83 F1-score.

cs.CV↗