Ilya Trofimov

Ilya Trofimov, Daniil Cherniavskii, Eduard Tulchinskii et al.

We propose a method for learning topology-preserving data representations (dimensionality reduction). The method aims to provide topological similarity between the data manifold and its latent representation via enforcing the similarity in topological features (clusters, loops, 2D voids, etc.) and their localization. The core of the method is the minimization of the Representation Topology Divergence (RTD) between original high-dimensional data and low-dimensional representation in latent space. RTD minimization provides closeness in topological features with strong theoretical guarantees. We develop a scheme for RTD differentiation and apply it as a loss term for the autoencoder. The proposed method "RTD-AE" better preserves the global structure and topology of the data manifold than state-of-the-art competitors as measured by linear correlation, triplet distance ranking accuracy, and Wasserstein distance between persistence barcodes.

Nikita Balabin, Daria Voronkova, Ilya Trofimov et al.

We propose TopDis (Topological Disentanglement), a method for learning disentangled representations via adding a multi-scale topological loss term. Disentanglement is a crucial property of data representations substantial for the explainability and robustness of deep learning models and a step towards high-level cognition. The state-of-the-art methods are based on VAE and encourage the joint distribution of latent variables to be factorized. We take a different perspective on disentanglement by analyzing topological properties of data manifolds. In particular, we optimize the topological similarity for data manifolds traversals. To the best of our knowledge, our paper is the first one to propose a differentiable topological loss for disentanglement learning. Our experiments have shown that the proposed TopDis loss improves disentanglement scores such as MIG, FactorVAE score, SAP score, and DCI disentanglement score with respect to state-of-the-art results while preserving the reconstruction quality. Our method works in an unsupervised manner, permitting us to apply it to problems without labeled factors of variation. The TopDis loss works even when factors of variation are correlated. Additionally, we show how to use the proposed topological loss to find disentangled directions in a trained GAN.

Ilya Trofimov, Daria Voronkova, Eduard Tulchinskii et al.

We propose a new topological tool for computer vision - Scalar Function Topology Divergence (SFTD), which measures the dissimilarity of multi-scale topology between sublevel sets of two functions having a common domain. Functions can be defined on an undirected graph or Euclidean space of any dimensionality. Most of the existing methods for comparing topology are based on Wasserstein distance between persistence barcodes and they don't take into account the localization of topological features. The minimization of SFTD ensures that the corresponding topological features of scalar functions are located in the same places. The proposed tool provides useful visualizations depicting areas where functions have topological dissimilarities. We provide applications of the proposed method to 3D computer vision. In particular, experiments demonstrate that SFTD as an additional loss improves the reconstruction of cellular 3D shapes from 2D fluorescence microscopy images, and helps to identify topological errors in 3D segmentation. Additionally, we show that SFTD outperforms Betti matching loss in 2D segmentation problems.

Igor Udovichenko, Egor Shvetsov, Denis Divitsky et al.

Neural Architecture Search (NAS) methods are widely used in various industries to obtain high quality taskspecific solutions with minimal human intervention. Event Sequences find widespread use in various industrial applications including churn prediction customer segmentation fraud detection and fault diagnosis among others. Such data consist of categorical and real-valued components with irregular timestamps. Despite the usefulness of NAS methods previous approaches only have been applied to other domains images texts or time series. Our work addresses this limitation by introducing a novel NAS algorithm SeqNAS specifically designed for event sequence classification. We develop a simple yet expressive search space that leverages commonly used building blocks for event sequence classification including multihead self attention convolutions and recurrent cells. To perform the search we adopt sequential Bayesian Optimization and utilize previously trained models as an ensemble of teachers to augment knowledge distillation. As a result of our work we demonstrate that our method surpasses state of the art NAS methods and popular architectures suitable for sequence classification and holds great potential for various industrial applications.

Serguei Barannikov, Ilya Trofimov, Grigorii Sotnikov et al.

We develop a framework for comparing data manifolds, aimed, in particular, towards the evaluation of deep generative models. We describe a novel tool, Cross-Barcode(P,Q), that, given a pair of distributions in a high-dimensional space, tracks multiscale topology spacial discrepancies between manifolds on which the distributions are concentrated. Based on the Cross-Barcode, we introduce the Manifold Topology Divergence score (MTop-Divergence) and apply it to assess the performance of deep generative models in various domains: images, 3D-shapes, time-series, and on different datasets: MNIST, Fashion MNIST, SVHN, CIFAR10, FFHQ, chest X-ray images, market stock data, ShapeNet. We demonstrate that the MTop-Divergence accurately detects various degrees of mode-dropping, intra-mode collapse, mode invention, and image disturbance. Our algorithm scales well (essentially linearly) with the increase of the dimension of the ambient high-dimensional space. It is one of the first TDA-based practical methodologies that can be applied universally to datasets of different sizes and dimensions, including the ones on which the most recent GANs in the visual domain are trained. The proposed method is domain agnostic and does not rely on pre-trained networks.

Serguei Barannikov, Daria Voronkova, Alexander Mironenko et al.

Neural network training is commonly based on SGD. However, the understanding of SGD's ability to converge to good local minima, given the non-convex nature of loss functions and the intricate geometric characteristics of loss landscapes, remains limited. In this paper, we apply topological data analysis methods to loss landscapes to gain insights into the learning process and generalization properties of deep neural networks. We use the loss function topology to relate the local behavior of gradient descent trajectories with the global properties of the loss surface. For this purpose, we define the neural network's Topological Obstructions score ("TO-score") with the help of robust topological invariants, barcodes of the loss function, which quantify the escapability of local minima for gradient-based optimization. Our two principal observations are: 1) the loss barcode of the neural network decreases with increasing depth and width, therefore the topological obstructions to learning diminish; 2) in certain situations there is a connection between the length of minima segments in the loss barcode and the minima's generalization errors. Our statements are based on extensive experiments with fully connected, convolutional, and transformer architectures and several datasets including MNIST, FMNIST, CIFAR10, CIFAR100, SVHN, and multilingual OSCAR text dataset.

Ilya Trofimov

Complementary products recommendation is an important problem in e-commerce. Such recommendations increase the average order price and the number of products in baskets. Complementary products are typically inferred from basket data. In this study, we propose the BB2vec model. The BB2vec model learns vector representations of products by analyzing jointly two types of data - Baskets and Browsing sessions (visiting web pages of products). These vector representations are used for making complementary products recommendation. The proposed model alleviates the cold start problem by delivering better recommendations for products having few or no purchases. We show that the BB2vec model has better performance than other models which use only basket data.

Ilya Trofimov, Alexander Genkin

Generalized linear model with $L_1$ and $L_2$ regularization is a widely used technique for solving classification, class probability estimation and regression problems. With the numbers of both features and examples growing rapidly in the fields like text mining and clickstream data analysis parallelization and the use of cluster architectures becomes important. We present a novel algorithm for fitting regularized generalized linear models in the distributed environment. The algorithm splits data between nodes by features, uses coordinate descent on each node and line search to merge results globally. Convergence proof is provided. A modifications of the algorithm addresses slow node problem. For an important particular case of logistic regression we empirically compare our program with several state-of-the art approaches that rely on different algorithmic and data spitting methods. Experiments demonstrate that our approach is scalable and superior when training on large and sparse datasets.

Afroze Ibrahim Baqapuri, Ilya Trofimov

Sponsored search is a multi-billion dollar industry and makes up a major source of revenue for search engines (SE). click-through-rate (CTR) estimation plays a crucial role for ads selection, and greatly affects the SE revenue, advertiser traffic and user experience. We propose a novel architecture for solving CTR prediction problem by combining artificial neural networks (ANN) with decision trees. First we compare ANN with respect to other popular machine learning models being used for this task. Then we go on to combine ANN with MatrixNet (proprietary implementation of boosted trees) and evaluate the performance of the system as a whole. The results show that our approach provides significant improvement over existing models.