arXiv subjects

Evgeny Burnaev

Publications and source records attributed to Evgeny Burnaev.

At least 109 records · Page 6Linked to original sources

arXiv2023

Kantorovich Strikes Back! Wasserstein GANs are not Optimal Transport?

Wasserstein Generative Adversarial Networks (WGANs) are the popular generative models built on the theory of Optimal Transport (OT) and the Kantorovich duality. Despite the success of WGANs, it is still unclear how well the underlying OT dual solvers approximate the OT cost (Wasserstein-1 distance, $\mathbb{W}_{1}$) and the OT gradient needed to update the generator. In this paper, we address these questions. We construct 1-Lipschitz functions and use them to build ray monotone transport plans. This strategy yields pairs of continuous benchmark distributions with the analytically known OT plan, OT cost and OT gradient in high-dimensional spaces such as spaces of images. We thoroughly evaluate popular WGAN dual form solvers (gradient penalty, spectral normalization, entropic regularization, etc.) using these benchmark pairs. Even though these solvers perform well in WGANs, none of them faithfully compute $\mathbb{W}_{1}$ in high dimensions. Nevertheless, many provide a meaningful approximation of the OT gradient. These observations suggest that these solvers should not be treated as good estimators of $\mathbb{W}_{1}$, but to some extent they indeed can be used in variational problems requiring the minimization of $\mathbb{W}_{1}$.

cs.LG↗

arXiv2022

Acceptability Judgements via Examining the Topology of Attention Maps

The role of the attention mechanism in encoding linguistic knowledge has received special interest in NLP. However, the ability of the attention heads to judge the grammatical acceptability of a sentence has been underexplored. This paper approaches the paradigm of acceptability judgments with topological data analysis (TDA), showing that the geometric properties of the attention graph can be efficiently exploited for two standard practices in linguistics: binary judgments and linguistic minimal pairs. Topological features enhance the BERT-based acceptability classifier scores by $8$%-$24$% on CoLA in three languages (English, Italian, and Swedish). By revealing the topological discrepancy between attention maps of minimal pairs, we achieve the human-level performance on the BLiMP benchmark, outperforming nine statistical and Transformer LM baselines. At the same time, TDA provides the foundation for analyzing the linguistic functions of attention heads and interpreting the correspondence between the graph features and grammatical phenomena.

cs.CL↗

arXiv2022

Data-Driven Short-Term Daily Operational Sea Ice Regional Forecasting

Global warming made the Arctic available for marine operations and created demand for reliable operational sea ice forecasts to make them safe. While ocean-ice numerical models are highly computationally intensive, relatively lightweight ML-based methods may be more efficient in this task. Many works have exploited different deep learning models alongside classical approaches for predicting sea ice concentration in the Arctic. However, only a few focus on daily operational forecasts and consider the real-time availability of data they need for operation. In this work, we aim to close this gap and investigate the performance of the U-Net model trained in two regimes for predicting sea ice for up to the next 10 days. We show that this deep learning model can outperform simple baselines by a significant margin and improve its quality by using additional weather data and training on multiple regions, ensuring its generalization abilities. As a practical outcome, we build a fast and flexible tool that produces operational sea ice forecasts in the Barents Sea, the Labrador Sea, and the Laptev Sea regions.

cs.LG↗

arXiv2022

Unpaired Depth Super-Resolution in the Wild

Depth maps captured with commodity sensors are often of low quality and resolution; these maps need to be enhanced to be used in many applications. State-of-the-art data-driven methods of depth map super-resolution rely on registered pairs of low- and high-resolution depth maps of the same scenes. Acquisition of real-world paired data requires specialized setups. Another alternative, generating low-resolution maps from high-resolution maps by subsampling, adding noise and other artificial degradation methods, does not fully capture the characteristics of real-world low-resolution images. As a consequence, supervised learning methods trained on such artificial paired data may not perform well on real-world low-resolution inputs. We consider an approach to depth super-resolution based on learning from unpaired data. While many techniques for unpaired image-to-image translation have been proposed, most fail to deliver effective hole-filling or reconstruct accurate surfaces using depth maps. We propose an unpaired learning method for depth super-resolution, which is based on a learnable degradation model, enhancement component and surface normal estimates as features to produce more accurate depth maps. We propose a benchmark for unpaired depth SR and demonstrate that our method outperforms existing unpaired methods and performs on par with paired.

cs.CV↗

arXiv2022

Representation Topology Divergence: A Method for Comparing Neural Network Representations

Comparison of data representations is a complex multi-aspect problem that has not enjoyed a complete solution yet. We propose a method for comparing two data representations. We introduce the Representation Topology Divergence (RTD), measuring the dissimilarity in multi-scale topology between two point clouds of equal size with a one-to-one correspondence between points. The data point clouds are allowed to lie in different ambient spaces. The RTD is one of the few TDA-based practical methods applicable to real machine learning datasets. Experiments show that the proposed RTD agrees with the intuitive assessment of data representation similarity and is sensitive to its topological structure. We apply RTD to gain insights on neural networks representations in computer vision and NLP domains for various problems: training dynamics analysis, data distribution shift, transfer learning, ensemble learning, disentanglement assessment.

cs.LG↗

arXiv2022

Transfer learning for ensembles: reducing computation time and keeping the diversity

Transferring a deep neural network trained on one problem to another requires only a small amount of data and little additional computation time. The same behaviour holds for ensembles of deep learning models typically superior to a single model. However, a transfer of deep neural networks ensemble demands relatively high computational expenses. The probability of overfitting also increases. Our approach for the transfer learning of ensembles consists of two steps: (a) shifting weights of encoders of all models in the ensemble by a single shift vector and (b) doing a tiny fine-tuning for each individual model afterwards. This strategy leads to a speed-up of the training process and gives an opportunity to add models to an ensemble with significantly reduced training time using the shift vector. We compare different strategies by computation time, the accuracy of an ensemble, uncertainty estimation and disagreement and conclude that our approach gives competitive results using the same computation complexity in comparison with the traditional approach. Also, our method keeps the ensemble's models' diversity higher.

cs.LG↗

arXiv2022

Towards OOD Detection in Graph Classification from Uncertainty Estimation Perspective

The problem of out-of-distribution detection for graph classification is far from being solved. The existing models tend to be overconfident about OOD examples or completely ignore the detection task. In this work, we consider this problem from the uncertainty estimation perspective and perform the comparison of several recently proposed methods. In our experiment, we find that there is no universal approach for OOD detection, and it is important to consider both graph representations and predictive categorical distribution.

cs.LG↗

arXiv2022

Scan2Part: Fine-grained and Hierarchical Part-level Understanding of Real-World 3D Scans

We propose Scan2Part, a method to segment individual parts of objects in real-world, noisy indoor RGB-D scans. To this end, we vary the part hierarchies of objects in indoor scenes and explore their effect on scene understanding models. Specifically, we use a sparse U-Net-based architecture that captures the fine-scale detail of the underlying 3D scan geometry by leveraging a multi-scale feature hierarchy. In order to train our method, we introduce the Scan2Part dataset, which is the first large-scale collection providing detailed semantic labels at the part level in the real-world setting. In total, we provide 242,081 correspondences between 53,618 PartNet parts of 2,477 ShapeNet objects and 1,506 ScanNet scenes, at two spatial resolutions of 2 cm$^3$ and 5 cm$^3$. As output, we are able to predict fine-grained per-object part labels, even when the geometry is coarse or partially missing.

cs.CV↗

arXiv2022

DEF: Deep Estimation of Sharp Geometric Features in 3D Shapes

We propose Deep Estimators of Features (DEFs), a learning-based framework for predicting sharp geometric features in sampled 3D shapes. Differently from existing data-driven methods, which reduce this problem to feature classification, we propose to regress a scalar field representing the distance from point samples to the closest feature line on local patches. Our approach is the first that scales to massive point clouds by fusing distance-to-feature estimates obtained on individual patches. We extensively evaluate our approach against related state-of-the-art methods on newly proposed synthetic and real-world 3D CAD model benchmarks. Our approach not only outperforms these (with improvements in Recall and False Positives Rates), but generalizes to real-world scans after training our model on synthetic data and fine-tuning it on a small dataset of scanned data. We demonstrate a downstream application, where we reconstruct an explicit representation of straight and curved sharp feature lines from range scan data.

cs.CV↗

arXiv2022

High Performance of Gradient Boosting in Binding Affinity Prediction

Prediction of protein-ligand (PL) binding affinity remains the key to drug discovery. Popular approaches in recent years involve graph neural networks (GNNs), which are used to learn the topology and geometry of PL complexes. However, GNNs are computationally heavy and have poor scalability to graph sizes. On the other hand, traditional machine learning (ML) approaches, such as gradient-boosted decision trees (GBDTs), are lightweight yet extremely efficient for tabular data. We propose to use PL interaction features along with PL graph-level features in GBDT. We show that this combination outperforms the existing solutions.

cs.LG↗

arXiv2022

Artificial Text Detection via Examining the Topology of Attention Maps

The impressive capabilities of recent generative models to create texts that are challenging to distinguish from the human-written ones can be misused for generating fake news, product reviews, and even abusive content. Despite the prominent performance of existing methods for artificial text detection, they still lack interpretability and robustness towards unseen models. To this end, we propose three novel types of interpretable topological features for this task based on Topological Data Analysis (TDA) which is currently understudied in the field of NLP. We empirically show that the features derived from the BERT model outperform count- and neural-based baselines up to 10\% on three common datasets, and tend to be the most robust towards unseen GPT-style generation models as opposed to existing methods. The probing analysis of the features reveals their sensitivity to the surface and syntactic properties. The results demonstrate that TDA is a promising line with respect to NLP tasks, specifically the ones that incorporate surface and structural information.

cs.CL↗

arXiv2022

3D Parametric Wireframe Extraction Based on Distance Fields

We present a pipeline for parametric wireframe extraction from densely sampled point clouds. Our approach processes a scalar distance field that represents proximity to the nearest sharp feature curve. In intermediate stages, it detects corners, constructs curve segmentation, and builds a topological graph fitted to the wireframe. As an output, we produce parametric spline curves that can be edited and sampled arbitrarily. We evaluate our method on 50 complex 3D shapes and compare it to the novel deep learning-based technique, demonstrating superior quality.

cs.CV↗

arXiv2022

NPBG++: Accelerating Neural Point-Based Graphics

We present a new system (NPBG++) for the novel view synthesis (NVS) task that achieves high rendering realism with low scene fitting time. Our method efficiently leverages the multiview observations and the point cloud of a static scene to predict a neural descriptor for each point, improving upon the pipeline of Neural Point-Based Graphics in several important ways. By predicting the descriptors with a single pass through the source images, we lift the requirement of per-scene optimization while also making the neural descriptors view-dependent and more suitable for scenes with strong non-Lambertian effects. In our comparisons, the proposed system outperforms previous NVS approaches in terms of fitting and rendering runtimes while producing images of similar quality.

cs.CV↗

arXiv2022

Generative Modeling with Optimal Transport Maps

With the discovery of Wasserstein GANs, Optimal Transport (OT) has become a powerful tool for large-scale generative modeling tasks. In these tasks, OT cost is typically used as the loss for training GANs. In contrast to this approach, we show that the OT map itself can be used as a generative model, providing comparable performance. Previous analogous approaches consider OT maps as generative models only in the latent spaces due to their poor performance in the original high-dimensional ambient space. In contrast, we apply OT maps directly in the ambient space, e.g., a space of high-dimensional images. First, we derive a min-max optimization algorithm to efficiently compute OT maps for the quadratic cost (Wasserstein-2 distance). Next, we extend the approach to the case when the input and output distributions are located in the spaces of different dimensions and derive error bounds for the computed OT map. We evaluate the algorithm on image generation and unpaired image restoration tasks. In particular, we consider denoising, colorization, and inpainting, where the optimality of the restoration map is a desired attribute, since the output (restored) image is expected to be close to the input (degraded) one.

cs.LG↗

arXiv2021

Can We Use Neural Regularization to Solve Depth Super-Resolution?

Depth maps captured with commodity sensors often require super-resolution to be used in applications. In this work we study a super-resolution approach based on a variational problem statement with Tikhonov regularization where the regularizer is parametrized with a deep neural network. This approach was previously applied successfully in photoacoustic tomography. We experimentally show that its application to depth map super-resolution is difficult, and provide suggestions about the reasons for that.

cs.CV↗

arXiv2021

BooVAE: Boosting Approach for Continual Learning of VAE

Variational autoencoder (VAE) is a deep generative model for unsupervised learning, allowing to encode observations into the meaningful latent space. VAE is prone to catastrophic forgetting when tasks arrive sequentially, and only the data for the current one is available. We address this problem of continual learning for VAEs. It is known that the choice of the prior distribution over the latent space is crucial for VAE in the non-continual setting. We argue that it can also be helpful to avoid catastrophic forgetting. We learn the approximation of the aggregated posterior as a prior for each task. This approximation is parametrised as an additive mixture of distributions induced by encoder evaluated at trainable pseudo-inputs. We use a greedy boosting-like approach with entropy regularisation to learn the components. This method encourages components diversity, which is essential as we aim at memorising the current task with the fewest components possible. Based on the learnable prior, we introduce an end-to-end approach for continual learning of VAEs and provide empirical studies on commonly used benchmarks (MNIST, Fashion MNIST, NotMNIST) and CelebA datasets. For each dataset, the proposed method avoids catastrophic forgetting in a fully automatic way.

cs.LG↗

arXiv2021

Manifold Topology Divergence: a Framework for Comparing Data Manifolds

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.

cs.LG↗

arXiv2021

Large-Scale Wasserstein Gradient Flows

Wasserstein gradient flows provide a powerful means of understanding and solving many diffusion equations. Specifically, Fokker-Planck equations, which model the diffusion of probability measures, can be understood as gradient descent over entropy functionals in Wasserstein space. This equivalence, introduced by Jordan, Kinderlehrer and Otto, inspired the so-called JKO scheme to approximate these diffusion processes via an implicit discretization of the gradient flow in Wasserstein space. Solving the optimization problem associated to each JKO step, however, presents serious computational challenges. We introduce a scalable method to approximate Wasserstein gradient flows, targeted to machine learning applications. Our approach relies on input-convex neural networks (ICNNs) to discretize the JKO steps, which can be optimized by stochastic gradient descent. Unlike previous work, our method does not require domain discretization or particle simulation. As a result, we can sample from the measure at each time step of the diffusion and compute its probability density. We demonstrate our algorithm's performance by computing diffusions following the Fokker-Planck equation and apply it to unnormalized density sampling as well as nonlinear filtering.

cs.LG↗