arXiv subjects
Publications and source records attributed to Evgeny Burnaev.
We consider the problem of online aggregation of expert predictions with the quadratic loss function. We propose an algorithm for aggregating expert predictions which does not require a prior knowledge of the upper bound on the losses. The algorithm is based on the exponential reweighing of expert losses.
In this paper we extend the setting of the online prediction with expert advice to function-valued forecasts. At each step of the online game several experts predict a function, and the learner has to efficiently aggregate these functional forecasts into a single forecast. We adapt basic mixable (and exponentially concave) loss functions to compare functional predictions and prove that these adaptations are also mixable (exp-concave). We call this phenomenon mixability (exp-concavity) of integral loss functions. As an application of our main result, we prove that various loss functions used for probabilistic forecasting are mixable (exp-concave). The considered losses include Sliced Continuous Ranked Probability Score, Energy-Based Distance, Optimal Transport Costs and Sliced Wasserstein-2 distance, Beta-2 and Kullback-Leibler divergences, Characteristic function and Maximum Mean Discrepancies.
Voronoi tessellation, also known as Voronoi diagram, is an important computational geometry technique that has applications in various scientific disciplines. It involves dividing a given space into regions based on the proximity to a set of points. Autodifferentiation is a powerful tool for solving optimization tasks. Autodifferentiation assumes constructing a computational graph that allows to compute gradients using backpropagation algorithm. However, often the Voronoi tessellation remains the only non-differentiable part of a pipeline, prohibiting end-to-end differentiation. We present the method for autodifferentiation of the 2D Voronoi tessellation. The method allows one to construct the Voronoi tessellation and pass gradients, making the construction end-to-end differentiable. We provide the implementation details and present several important applications. To the best of our knowledge this is the first autodifferentiable realization of the Voronoi tessellation providing full set of Voronoi geometrical parameters in a differentiable way.
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.
The Schrödinger Bridge (SB) problem offers a powerful framework for combining optimal transport and diffusion models. A promising recent approach to solve the SB problem is the Iterative Markovian Fitting (IMF) procedure, which alternates between Markovian and reciprocal projections of continuous-time stochastic processes. However, the model built by the IMF procedure has a long inference time due to using many steps of numerical solvers for stochastic differential equations. To address this limitation, we propose a novel Discrete-time IMF (D-IMF) procedure in which learning of stochastic processes is replaced by learning just a few transition probabilities in discrete time. Its great advantage is that in practice it can be naturally implemented using the Denoising Diffusion GAN (DD-GAN), an already well-established adversarial generative modeling technique. We show that our D-IMF procedure can provide the same quality of unpaired domain translation as the IMF, using only several generation steps instead of hundreds. We provide the code at https://github.com/Daniil-Selikhanovych/ASBM.
We propose a novel algorithm for offline reinforcement learning using optimal transport. Typically, in offline reinforcement learning, the data is provided by various experts and some of them can be sub-optimal. To extract an efficient policy, it is necessary to \emph{stitch} the best behaviors from the dataset. To address this problem, we rethink offline reinforcement learning as an optimal transportation problem. And based on this, we present an algorithm that aims to find a policy that maps states to a \emph{partial} distribution of the best expert actions for each given state. We evaluate the performance of our algorithm on continuous control problems from the D4RL suite and demonstrate improvements over existing methods.
Recently, neural network-based methods for computing optimal transport maps have been effectively applied to style transfer problems. However, the application of these methods to voice conversion is underexplored. In our paper, we fill this gap by investigating optimal transport as a framework for voice conversion. We present a variety of optimal transport algorithms designed for different data representations, such as mel-spectrograms and latent representation of self-supervised speech models. For the mel-spectogram data representation, we achieve strong results in terms of Frechet Audio Distance (FAD). This performance is consistent with our theoretical analysis, which suggests that our method provides an upper bound on the FAD between the target and generated distributions. Within the latent space of the WavLM encoder, we achived state-of-the-art results and outperformed existing methods even with limited reference speaker data.
The increase in Arctic marine activity due to rapid warming and significant sea ice loss necessitates highly reliable, short-term sea ice forecasts to ensure maritime safety and operational efficiency. In this work, we present a novel data-driven approach for sea ice condition forecasting in the Gulf of Ob, leveraging sequences of radar images from Sentinel-1, weather observations, and GLORYS forecasts. Our approach integrates advanced video prediction models, originally developed for vision tasks, with domain-specific data preprocessing and augmentation techniques tailored to the unique challenges of Arctic sea ice dynamics. Central to our methodology is the use of uncertainty quantification to assess the reliability of predictions, ensuring robust decision-making in safety-critical applications. Furthermore, we propose a confidence-based model mixture mechanism that enhances forecast accuracy and model robustness, crucial for reliable operations in volatile Arctic environments. Our results demonstrate substantial improvements over baseline approaches, underscoring the importance of uncertainty quantification and specialized data handling for effective and safe operations and reliable forecasting.
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.
Parameter Efficient Fine-Tuning (PEFT) methods have gained popularity and democratized the usage of Large Language Models (LLMs). Recent studies have shown that a small subset of weights significantly impacts performance. Based on this observation, we introduce a novel PEFT method, called Gaussian noise Injected Fine Tuning of Salient Weights (GIFT-SW). Our method updates only salient columns, while injecting Gaussian noise into non-salient ones. To identify these columns, we developeda generalized sensitivity metric that extends and unifies metrics from previous studies. Experiments with LLaMA models demonstrate that GIFT-SW outperforms full fine-tuning and modern PEFT methods under the same computational budget. Moreover, GIFT-SW offers practical advantages to recover performance of models subjected to mixed-precision quantization with keeping salient weights in full precision.
Schrödinger Bridges (SB) have recently gained the attention of the ML community as a promising extension of classic diffusion models which is also interconnected to the Entropic Optimal Transport (EOT). Recent solvers for SB exploit the pervasive bridge matching procedures. Such procedures aim to recover a stochastic process transporting the mass between distributions given only a transport plan between them. In particular, given the EOT plan, these procedures can be adapted to solve SB. This fact is heavily exploited by recent works giving rise to matching-based SB solvers. The cornerstone here is recovering the EOT plan: recent works either use heuristical approximations (e.g., the minibatch OT) or establish iterative matching procedures which by the design accumulate the error during the training. We address these limitations and propose a novel procedure to learn SB which we call the \textbf{optimal Schrödinger bridge matching}. It exploits the optimal parameterization of the diffusion process and provably recovers the SB process \textbf{(a)} with a single bridge matching step and \textbf{(b)} with arbitrary transport plan as the input. Furthermore, we show that the optimal bridge matching objective coincides with the recently discovered energy-based modeling (EBM) objectives to learn EOT/SB. Inspired by this observation, we develop a light solver (which we call LightSB-M) to implement optimal matching in practice using the Gaussian mixture parameterization of the adjusted Schrödinger potential. We experimentally showcase the performance of our solver in a range of practical tasks. The code for our solver can be found at https://github.com/SKholkin/LightSB-Matching.
This study explores the application of self-supervised learning techniques for event sequences. It is a key modality in various applications such as banking, e-commerce, and healthcare. However, there is limited research on self-supervised learning for event sequences, and methods from other domains like images, texts, and speech may not easily transfer. To determine the most suitable approach, we conduct a detailed comparative analysis of previously identified best-performing methods. We find that neither the contrastive nor generative method is superior. Our assessment includes classifying event sequences, predicting the next event, and evaluating embedding quality. These results further highlight the potential benefits of combining both methods. Given the lack of research on hybrid models in this domain, we initially adapt the baseline model from another domain. However, upon observing its underperformance, we develop a novel method called the Multimodal-Learning Event Model (MLEM). MLEM treats contrastive learning and generative modeling as distinct yet complementary modalities, aligning their embeddings. The results of our study demonstrate that combining contrastive and generative approaches into one procedure with MLEM achieves superior performance across multiple metrics.
Given a collection of probability measures, a practitioner sometimes needs to find an "average" distribution which adequately aggregates reference distributions. A theoretically appealing notion of such an average is the Wasserstein barycenter, which is the primal focus of our work. By building upon the dual formulation of Optimal Transport (OT), we propose a new scalable approach for solving the Wasserstein barycenter problem. Our methodology is based on the recent Neural OT solver: it has bi-level adversarial learning objective and works for general cost functions. These are key advantages of our method since the typical adversarial algorithms leveraging barycenter tasks utilize tri-level optimization and focus mostly on quadratic cost. We also establish theoretical error bounds for our proposed approach and showcase its applicability and effectiveness in illustrative scenarios and image data setups. Our source code is available at https://github.com/justkolesov/NOTBarycenters.
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.
We introduce a novel neural network-based algorithm to compute optimal transport (OT) plans for general cost functionals. In contrast to common Euclidean costs, i.e., $\ell^1$ or $\ell^2$, such functionals provide more flexibility and allow using auxiliary information, such as class labels, to construct the required transport map. Existing methods for general costs are discrete and have limitations in practice, i.e. they do not provide an out-of-sample estimation. We address the challenge of designing a continuous OT approach for general costs that generalizes to new data points in high-dimensional spaces, such as images. Additionally, we provide the theoretical error analysis for our recovered transport plans. As an application, we construct a cost functional to map data distributions while preserving the class-wise structure.
Despite the recent advances in the field of computational Schrödinger Bridges (SB), most existing SB solvers are still heavy-weighted and require complex optimization of several neural networks. It turns out that there is no principal solver which plays the role of simple-yet-effective baseline for SB just like, e.g., $k$-means method in clustering, logistic regression in classification or Sinkhorn algorithm in discrete optimal transport. We address this issue and propose a novel fast and simple SB solver. Our development is a smart combination of two ideas which recently appeared in the field: (a) parameterization of the Schrödinger potentials with sum-exp quadratic functions and (b) viewing the log-Schrödinger potentials as the energy functions. We show that combined together these ideas yield a lightweight, simulation-free and theoretically justified SB solver with a simple straightforward optimization objective. As a result, it allows solving SB in moderate dimensions in a matter of minutes on CPU without a painful hyperparameter selection. Our light solver resembles the Gaussian mixture model which is widely used for density estimation. Inspired by this similarity, we also prove an important theoretical result showing that our light solver is a universal approximator of SBs. Furthemore, we conduct the analysis of the generalization error of our light solver. The code for our solver can be found at https://github.com/ngushchin/LightSB
Energy-based models (EBMs) are known in the Machine Learning community for decades. Since the seminal works devoted to EBMs dating back to the noughties, there have been a lot of efficient methods which solve the generative modelling problem by means of energy potentials (unnormalized likelihood functions). In contrast, the realm of Optimal Transport (OT) and, in particular, neural OT solvers is much less explored and limited by few recent works (excluding WGAN-based approaches which utilize OT as a loss function and do not model OT maps themselves). In our work, we bridge the gap between EBMs and Entropy-regularized OT. We present a novel methodology which allows utilizing the recent developments and technical improvements of the former in order to enrich the latter. From the theoretical perspective, we prove generalization bounds for our technique. In practice, we validate its applicability in toy 2D and image domains. To showcase the scalability, we empower our method with a pre-trained StyleGAN and apply it to high-res AFHQ $512\times 512$ unpaired I2I translation. For simplicity, we choose simple short- and long-run EBMs as a backbone of our Energy-guided Entropic OT approach, leaving the application of more sophisticated EBMs for future research. Our code is available at: https://github.com/PetrMokrov/Energy-guided-Entropic-OT
There is a constant need for high-performing and computationally efficient neural network models for image super-resolution: computationally efficient models can be used via low-capacity devices and reduce carbon footprints. One way to obtain such models is to compress models, e.g. quantization. Another way is a neural architecture search that automatically discovers new, more efficient solutions. We propose a novel quantization-aware procedure, the QuantNAS that combines pros of these two approaches. To make QuantNAS work, the procedure looks for quantization-friendly super-resolution models. The approach utilizes entropy regularization, quantization noise, and Adaptive Deviation for Quantization (ADQ) module to enhance the search procedure. The entropy regularization technique prioritizes a single operation within each block of the search space. Adding quantization noise to parameters and activations approximates model degradation after quantization, resulting in a more quantization-friendly architectures. ADQ helps to alleviate problems caused by Batch Norm blocks in super-resolution models. Our experimental results show that the proposed approximations are better for search procedure than direct model quantization. QuantNAS discovers architectures with better PSNR/BitOps trade-off than uniform or mixed precision quantization of fixed architectures. We showcase the effectiveness of our method through its application to two search spaces inspired by the state-of-the-art SR models and RFDN. Thus, anyone can design a proper search space based on an existing architecture and apply our method to obtain better quality and efficiency. The proposed procedure is 30\% faster than direct weight quantization and is more stable.