arXiv subjects

Mateusz Baran

Publications and source records attributed to Mateusz Baran.

7 recordsLinked to original sources

arXiv2026

A modified Riemannian Levenberg-Marquardt Algorithm for robust or constraint optimization on manifolds

We extend the Levenberg-Marquardt method on Riemannian manifolds to a robust variant that allows to tackle problems from applications where outliers are to be expected. We formally state the framework for a block-wise variant of the Robust Riemannian Levenberg-Marquardt algorithm and discuss how known convergence results can be applied here as well. We further discuss several alternatives for phrasing the sub problem that has to be solved. Finally we illustrate how the accompanying open source implementation in Manopt$.$jl can be used to efficiently solve problems such as geodesic regression, Procrustes analysis, subspace Procrustes analysis and bundle adjustment robustly and compare the Levenberg-Marquardt solver to other solvers for nonsmooth Riemannian optimization.

math.OC↗

arXiv2026

A Riemannian quasi-Newton algorithm for optimization with Euclidean bounds

We propose a Riemannian limited-memory BFGS method for optimization problems with Euclidean bounds. The method combines a limited-memory quasi-Newton update in the tangent space with a Riemannian adaptation of the generalized Cauchy point strategy from classical L-BFGS-B, enabling efficient handling of Euclidean bounds while exploiting the geometric structure of the optimization domain. This setting is important in several applications, including covariance matrix estimation with bounded variance, neuroimaging, EEG signal classification, and other signal processing or computer-vision tasks that couple manifold variables with constrained Euclidean parameters. We provide a generic algorithmic framework and an implementation of the algorithm in the Manopt.jl library. Numerical experiments on benchmark problems indicate only minor reduction in performance on Euclidean problems compared to the classical L-BFGS-B method, while outperforming interior-point methods. Furthermore, the algorithm was tested on two mixed manifold and bounded Euclidean problems: amplitude-limited blind source separation with Gaussianity penalization and bounded-variance maximum likelihood common principal components analysis. The proposed method outperforms existing methods by several orders of magnitude.

math.OC↗

arXiv2025

A geometric perspective of state estimation using Kalman filters

Geometry of the state space is known to play a crucial role in many applications of Kalman filters, especially robotics and motion tracking. The Lie group-centric approach is currently very common, although a Riemannian approach has also been developed. In this work we explore the relationship between these two approaches and develop a novel description of Kalman filters based on affine connections that generalizes both commonly encountered descriptions. We illustrate the results on two test problems involving the special Euclidean group and the tangent bundle of a sphere in which the state is tracked by geometric variants of the extended Kalman filter and the unscented Kalman filter. The examples use a newly developed library GeometricKalman.jl. The new approach provides a greater freedom in selecting the structure of the state space for state estimation and can be easily integrated with standard techniques such as parameter estimation or covariance matrix estimation.

math.OC↗

arXiv2023

Classical Out-of-Distribution Detection Methods Benchmark in Text Classification Tasks

State-of-the-art models can perform well in controlled environments, but they often struggle when presented with out-of-distribution (OOD) examples, making OOD detection a critical component of NLP systems. In this paper, we focus on highlighting the limitations of existing approaches to OOD detection in NLP. Specifically, we evaluated eight OOD detection methods that are easily integrable into existing NLP systems and require no additional OOD data or model modifications. One of our contributions is providing a well-structured research environment that allows for full reproducibility of the results. Additionally, our analysis shows that existing OOD detection methods for NLP tasks are not yet sufficiently sensitive to capture all samples characterized by various types of distributional shifts. Particularly challenging testing scenarios arise in cases of background shift and randomly shuffled word order within in domain texts. This highlights the need for future work to develop more effective OOD detection approaches for the NLP problems, and our work provides a well-defined foundation for further research in this area.

cs.CL↗

arXiv2023

Electoral Agitation Data Set: The Use Case of the Polish Election

The popularity of social media makes politicians use it for political advertisement. Therefore, social media is full of electoral agitation (electioneering), especially during the election campaigns. The election administration cannot track the spread and quantity of messages that count as agitation under the election code. It addresses a crucial problem, while also uncovering a niche that has not been effectively targeted so far. Hence, we present the first publicly open data set for detecting electoral agitation in the Polish language. It contains 6,112 human-annotated tweets tagged with four legally conditioned categories. We achieved a 0.66 inter-annotator agreement (Cohen's kappa score). An additional annotator resolved the mismatches between the first two improving the consistency and complexity of the annotation process. The newly created data set was used to fine-tune a Polish Language Model called HerBERT (achieving a 68% F1 score). We also present a number of potential use cases for such data sets and models, enriching the paper with an analysis of the Polish 2020 Presidential Election on Twitter.

cs.CL↗

arXiv2023

Domain-Agnostic Neural Architecture for Class Incremental Continual Learning in Document Processing Platform

Production deployments in complex systems require ML architectures to be highly efficient and usable against multiple tasks. Particularly demanding are classification problems in which data arrives in a streaming fashion and each class is presented separately. Recent methods with stochastic gradient learning have been shown to struggle in such setups or have limitations like memory buffers, and being restricted to specific domains that disable its usage in real-world scenarios. For this reason, we present a fully differentiable architecture based on the Mixture of Experts model, that enables the training of high-performance classifiers when examples from each class are presented separately. We conducted exhaustive experiments that proved its applicability in various domains and ability to learn online in production environments. The proposed technique achieves SOTA results without a memory buffer and clearly outperforms the reference methods.

cs.LG↗

arXiv2023

Manifolds.jl: An Extensible Julia Framework for Data Analysis on Manifolds

We present the Julia package Manifolds$.$jl, providing a fast and easy-to-use library of Riemannian manifolds and Lie groups. This package enables working with data defined on a Riemannian manifold, such as the circle, the sphere, symmetric positive definite matrices, or one of the models for hyperbolic spaces. We introduce a common interface, available in ManifoldsBase$.$jl, with which new manifolds, applications, and algorithms can be implemented. We demonstrate the utility of Manifolds$.$jl using Bézier splines, an optimization task on manifolds, and principal component analysis on nonlinear data. In a benchmark, Manifolds$.$jl outperforms all comparable packages for low-dimensional manifolds in speed; over Python and Matlab packages, the improvement is often several orders of magnitude, while over C/C++ packages, the improvement is two-fold. For high-dimensional manifolds, it outperforms all packages except for Tensorflow-Riemopt, which is specifically tailored for high-dimensional manifolds.

cs.MS↗