arXiv subjects

Maksym Shamrai

Publications and source records attributed to Maksym Shamrai.

7 recordsLinked to original sources

arXiv2026

Concatenated Matrix SVD: Compression Bounds, Incremental Approximation, and Error-Constrained Clustering

Large collections of matrices arise throughout modern machine learning, signal processing, and scientific computing, where they are commonly compressed by concatenation followed by truncated singular value decomposition (SVD). This strategy enables parameter sharing and efficient reconstruction and has been widely adopted across domains ranging from multi-view learning and signal processing to neural network compression. However, it leaves a fundamental question unanswered: which matrices can be safely concatenated and compressed together under explicit reconstruction error constraints? Existing approaches rely on heuristic or architecture-specific grouping and provide no principled guarantees on the resulting SVD approximation error. In the present work, we introduce a theory-driven framework for compression-aware clustering of matrices under SVD compression constraints. Our analysis establishes new spectral bounds for horizontally concatenated matrices, deriving global upper bounds on the optimal rank-$r$ SVD reconstruction error from lower bounds on singular value growth. The first bound follows from Weyl-type monotonicity under blockwise extensions, while the second leverages singular values of incremental residuals to yield tighter, per-block guarantees. We further develop an efficient approximate estimator based on incremental truncated SVD that tracks dominant singular values without forming the full concatenated matrix. Therefore, we propose three clustering algorithms that merge matrices only when their predicted joint SVD compression error remains below a user-specified threshold. The algorithms span a trade-off between speed, provable accuracy, and scalability, enabling compression-aware clustering with explicit error control.

math.NA↗

arXiv2026

MacArena: Benchmarking Computer Use Agents on an Online macOS Environment

Computer-use agents (CUAs) operate graphical user interfaces (GUIs) through vision and control primitives, and their capabilities have advanced rapidly, driven in part by standardized online evaluation benchmarks such as OSWorld, which serve both as evaluation tools and as training environments for reinforcement learning. However, macOS remains underserved in this landscape: the only existing benchmark, macOSWorld, covers a narrow slice of first-party applications with simpler tasks, and runs on x86 virtual machines incompatible with Apple Silicon. We introduce MacArena, a benchmark of 421 manually verified tasks spanning 50 applications that combines a curated port of OSWorld tasks, content sourced from macOSWorld, and 49 new macOS-native tasks, all running on Apple's native Virtualization framework on Apple Silicon. We argue that macOS presents distinct GUI challenges beyond what Linux-based benchmarks capture, and our evaluation supports this claim: strong model performance on existing benchmarks can reflect familiarity with task distributions rather than genuine cross-platform GUI competence. Notably, model rankings invert between ported and macOS-native tasks, with a leading model trailing by over 26% on the MacArena subset, suggesting that macOS poses a genuinely harder environment for current GUI agents.

cs.LG↗

arXiv2026

GUIrilla: A Scalable Framework for Automated Desktop UI Exploration

The performance and generalization of foundation models for interactive systems critically depend on the availability of large-scale, realistic training data. While recent advances in large language models (LLMs) have improved GUI understanding, progress in desktop automation remains constrained by the scarcity of high-quality, publicly available desktop interaction data, particularly for macOS. We introduce GUIRILLA, a scalable data crawling framework for automated exploration of desktop GUIs. GUIRILLA is not an autonomous agent; instead, it systematically collects realistic interaction traces and accessibility metadata intended to support the training, evaluation, and stabilization of downstream foundation models and GUI agents. The framework targets macOS, a largely underrepresented platform in existing resources, and organizes explored interfaces into hierarchical MacApp Trees derived from accessibility states and user actions. As part of this work, we release these MacApp Trees as a reusable structural representation of macOS applications, enabling downstream analysis, retrieval, testing, and future agent training. We additionally release macapptree, an open-source library for reproducible accessibility-driven GUI data collection, along with the full framework implementation to support open research in desktop autonomy.

cs.LG↗

arXiv2025

Deep Language Geometry: Constructing a Metric Space from LLM Weights

We introduce a novel framework that utilizes the internal weight activations of modern Large Language Models (LLMs) to construct a metric space of languages. Unlike traditional approaches based on hand-crafted linguistic features, our method automatically derives high-dimensional vector representations by computing weight importance scores via an adapted pruning algorithm. Our approach captures intrinsic language characteristics that reflect linguistic phenomena. We validate our approach across diverse datasets and multilingual LLMs, covering 106 languages. The results align well with established linguistic families while also revealing unexpected inter-language connections that may indicate historical contact or language evolution. The source code, computed language latent vectors, and visualization tool are made publicly available at https://github.com/mshamrai/deep-language-geometry.

cs.CL↗

arXiv2025

Screen2AX: Vision-Based Approach for Automatic macOS Accessibility Generation

Desktop accessibility metadata enables AI agents to interpret screens and supports users who depend on tools like screen readers. Yet, many applications remain largely inaccessible due to incomplete or missing metadata provided by developers - our investigation shows that only 33% of applications on macOS offer full accessibility support. While recent work on structured screen representation has primarily addressed specific challenges, such as UI element detection or captioning, none has attempted to capture the full complexity of desktop interfaces by replicating their entire hierarchical structure. To bridge this gap, we introduce Screen2AX, the first framework to automatically create real-time, tree-structured accessibility metadata from a single screenshot. Our method uses vision-language and object detection models to detect, describe, and organize UI elements hierarchically, mirroring macOS's system-level accessibility structure. To tackle the limited availability of data for macOS desktop applications, we compiled and publicly released three datasets encompassing 112 macOS applications, each annotated for UI element detection, grouping, and hierarchical accessibility metadata alongside corresponding screenshots. Screen2AX accurately infers hierarchy trees, achieving a 77% F1 score in reconstructing a complete accessibility tree. Crucially, these hierarchy trees improve the ability of autonomous agents to interpret and interact with complex desktop interfaces. We introduce Screen2AX-Task, a benchmark specifically designed for evaluating autonomous agent task execution in macOS desktop environments. Using this benchmark, we demonstrate that Screen2AX delivers a 2.2x performance improvement over native accessibility representations and surpasses the state-of-the-art OmniParser V2 system on the ScreenSpot benchmark.

cs.LG↗

arXiv2025

Perturbation Analysis of Singular Values in Concatenated Matrices

Concatenating matrices is a common technique for uncovering shared structures in data through singular value decomposition (SVD) and low-rank approximations. The fundamental question arises: How does the singular value spectrum of the concatenated matrix relate to the spectra of its individual components? In the present work, we develop a perturbation technique that extends classical results such as Weyl's inequality to concatenated matrices. We setup analytical bounds that quantify stability of singular values under small perturbations in submatrices. The results demonstrate that if submatrices are close in a norm, dominant singular values of the concatenated matrix remain stable enabling controlled trade-offs between accuracy and compression. These provide a theoretical basis for improved matrix clustering and compression strategies with applications in the numerical linear algebra, signal processing, and data-driven modeling.

cs.LG↗

arXiv2025

Closed-Form Robustness Bounds for Second-Order Pruning of Neural Controller Policies

Deep neural policies have unlocked agile flight for quadcopters, adaptive grasping for manipulators, and reliable navigation for ground robots, yet their millions of weights conflict with the tight memory and real-time constraints of embedded microcontrollers. Second-order pruning methods, such as Optimal Brain Damage (OBD) and its variants, including Optimal Brain Surgeon (OBS) and the recent SparseGPT, compress networks in a single pass by leveraging the local Hessian, achieving far higher sparsity than magnitude thresholding. Despite their success in vision and language, the consequences of such weight removal on closed-loop stability, tracking accuracy, and safety have remained unclear. We present the first mathematically rigorous robustness analysis of second-order pruning in nonlinear discrete-time control. The system evolves under a continuous transition map, while the controller is an $L$-layer multilayer perceptron with ReLU-type activations that are globally 1-Lipschitz. Pruning the weight matrix of layer $k$ replaces $W_k$ with $W_k+δW_k$, producing the perturbed parameter vector $\widehatΘ=Θ+δΘ$ and the pruned policy $π(\cdot;\widehatΘ)$. For every input state $s\in X$ we derive the closed-form inequality $ \|π(s;Θ)-π(s;\widehatΘ)\|_2 \le C_k(s)\,\|δW_k\|_2, $ where the constant $C_k(s)$ depends only on unpruned spectral norms and biases, and can be evaluated in closed form from a single forward pass. The derived bounds specify, prior to field deployment, the maximal admissible pruning magnitude compatible with a prescribed control-error threshold. By linking second-order network compression with closed-loop performance guarantees, our work narrows a crucial gap between modern deep-learning tooling and the robustness demands of safety-critical autonomous systems.

cs.RO↗