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. Code is available online.

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.