Background: Agents for computer use (ACUs) are systems that execute complex tasks on digital devices – such as personal computers or mobile phones – given instructions in natural language. These agents automate tasks by controlling software through low-level actions like mouse clicks and touchscreen gestures. However, despite rapid progress, ACUs are not yet mature for everyday use. Objectives: This survey examines the current state-of-the-art, identifies trends, and points out research gaps in the development of practical ACUs. The goal is to provide a comprehensive review and analysis that helps advance general-purpose, robust, and scalable agents for real-world computer use. Methods: We introduce a multifaceted taxonomy of ACUs across three dimensions: (I) the domain perspective, characterizing the contexts in which agents operate; (II) the interaction perspective, describing observation modalities (e.g., screenshots, HTML) and action modalities (e.g., mouse, keyboard, code execution); and (III) the agent perspective, detailing how agents perceive, reason, and learn. We review 87 original research papers about ACUs and 33 relevant datasets, covering both foundation model-based and specialized approaches. Results: Our taxonomy comprehensively structures state-of-the-art approaches and establishes the groundwork for guiding future ACU research. We found that the field is transitioning from specialized agents toward foundation-model-based agents, a shift from text to image-based observation space, and an increasing adoption of behavior cloning methodologies. Furthermore, we identify six key research gaps: insufficient generalization, inefficient learning, limited planning, low task complexity in benchmarks, non-standardized evaluation, and a disconnect between research and practical conditions. Conclusions: To continue rapid improvements in the field, we recommend focusing on: (a) vision-based observations and low-level control to enhance generalization; (b) adaptive learning beyond static prompting; (c) effective planning and reasoning capabilities; (d) realistic, high-complexity benchmarks; (e) standardized evaluation criteria based on task success; and (f) aligning agent design with real-world deployment constraints. Collectively, our findings and proposed directions help develop more general-purpose agents for everyday digital tasks.

Self-attention is essential to Transformer architectures, yet how information is embedded in the self-attention matrices and how different objective functions impact this process remains unclear. We present a mathematical framework to analyze self-attention matrices by deriving the structures governing their weight updates. Using this framework, we demonstrate that bidirectional training induces symmetry in the weight matrices, while autoregressive training results in directionality and column dominance. Our theoretical findings are validated across multiple Transformer models — including ModernBERT, GPT, LLaMA3, and Mistral — and input modalities like text, vision, and audio. Finally, we apply these insights by showing that symmetric initialization improves the performance of encoder-only models on language tasks. This mathematical analysis offers a novel theoretical perspective on how information is embedded through self-attention, thereby improving the interpretability of Transformer models.