<ul><li>Complexity science provides measures for quantifying unpredictability, structure, and information, but lacks a systematic conceptual organization of these measures.</li><li>A unified framework has been introduced to locate statistical, algorithmic, and dynamical measures based on regularity, randomness, and complexity along three axes in a common conceptual space.</li><li>The taxonomy reveals challenges due to uncomputability and emphasizes the emergence of data-driven methods like autoencoders, latent dynamical models, and physics-informed neural networks as practical approximations to classical complexity ideals.</li><li>The operational arenas of latent spaces are highlighted as areas where regularity extraction, noise management, and structured compression converge, connecting theoretical foundations with modeling in high-dimensional systems.</li></ul>

Compression, Regularity, Randomness and Emergent Structure: Rethinking Physical Complexity in the Data-Driven Era

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