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

arXiv 2505.07222 ↗First posted 12 May 2025cs.LG cond-mat.stat-mech cs.ITcited by 0

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Abstract (arXiv)

Complexity science offers a wide range of measures for quantifying unpredictability, structure, and information. Yet, a systematic conceptual organization of these measures is still missing. We present a unified framework that locates statistical, algorithmic, and dynamical measures along three axes (regularity, randomness, and complexity) and situates them in a common conceptual space. We map statistical, algorithmic, and dynamical measures into this conceptual space, discussing their computational accessibility and approximability. This taxonomy reveals the deep challenges posed by uncomputability and highlights the emergence of modern data-driven methods (including autoencoders, latent dynamical models, symbolic regression, and physics-informed neural networks) as pragmatic approximations to classical complexity ideals. Latent spaces emerge as operational arenas where regularity extraction, noise management, and structured compression converge, bridging theoretical foundations with practical modeling in high-dimensional systems. We close by outlining implications for physics-informed AI and AI-guided discovery in complex physical systems, arguing that classical questions of complexity remain central to next-generation scientific modeling.

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References · 20

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8 more
  1. 2017Linearly-Recurrent Autoencoder Networks for Learning Dynamicscited by 145
  2. 2018Gaussian Process Prior Variational Autoencoderscited by 72
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  8. 2023Symmetry's Edge in Cortical Dynamics: Multiscale Dynamics of Ensemble Excitation and Inhibitioncited by 1

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