Emergent universal long-range structure in random-organizing systems
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918415639248896 |
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| author | Anand, Satyam Zhang, Guanming Martiniani, Stefano |
| author_facet | Anand, Satyam Zhang, Guanming Martiniani, Stefano |
| contents | Self-organization through noisy interactions is ubiquitous across physics, mathematics, and machine learning, yet how long-range structure emerges from local noisy dynamics remains poorly understood. Here, we investigate three paradigmatic random-organizing particle systems drawn from distinct domains: models from soft matter physics (random organization, biased random organization) and machine learning (stochastic gradient descent), each characterized by distinct sources of noise. We discover universal long-range behavior across all systems, namely the suppression of long-range density fluctuations, governed solely by the noise correlation between particles. Furthermore, we establish a connection between the emergence of long-range order and the tendency of stochastic gradient descent to favor flat minima -- a phenomenon widely observed in machine learning. To rationalize these findings, we develop a fluctuating hydrodynamic theory that quantitatively captures all observations. Our study resolves long-standing questions about the microscopic origin of noise-induced hyperuniformity, uncovers striking parallels between stochastic gradient descent dynamics on particle system energy landscapes and neural network loss landscapes, and should have wide-ranging applications -- from the self-assembly of hyperuniform materials to ecological population dynamics and the design of generalizable learning algorithms. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_22933 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Emergent universal long-range structure in random-organizing systems Anand, Satyam Zhang, Guanming Martiniani, Stefano Soft Condensed Matter Disordered Systems and Neural Networks Statistical Mechanics Self-organization through noisy interactions is ubiquitous across physics, mathematics, and machine learning, yet how long-range structure emerges from local noisy dynamics remains poorly understood. Here, we investigate three paradigmatic random-organizing particle systems drawn from distinct domains: models from soft matter physics (random organization, biased random organization) and machine learning (stochastic gradient descent), each characterized by distinct sources of noise. We discover universal long-range behavior across all systems, namely the suppression of long-range density fluctuations, governed solely by the noise correlation between particles. Furthermore, we establish a connection between the emergence of long-range order and the tendency of stochastic gradient descent to favor flat minima -- a phenomenon widely observed in machine learning. To rationalize these findings, we develop a fluctuating hydrodynamic theory that quantitatively captures all observations. Our study resolves long-standing questions about the microscopic origin of noise-induced hyperuniformity, uncovers striking parallels between stochastic gradient descent dynamics on particle system energy landscapes and neural network loss landscapes, and should have wide-ranging applications -- from the self-assembly of hyperuniform materials to ecological population dynamics and the design of generalizable learning algorithms. |
| title | Emergent universal long-range structure in random-organizing systems |
| topic | Soft Condensed Matter Disordered Systems and Neural Networks Statistical Mechanics |
| url | https://arxiv.org/abs/2505.22933 |