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Emergent universal long-range structure in random-organizing systems
Satyam Anand1,2, Guanming Zhang3,4, Stefano Martiniani5,6,7,8
1Courant Institute of Mathematical Sciences, New York University, New York, NY, 10003, USA. sa7483@nyu.edu.
Nature Communications
|January 23, 2026
Summary
Long-range structure emerges from noisy particle interactions, suppressing density fluctuations universally across physics and machine learning. This finding connects stochastic gradient descent to hyperuniformity and has broad applications.
Area of Science:
- Physics
- Machine Learning
- Mathematics
Background:
- Self-organization from local noisy dynamics is common but poorly understood.
- Emergence of long-range structure from local interactions is a key challenge.
Purpose of the Study:
- Investigate universal long-range behavior in random-organizing particle systems.
- Connect noise-induced hyperuniformity to machine learning dynamics.
- Develop a theory for noise-driven self-organization.
Main Methods:
- Studied three paradigmatic systems: soft matter physics models and stochastic gradient descent.
- Analyzed noise correlation effects on density fluctuations.
- Developed a fluctuating hydrodynamic theory.
Main Results:
- Discovered universal suppression of long-range density fluctuations.
- Noise correlation solely governs this long-range behavior.
- Linked emergent structure to stochastic gradient descent favoring flat energy landscapes.
Conclusions:
- Resolved microscopic origins of noise-induced hyperuniformity.
- Revealed parallels between particle systems and neural network loss landscapes.
- Suggests applications in materials science, ecology, and AI algorithm design.
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