How noise creates order: A universal principle linking physics and machine learning Noise is usually the enemy of structure. Yet in certain systems—from sheared colloidal suspensions to stochastic optimization algorithms—noisy local interactions paradoxically generate long-range spatial order. This phenomenon, called hyperuniformity, suppresses density fluctuations at large scales, but how it emerges from purely local, noisy dynamics has remained an open question for two decades. Satyam Anand, Guanming Zhang, and Stefano Martiniani study three paradigmatic systems: random organization (RO) and biased random organization (BRO) from soft matter physics, and stochastic gradient descent (SGD) from machine learning. Each system has fundamentally different microscopic noise sources—random kick directions in RO, random kick magnitudes in BRO, and random particle selection in SGD—yet all undergo the same absorbing-to-active phase transition as particle density increases. The key finding: despite these microscopic differences, all three systems display identical universal long-range behavior, governed by a single parameter—the noise correlation coefficient c between particle pairs. When pairwise noise is uncorrelated (c = 0), the systems remain disordered. As c approaches −1 (anti-correlated, momentum-conserving kicks), the crossover length scale for density suppression diverges, and the systems become strongly hyperuniform. The authors develop a fluctuating hydrodynamic theory that quantitatively predicts the structure factor across all systems without free parameters. Perhaps most striking is the connection to machine learning: the same anti-correlated noise that produces hyperuniformity also biases SGD toward flatter regions of the energy landscape—the very feature linked to robust generalization in neural networks. Lower batch fractions and higher learning rates, known empirically to improve generalization, produce both stronger long-range structure and flatter minima in particle systems. The implication is powerful: the tendency of SGD to find flat minima is not a quirk of neural network loss landscapes but a universal hallmark of stochastic optimization in high-dimensional spaces—opening new avenues from designing hyperuniform materials to understanding why deep learning generalizes. Paper: