SGD weight-matrix eigenvalue fluctuations follow random matrix predictions, with variance proportional to learning rate divided by batch size, the linear scaling rule.
Wigner,Characteristic vectors of bordered matrices with infinite dimensions, Annals of Mathematics 62(1955) 548
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Random Matrix Theory for Stochastic Gradient Descent
SGD weight-matrix eigenvalue fluctuations follow random matrix predictions, with variance proportional to learning rate divided by batch size, the linear scaling rule.