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High-dimensional SGD aligns with emerging outlier eigenspaces
We rigorously study the joint evolution of training dynamics via stochastic gradient descent (SGD) and the spectra of empirical Hessian and gradient matrices.
High-dimensional limit theorems for SGD: Effective dynamics and critical scaling
We prove limit theorems for the trajectories of summary statistics (i. e., finite-dimensional functions) of SGD as the dimension goes to infinity.
Online stochastic gradient descent on non-convex losses from high-dimensional inference
Here one produces an estimator of an unknown parameter from independent samples of data by iteratively optimizing a loss function.
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