In the high-dimensional regime, SGD on diagonal linear networks is approximated by an SDE and a deterministic PDE that together give an explicit non-asymptotic description of convergence to zero risk.
High-dimensional limit theorems for SGD: Effective dynamics and critical scaling
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High-dimensional Limit of SGD for Diagonal Linear Networks
In the high-dimensional regime, SGD on diagonal linear networks is approximated by an SDE and a deterministic PDE that together give an explicit non-asymptotic description of convergence to zero risk.