By modeling robustness in terms of the condition number of the neural network, we argue that this loss of robustness is due to the exploding singular values of the low-rank weight matrices.

Estimating a vector x from noisy linear measurements Ax + w often requires use of prior knowledge or structural constraints on x for accurate reconstruction. Several recent works have considered combining linear least-squares estimation with a generic or "plug-in" denoiser function that can be designed in a modular manner based on the prior knowledge about x.

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Surprisingly, we show that even the addition ofnon-realistic random data (generated byGaussian sampling) can improverobustness.

Theirdifference,albeitobvious,shouldalsobeemphasized: GD isdeterministic, and the same constant initial condition will always lead to the same iterates.

We individually consider the gap-independent vs. gap-dependent