Under MSE training of deep linear networks, data augmentation and hard-wired invariance share global optima and critical points; regularization adds saddles and its solution path limits to the hard-wired optimum.
That is to say,G is a projection operator fromX to the subspace allG-fixed points
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Understanding Learning Invariance in Deep Linear Networks
Under MSE training of deep linear networks, data augmentation and hard-wired invariance share global optima and critical points; regularization adds saddles and its solution path limits to the hard-wired optimum.