Many applications seek to recover low-rank approximations of noisy tensor data.

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The third entry varies under perturbation. Wecan compute the local indicator matrices atthis layer accordingly. We inherit the notations from the main text, and useIL to denote 13 theindicator matrixforlinearReLUoutputs. The key observation from this approach is that we can "merge" the weight matrices together for linearneurons(thefirstterminEq(19)).ThenwehavekW3D2LW2D1LW1k kW3kkW2kkW1k. Consider a neural network that maps inputx to output z = F(x), where z RN.

See Figure 1 for an illustration of the different SNR thresholds and Section 2.1 for more