Hardness of Learning Neural Networks under the Manifold Hypothesis Bobak T. Kiani Jason Wang Melanie Weber

The manifold hypothesis presumes that high-dimensional data lies on or near a low-dimensional manifold. While the utility of encoding geometric structure has been demonstrated empirically, rigorous analysis of its impact on the learnabil-ity of neural networks is largely missing. Several recent results have established hardness results for learning feedforward and equivariant neural networks under i.i.d.