[D] Is gradient descent in deep neural networks an implicit Ricci flow?

Deep neural networks work under the manifold hypothesis, that is, that the training data lie on a lower-dimensional manifold. In particular, the last layer is a linear layer, which, in order to work properly, must mean that the target manifold curvature must be about constant since a consistent curvature is needed for a linear subspace to approximate the target manifold (in case of regression) or separate it (in case of classification). That is, the sequence of manifolds generated by gradient …

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