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Lower Bounds on the Generalization Error of Nonlinear Learning Models
We study in this paper lower bounds for the generalization error of models derived from multi-layer neural networks, in the regime where the size of the layers is commensurate with the number of samples in the training data.
Directed polymers on infinite graphs
We study the directed polymer model for general graphs (beyond $\mathbb Z^d$) and random walks.
Probability
On the Limitation of Spectral Methods: From the Gaussian Hidden Clique Problem to Rank-One Perturbations of Gaussian Tensors
We consider the following detection problem: given a realization of asymmetric matrix $X$ of dimension $n$, distinguish between the hypothesisthat all upper triangular variables are i. i. d.
