Nonetheless, most of the existing methods could only optimize P AUC approximately, leading to inevitable biases that are not controllable.

This yields continuous-time counterparts of Fast Weight Programmers and linear Transformers.

Given a symmetric matrix M and a vector, we present new bounds on the Frobenius-distance utility of the Gaussian mechanism for approximating M by a matrix whose spectrum is,u n d e r ( Á, ") -di erential privacy. Our bounds depend on both and the gaps in the eigenvalues of M, and hold whenever the top k +1 eigenvalues of M have su ciently large gaps. When applied to the problems of private rank-k covariance matrix approximation and subspace recovery, our bounds yield improvements over previous bounds. Our bounds are obtained by viewing the addition of Gaussian noise as a continuous-time matrix Brownian motion. This viewpoint allows us to track the evolution of eigenvalues and eigenvectors of the matrix, which are governed by stochastic di erential equations discovered by Dyson. These equations allow us to bound the utility as the square-root of a sum-of-squares of perturbations to the eigenvectors, as opposed to a sum of perturbation bounds obtained via Davis-Kahan-type theorems.

While significant theoretical progress has been achieved, unveiling the generalization mystery of overparameterized neural networks still remains largely elusive. In this paper, we study the generalization behavior of shallow neural networks (SNNs) by leveraging the concept of algorithmic stability. We consider gradient descent (GD) and stochastic gradient descent (SGD) to train SNNs, for both of which we develop consistent excess risk bounds by balancing the optimization and generalization via early-stopping.

Neural Information Processing Systems http://nips.cc/

Prompted by these insights, we reviewed over 1.5 million scientific papers to understand the origin of this invalid