ﻻ يوجد ملخص باللغة العربية
Recently it was shown in several papers that backpropagation is able to find the global minimum of the empirical risk on the training data using over-parametrized deep neural networks. In this paper a similar result is shown for deep neural networks with the sigmoidal squasher activation function in a regression setting, and a lower bound is presented which proves that these networks do not generalize well on a new data in the sense that they do not achieve the optimal minimax rate of convergence for estimation of smooth regression functions.
This work is substituted by the paper in arXiv:2011.14066. Stochastic gradient descent is the de facto algorithm for training deep neural networks (DNNs). Despite its popularity, it still requires fine tuning in order to achieve its best performanc
In this paper, we study the properties of robust nonparametric estimation using deep neural networks for regression models with heavy tailed error distributions. We establish the non-asymptotic error bounds for a class of robust nonparametric regress
In non-convex settings, it is established that the behavior of gradient-based algorithms is different in the vicinity of local structures of the objective function such as strict and non-strict saddle points, local and global minima and maxima. It is
Neural networks are becoming an increasingly important tool in applications. However, neural networks are not widely used in statistical genetics. In this paper, we propose a new neural networks method called expectile neural networks. When the size
We consider the dynamic of gradient descent for learning a two-layer neural network. We assume the input $xinmathbb{R}^d$ is drawn from a Gaussian distribution and the label of $x$ satisfies $f^{star}(x) = a^{top}|W^{star}x|$, where $ainmathbb{R}^d$