Related papers: An Approximation Algorithm for training One-Node R…

Deep neural networks have yielded superior performance in many applications; however, the gradient computation in a deep model with millions of instances lead to a lengthy training process even with modern GPU/TPU hardware acceleration. In…

This paper introduces the first globally optimal algorithm for the empirical risk minimization problem of two-layer maxout and ReLU networks, i.e., minimizing the number of misclassifications. The algorithm has a worst-case time complexity…

We analyse the convergence of one-hidden-layer ReLU networks trained by gradient flow on $n$ data points. Our main contribution leverages the high dimensionality of the ambient space, which implies low correlation of the input samples, to…

In this work, we propose to train a deep neural network by distributed optimization over a graph. Two nonlinear functions are considered: the rectified linear unit (ReLU) and a linear unit with both lower and upper cutoffs (DCutLU). The…

Although deep learning based approximation algorithms have been applied very successfully to numerous problems, at the moment the reasons for their performance are not entirely understood from a mathematical point of view. Recently,…

Recursive least squares (RLS) algorithms were once widely used for training small-scale neural networks, due to their fast convergence. However, previous RLS algorithms are unsuitable for training deep neural networks (DNNs), since they…

We study the role of depth in training randomly initialized overparameterized neural networks. We give a general result showing that depth improves trainability of neural networks by improving the conditioning of certain kernel matrices of…

There has been a growing interest in expressivity of deep neural networks. However, most of the existing work about this topic focuses only on the specific activation function such as ReLU or sigmoid. In this paper, we investigate the…

Adversarial training is a widely used strategy for making neural networks resistant to adversarial perturbations. For a neural network of width $m$, $n$ input training data in $d$ dimension, it takes $\Omega(mnd)$ time cost per training…

In this paper, we consider regression problems with one-hidden-layer neural networks (1NNs). We distill some properties of activation functions that lead to $\mathit{local~strong~convexity}$ in the neighborhood of the ground-truth…

We present SiLU network constructions whose approximation efficiency depends critically on proper hyperparameter tuning. For the square function $x^2$, with optimally chosen shift $a$ and scale $\beta$, we achieve approximation error…

We provide a convergence analysis of gradient descent for the problem of agnostically learning a single ReLU function with moderate bias under Gaussian distributions. Unlike prior work that studies the setting of zero bias, we consider the…

Implicit neural networks have become increasingly attractive in the machine learning community since they can achieve competitive performance but use much less computational resources. Recently, a line of theoretical works established the…

We consider the problem of learning the best-fitting single neuron as measured by the expected square loss $\mathbb{E}_{(x,y)\sim \mathcal{D}}[(\sigma(w^\top x)-y)^2]$ over some unknown joint distribution $\mathcal{D}$ by using gradient…

Reverse engineering deep ReLU networks is a critical problem in understanding the complex behavior and interpretability of neural networks. In this research, we present a novel method for reconstructing deep ReLU networks by leveraging…

We consider the stochastic approximation problem where a convex function has to be minimized, given only the knowledge of unbiased estimates of its gradients at certain points, a framework which includes machine learning methods based on…

Recent theoretical work has demonstrated that deep neural networks have superior performance over shallow networks, but their training is more difficult, e.g., they suffer from the vanishing gradient problem. This problem can be typically…

We introduce a machine-learning framework to learn the hyperparameter sequence of first-order methods (e.g., the step sizes in gradient descent) to quickly solve parametric convex optimization problems. Our computational architecture…

We consider a deep ReLU / Leaky ReLU student network trained from the output of a fixed teacher network of the same depth, with Stochastic Gradient Descent (SGD). The student network is \emph{over-realized}: at each layer $l$, the number…

Deep learning algorithms -- typically consisting of a class of deep artificial neural networks (ANNs) trained by a stochastic gradient descent (SGD) optimization method -- are nowadays an integral part in many areas of science, industry,…