相关论文: An Approximation Algorithm for training One-Node R…

Recent work has shown that the training of a one-hidden-layer, scalar-output fully-connected ReLU neural network can be reformulated as a finite-dimensional convex program. Unfortunately, the scale of such a convex program grows…

We investigate the complexity of training a two-layer ReLU neural network with weight decay regularization. Previous research has shown that the optimal solution of this problem can be found by solving a standard cone-constrained convex…

We study the problem of learning one-hidden-layer neural networks with Rectified Linear Unit (ReLU) activation function, where the inputs are sampled from standard Gaussian distribution and the outputs are generated from a noisy teacher…

We prove several hardness results for training depth-2 neural networks with the ReLU activation function; these networks are simply weighted sums (that may include negative coefficients) of ReLUs. Our goal is to output a depth-2 neural…

We study the sample complexity of learning one-hidden-layer convolutional neural networks (CNNs) with non-overlapping filters. We propose a novel algorithm called approximate gradient descent for training CNNs, and show that, with high…

We derive approximation bounds for learning single neuron models using thresholded gradient descent when both the labels and the covariates are possibly corrupted adversarially. We assume the data follows the model $y =…

We consider the computational complexity of training depth-2 neural networks composed of rectified linear units (ReLUs). We show that, even for the case of a single ReLU, finding a set of weights that minimizes the squared error (even…

We study the problem of training deep neural networks with Rectified Linear Unit (ReLU) activation function using gradient descent and stochastic gradient descent. In particular, we study the binary classification problem and show that for…

We consider the well-studied problem of learning a linear combination of $k$ ReLU activations with respect to a Gaussian distribution on inputs in $d$ dimensions. We give the first polynomial-time algorithm that succeeds whenever $k$ is a…

Neural Networks (NNs) are the method of choice for building learning algorithms. Their popularity stems from their empirical success on several challenging learning problems. However, most scholars agree that a convincing theoretical…

In this paper, we explore some basic questions on the complexity of training neural networks with ReLU activation function. We show that it is NP-hard to train a two-hidden layer feedforward ReLU neural network. If dimension of the input…

In this paper, we study the optimality gap between two-layer ReLU networks regularized with weight decay and their convex relaxations. We show that when the training data is random, the relative optimality gap between the original problem…

The slow convergence rate and pathological curvature issues of first-order gradient methods for training deep neural networks, initiated an ongoing effort for developing faster $\mathit{second}$-$\mathit{order}$ optimization algorithms…

Neural networks with REctified Linear Unit (ReLU) activation functions (a.k.a. ReLU networks) have achieved great empirical success in various domains. Nonetheless, existing results for learning ReLU networks either pose assumptions on the…

We consider the problem of learning an arbitrarily-biased ReLU activation (or neuron) over Gaussian marginals with the squared loss objective. Despite the ReLU neuron being the basic building block of modern neural networks, we still do not…

ReLU is widely seen as the default choice for activation functions in neural networks. However, there are cases where more complicated functions are required. In particular, recurrent neural networks (such as LSTMs) make extensive use of…

In many numerical simulations stochastic gradient descent (SGD) type optimization methods perform very effectively in the training of deep neural networks (DNNs) but till this day it remains an open problem of research to provide a…

One of the mysteries in the success of neural networks is randomly initialized first order methods like gradient descent can achieve zero training loss even though the objective function is non-convex and non-smooth. This paper demystifies…

The training of artificial neural networks (ANNs) with rectified linear unit (ReLU) activation via gradient descent (GD) type optimization schemes is nowadays a common industrially relevant procedure. Till this day in the scientific…

When optimizing a nonlinear objective, one can employ a neural network as a surrogate for the nonlinear function. However, the resulting optimization model can be time-consuming to solve globally with exact methods. As a result, local…