相关论文: Agnostic Learning of a Single Neuron with Gradient…

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…

We theoretically study the fundamental problem of learning a single neuron with a bias term ($\mathbf{x} \mapsto \sigma(<\mathbf{w},\mathbf{x}> + b)$) in the realizable setting with the ReLU activation, using gradient descent. Perhaps…

We study the fundamental problem of learning a single neuron, i.e., a function of the form $\mathbf{x}\mapsto\sigma(\mathbf{w}\cdot\mathbf{x})$ for monotone activations $\sigma:\mathbb{R}\mapsto\mathbb{R}$, with respect to the $L_2^2$-loss…

Deep learning models are often successfully trained using gradient descent, despite the worst case hardness of the underlying non-convex optimization problem. The key question is then under what conditions can one prove that optimization…

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 =…

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…

We consider the problem of active learning for single neuron models, also sometimes called ``ridge functions'', in the agnostic setting (under adversarial label noise). Such models have been shown to be broadly effective in modeling…

We study the problem of learning a single neuron $\mathbf{x}\mapsto \sigma(\mathbf{w}^T\mathbf{x})$ with gradient descent (GD). All the existing positive results are limited to the case where $\sigma$ is monotonic. However, it is recently…

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…

In this article we study the stochastic gradient descent (SGD) optimization method in the training of fully-connected feedforward artificial neural networks with ReLU activation. The main result of this work proves that the risk of the SGD…

Gradient descent (GD) type optimization methods are the standard instrument to train artificial neural networks (ANNs) with rectified linear unit (ReLU) activation. Despite the great success of GD type optimization methods in numerical…

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…

Fitting a function by using linear combinations of a large number $N$ of `simple' components is one of the most fruitful ideas in statistical learning. This idea lies at the core of a variety of methods, from two-layer neural networks to…

We consider the problem of learning a one-hidden-layer neural network with non-overlapping convolutional layer and ReLU activation, i.e., $f(\mathbf{Z}, \mathbf{w}, \mathbf{a}) = \sum_j a_j\sigma(\mathbf{w}^T\mathbf{Z}_j)$, in which both…

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…

The theory of training deep networks has become a central question of modern machine learning and has inspired many practical advancements. In particular, the gradient descent (GD) optimization algorithm has been extensively studied in…

We consider the fundamental problem of learning a single neuron $x \mapsto\sigma(w^\top x)$ using standard gradient methods. As opposed to previous works, which considered specific (and not always realistic) input distributions and…

In this paper, we study the implicit regularization of the gradient descent algorithm in homogeneous neural networks, including fully-connected and convolutional neural networks with ReLU or LeakyReLU activations. In particular, we study…

We study the problem of learning a single neuron with respect to the $L_2^2$-loss in the presence of adversarial distribution shifts, where the labels can be arbitrary, and the goal is to find a ``best-fit'' function. More precisely, given…

We study the complexity of training neural network models with one hidden nonlinear activation layer and an output weighted sum layer. We analyze Gradient Descent applied to learning a bounded target function on $n$ real-valued inputs. We…