Related papers: Approximation Schemes for ReLU Regression
We give the first polynomial-time algorithm for performing linear or polynomial regression resilient to adversarial corruptions in both examples and labels. Given a sufficiently large (polynomial-size) training set drawn i.i.d. from…
In this paper, we consider robust nonparametric regression using deep neural networks with ReLU activation function. While several existing theoretically justified methods are geared towards robustness against identical heavy-tailed noise…
We study the fundamental problem of ReLU regression, where the goal is to fit Rectified Linear Units (ReLUs) to data. This supervised learning task is efficiently solvable in the realizable setting, but is known to be computationally hard…
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…
Neural networks can be trained to solve regression problems by using gradient-based methods to minimize the square loss. However, practitioners often prefer to reformulate regression as a classification problem, observing that training on…
Weight decay is one of the most widely used forms of regularization in deep learning, and has been shown to improve generalization and robustness. The optimization objective driving weight decay is a sum of losses plus a term proportional…
We develop fast algorithms and robust software for convex optimization of two-layer neural networks with ReLU activation functions. Our work leverages a convex reformulation of the standard weight-decay penalized training problem as a set…
We consider the problem of computing the best-fitting ReLU with respect to square-loss on a training set when the examples have been drawn according to a spherical Gaussian distribution (the labels can be arbitrary). Let $\mathsf{opt} < 1$…
Large language models (LLMs), such as ChatGPT and GPT4, have shown outstanding performance in many human life task. Attention computation plays an important role in training LLMs. Softmax unit and ReLU unit are the key structure in…
Training a one-node neural network with ReLU activation function (One-Node-ReLU) is a fundamental optimization problem in deep learning. In this paper, we begin with proving the NP-hardness of training One-Node-ReLU. We then present an…
This paper proposes and analyzes a communication-efficient distributed optimization framework for general nonconvex nonsmooth signal processing and machine learning problems under an asynchronous protocol. At each iteration, worker machines…
High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs,…
The non-convexity of the artificial neural network (ANN) training landscape brings inherent optimization difficulties. While the traditional back-propagation stochastic gradient descent (SGD) algorithm and its variants are effective in…
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…
We provide the first global model recovery results for the IRLS (iteratively reweighted least squares) heuristic for robust regression problems. IRLS is known to offer excellent performance, despite bad initializations and data corruption,…
We explore algorithms and limitations for sparse optimization problems such as sparse linear regression and robust linear regression. The goal of the sparse linear regression problem is to identify a small number of key features, while the…
In real-world applications, it is important for machine learning algorithms to be robust against data outliers or corruptions. In this paper, we focus on improving the robustness of a large class of learning algorithms that are formulated…
We consider in this paper the optimal approximations of convex univariate functions with feed-forward Relu neural networks. We are interested in the following question: what is the minimal approximation error given the number of…
We study the task of agnostically learning halfspaces under the Gaussian distribution. Specifically, given labeled examples $(\mathbf{x},y)$ from an unknown distribution on $\mathbb{R}^n \times \{ \pm 1\}$, whose marginal distribution on…
This paper deals with robust regression and subspace estimation and more precisely with the problem of minimizing a saturated loss function. In particular, we focus on computational complexity issues and show that an exact algorithm with…