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We focus on the classification problem with a separable dataset, one of the most important and classical problems from machine learning. The standard approach to this task is logistic regression with gradient descent (LR+GD). Recent studies…
The large amount of online data and vast array of computing resources enable current researchers in both industry and academia to employ the power of deep learning with neural networks. While deep models trained with massive amounts of data…
We study the problem of learning a single neuron under standard squared loss in the presence of arbitrary label noise and group-level distributional shifts, for a broad family of covariate distributions. Our goal is to identify a…
We study depth separation in infinite-width neural networks, where complexity is controlled by the overall squared $\ell_2$-norm of the weights (sum of squares of all weights in the network). Whereas previous depth separation results…
This paper studies transfer learning for ridge-regularized robust linear regression in the moderate-dimensional regime, where the number of predictors is of the same order as the sample size and the regression coefficients are not assumed…
Stochastic gradient descent (SGD) is a widely used algorithm in machine learning, particularly for neural network training. Recent studies on SGD for canonical quadratic optimization or linear regression show it attains well generalization…
We give a simple proof for the global convergence of gradient descent in training deep ReLU networks with the standard square loss, and show some of its improvements over the state-of-the-art. In particular, while prior works require all…
We study multigrade deep learning (MGDL) as a principled framework for structured error refinement in deep neural networks. While the approximation power of neural networks is now relatively well understood, training very deep architectures…
We study the common continual learning setup where an overparameterized model is sequentially fitted to a set of jointly realizable tasks. We analyze forgetting, defined as the loss on previously seen tasks, after $k$ iterations. For…
Adversarial training is a popular method to give neural nets robustness against adversarial perturbations. In practice adversarial training leads to low robust training loss. However, a rigorous explanation for why this happens under…
We study the convergence of model-based policy gradient for the deterministic, scalar, discounted linear-quadratic regulator when the controller is an overparameterized one-hidden-layer ReLU network without biases. Although the optimal LQR…
In this paper we study the problem of learning Rectified Linear Units (ReLUs) which are functions of the form $max(0,<w,x>)$ with $w$ denoting the weight vector. We study this problem in the high-dimensional regime where the number of…
We design a ReLU-based multilayer neural network by mapping the feature vectors to a higher dimensional space in every layer. We design the weight matrices in every layer to ensure a reduction of the training cost as the number of layers…
In this paper, we propose a structure-guided Gauss-Newton (SgGN) method for solving least squares problems using a shallow ReLU neural network. The method effectively takes advantage of both the least squares structure and the neural…
Recurrent neural networks (RNNs) are widely used to model sequential data but their non-linear dependencies between sequence elements prevent parallelizing training over sequence length. We show the training of RNNs with only linear…
Hyperparameter tuning is a bothersome step in the training of deep learning models. One of the most sensitive hyperparameters is the learning rate of the gradient descent. We present the 'All Learning Rates At Once' (Alrao) optimization…
Large language models (LLMs) often develop learned mechanisms specialized to specific datasets, such as reliance on domain-specific correlations, which yield high-confidence predictions without generalizable reasoning. While beneficial in…
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…
We study how well generative adversarial networks (GAN) learn probability distributions from finite samples by analyzing the convergence rates of these models. Our analysis is based on a new oracle inequality that decomposes the estimation…
We study the problem of estimating an unknown function from noisy data using shallow ReLU neural networks. The estimators we study minimize the sum of squared data-fitting errors plus a regularization term proportional to the squared…