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Deep feedforward neural networks with piecewise linear activations are currently producing the state-of-the-art results in several public datasets. The combination of deep learning models and piecewise linear activation functions allows for…

Deep artificial neural networks achieve surprising generalization abilities that remain poorly understood. In this paper, we present a new approach to analyzing generalization for deep feed-forward ReLU networks that takes advantage of the…

Although Gaussian processes (GPs) with deep kernels have been successfully used for meta-learning in regression tasks, its uncertainty estimation performance can be poor. We propose a meta-learning method for calibrating deep kernel GPs for…

The increasing complexity of deep learning architectures is resulting in training time requiring weeks or even months. This slow training is due in part to vanishing gradients, in which the gradients used by back-propagation are extremely…

Implicit deep learning has recently become popular in the machine learning community since these implicit models can achieve competitive performance with state-of-the-art deep networks while using significantly less memory and computational…

Neural scaling laws describe how the performance of deep neural networks scales with key factors such as training data size, model complexity, and training time, often following power-law behaviors over multiple orders of magnitude. Despite…

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…

Image reconstruction using deep learning algorithms offers improved reconstruction quality and lower reconstruction time than classical compressed sensing and model-based algorithms. Unfortunately, clean and fully sampled ground-truth data…

A significant advance in accelerating neural network training has been the development of normalization methods, permitting the training of deep models both faster and with better accuracy. These advances come with practical challenges: for…

The paper briefy reviews several recent results on hierarchical architectures for learning from examples, that may formally explain the conditions under which Deep Convolutional Neural Networks perform much better in function approximation…

Scaling issues are mundane yet irritating for practitioners of reinforcement learning. Error scales vary across domains, tasks, and stages of learning; sometimes by many orders of magnitude. This can be detrimental to learning speed and…

This dissertation studies a fundamental open challenge in deep learning theory: why do deep networks generalize well even while being overparameterized, unregularized and fitting the training data to zero error? In the first part of the…

We consider online learning with linear models, where the algorithm predicts on sequentially revealed instances (feature vectors), and is compared against the best linear function (comparator) in hindsight. Popular algorithms in this…

Among the several paradigms of artificial intelligence (AI) or machine learning (ML), a remarkably successful paradigm is deep learning. Deep learning's phenomenal success has been hoped to be interpreted via fundamental research on the…

We investigate the approximation efficiency of score functions by deep neural networks in diffusion-based generative modeling. While existing approximation theories utilize the smoothness of score functions, they suffer from the curse of…

A number of machine learning tasks entail a high degree of invariance: the data distribution does not change if we act on the data with a certain group of transformations. For instance, labels of images are invariant under translations of…

Rectified linear unit (ReLU) is a widely used activation function for deep convolutional neural networks. However, because of the zero-hard rectification, ReLU networks miss the benefits from negative values. In this paper, we propose a…

Recognizing symmetries in data allows for significant boosts in neural network training, which is especially important where training data are limited. In many cases, however, the exact underlying symmetry is present only in an idealized…

Neural networks trained via gradient descent with random initialization and without any regularization enjoy good generalization performance in practice despite being highly overparametrized. A promising direction to explain this phenomenon…

We extend and combine several tools of the literature to design fast, adaptive, anytime and scale-free online learning algorithms. Scale-free regret bounds must scale linearly with the maximum loss, both toward large losses and toward very…