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Deep neural networks have seen enormous success in various real-world applications. Beyond their predictions as point estimates, increasing attention has been focused on quantifying the uncertainty of their predictions. In this review, we…
We propose a novel regularization algorithm to train deep neural networks, in which data at training time is severely biased. Since a neural network efficiently learns data distribution, a network is likely to learn the bias information to…
Training Deep Convolutional Neural Networks (CNNs) is based on the notion of using multiple kernels and non-linearities in their subsequent activations to extract useful features. The kernels are used as general feature extractors without…
Much as replacing hand-designed features with learned functions has revolutionized how we solve perceptual tasks, we believe learned algorithms will transform how we train models. In this work we focus on general-purpose learned optimizers…
In recent years, deep neural networks (DNNs) have known an important rise in popularity. However, although they are state-of-the-art in many machine learning challenges, they still suffer from several limitations. For example, DNNs require…
Deep neural networks are powerful tools to detect hidden patterns in data and leverage them to make predictions, but they are not designed to understand uncertainty and estimate reliable probabilities. In particular, they tend to be…
Deep neural networks (DNNs) play a crucial role in the field of machine learning, demonstrating state-of-the-art performance across various application domains. However, despite their success, DNN-based models may occasionally exhibit…
These notes are based on a lecture delivered by NC on March 2021, as part of an advanced course in Princeton University on the mathematical understanding of deep learning. They present a theory (developed by NC, NR and collaborators) of…
Deep neural networks are widely used prediction algorithms whose performance often improves as the number of weights increases, leading to over-parametrization. We consider a two-layered neural network whose first layer is frozen while the…
Training neural networks is an optimization problem, and finding a decent set of parameters through gradient descent can be a difficult task. A host of techniques has been developed to aid this process before and during the training phase.…
Deep learning is recognized to be capable of discovering deep features for representation learning and pattern recognition without requiring elegant feature engineering techniques by taking advantage of human ingenuity and prior knowledge.…
Deep learning, in general, focuses on training a neural network from large labeled datasets. Yet, in many cases there is value in training a network just from the input at hand. This is particularly relevant in many signal and image…
The success of deep neural networks is mostly due their ability to learn meaningful features from the data. Features learned in the hidden layers of deep neural networks trained in computer vision tasks have been shown to be similar to…
Regularizing the gradient norm of the output of a neural network with respect to its inputs is a powerful technique, rediscovered several times. This paper presents evidence that gradient regularization can consistently improve…
Despite the extreme popularity of deep learning in science and industry, its formal understanding is limited. This thesis puts forth notions of rank as key for developing a theory of deep learning, focusing on the fundamental aspects of…
In an attempt to better understand generalization in deep learning, we study several possible explanations. We show that implicit regularization induced by the optimization method is playing a key role in generalization and success of deep…
Learning curves model a classifier's test error as a function of the number of training samples. Prior works show that learning curves can be used to select model parameters and extrapolate performance. We investigate how to use learning…
Recent advances in deep learning theory have evoked the study of generalizability across different local minima of deep neural networks (DNNs). While current work focused on either discovering properties of good local minima or developing…
Our goal is to provide a review of deep learning methods which provide insight into structured high-dimensional data. Rather than using shallow additive architectures common to most statistical models, deep learning uses layers of…
Network representation learning (NRL) is an effective graph analytics technique and promotes users to deeply understand the hidden characteristics of graph data. It has been successfully applied in many real-world tasks related to network…