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In this paper, we provide a mathematical framework for improving generalization in a class of learning problems which is related to point estimations for modeling of high-dimensional nonlinear functions. In particular, we consider a…
Although recent works have brought some insights into the performance improvement of techniques used in state-of-the-art deep-learning models, more work is needed to understand their generalization properties. We shed light on this matter…
Works on implicit regularization have studied gradient trajectories during the optimization process to explain why deep networks favor certain kinds of solutions over others. In deep linear networks, it has been shown that gradient descent…
Deep neural networks (DNNs) have set benchmarks on a wide array of supervised learning tasks. Trained DNNs, however, often lack robustness to minor adversarial perturbations to the input, which undermines their true practicality. Recent…
Generalization is a central problem in Machine Learning. Most prediction methods require careful calibration of hyperparameters carried out on a hold-out \textit{validation} dataset to achieve generalization. The main goal of this paper is…
Stochastic optimization plays a crucial role in the advancement of deep learning technologies. Over the decades, significant effort has been dedicated to improving the training efficiency and robustness of deep neural networks, via various…
Improving performance of deep learning models and reducing their training times are ongoing challenges in deep neural networks. There are several approaches proposed to address these challenges one of which is to increase the depth of the…
In this work, we propose to progressively increase the training difficulty during learning a neural network model via a novel strategy which we call mini-batch trimming. This strategy makes sure that the optimizer puts its focus in the…
We present a novel regularization approach to train neural networks that enjoys better generalization and test error than standard stochastic gradient descent. Our approach is based on the principles of cross-validation, where a validation…
Overfitting is one of the most critical challenges in deep neural networks, and there are various types of regularization methods to improve generalization performance. Injecting noises to hidden units during training, e.g., dropout, is…
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.…
To fully uncover the great potential of deep neural networks (DNNs), various learning algorithms have been developed to improve the model's generalization ability. Recently, sharpness-aware minimization (SAM) establishes a generic scheme…
Convolutional neural network is an important model in deep learning. To avoid exploding/vanishing gradient problems and to improve the generalizability of a neural network, it is desirable to have a convolution operation that nearly…
In high-dimensional and/or non-parametric regression problems, regularization (or penalization) is used to control model complexity and induce desired structure. Each penalty has a weight parameter that indicates how strongly the structure…
Translating machine learning algorithms into clinical applications requires addressing challenges related to interpretability, such as accounting for the effect of confounding variables (or metadata). Confounding variables affect the…
Proper regularization is critical for speeding up training, improving generalization performance, and learning compact models that are cost efficient. We propose and analyze regularized gradient descent algorithms for learning shallow…
Deep neural networks (DNN) have achieved remarkable success in various fields, including computer vision and natural language processing. However, training an effective DNN model still poses challenges. This paper aims to propose a method…
Deep neural networks have gained tremendous popularity in last few years. They have been applied for the task of classification in almost every domain. Despite the success, deep networks can be incredibly slow to train for even moderate…
Finding parameters in a deep neural network (NN) that fit training data is a nonconvex optimization problem, but a basic first-order optimization method (gradient descent) finds a global optimizer with perfect fit (zero-loss) in many…
In this paper, we propose a novel normalization method called gradient normalization (GN) to tackle the training instability of Generative Adversarial Networks (GANs) caused by the sharp gradient space. Unlike existing work such as gradient…