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Representation learning (RL) methods learn objects' latent embeddings where information is preserved by distances. Since distances are invariant to certain linear transformations, one may obtain different embeddings while preserving the…

While deep learning through empirical risk minimization (ERM) has succeeded at achieving human-level performance at a variety of complex tasks, ERM is not robust to distribution shifts or adversarial attacks. Synthetic data augmentation…

We analyze the effect of quantizing weights and activations of neural networks on their loss and derive a simple regularization scheme that improves robustness against post-training quantization. By training quantization-ready networks, our…

Consider the use of $\ell_{1}/\ell_{\infty}$-regularized regression for joint estimation of a $\pdim \times \numreg$ matrix of regression coefficients. We analyze the high-dimensional scaling of $\ell_1/\ell_\infty$-regularized quadratic…

In the Machine Learning research community, there is a consensus regarding the relationship between model complexity and the required amount of data and computation power. In real world applications, these computational requirements are not…

The $\ell_{1\text{-}2}$ regularization method has a strong sparsity promoting capability in approaching sparse solutions of linear inverse problems and gained successful applications in various mathematics and applied science fields. This…

Deep neural networks have become popular in many supervised learning tasks, but they may suffer from overfitting when the training dataset is limited. To mitigate this, many researchers use data augmentation, which is a widely used and…

Mixup is a data augmentation technique that creates new examples as convex combinations of training points and labels. This simple technique has empirically shown to improve the accuracy of many state-of-the-art models in different settings…

Several image processing tasks, such as image classification and object detection, have been significantly improved using Convolutional Neural Networks (CNN). Like ResNet and EfficientNet, many architectures have achieved outstanding…

The complexity and non-Euclidean structure of graph data hinder the development of data augmentation methods similar to those in computer vision. In this paper, we propose a feature augmentation method for graph nodes based on topological…

Tabular neural network (NN) has attracted remarkable attentions and its recent advances have gradually narrowed the performance gap with respect to tree-based models on many public datasets. While the mainstreams focus on calibrating NN to…

Convex $\ell_1$ regularization using an infinite dictionary of neurons has been suggested for constructing neural networks with desired approximation guarantees, but can be affected by an arbitrary amount of over-parametrization. This can…

Modern technologies are producing a wealth of data with complex structures. For instance, in two-dimensional digital imaging, flow cytometry, and electroencephalography, matrix type covariates frequently arise when measurements are obtained…

Data augmentation is widely known as a simple yet surprisingly effective technique for regularizing deep networks. Conventional data augmentation schemes, e.g., flipping, translation or rotation, are low-level, data-independent and…

Compressed Sensing using $\ell_1$ regularization is among the most powerful and popular sparsification technique in many applications, but why has it not been used to obtain sparse deep learning model such as convolutional neural network…

There is growing body of learning problems for which it is natural to organize the parameters into matrix, so as to appropriately regularize the parameters under some matrix norm (in order to impose some more sophisticated prior knowledge).…

Deep Neural Networks have achieved remarkable success relying on the developing high computation capability of GPUs and large-scale datasets with increasing network depth and width in image recognition, object detection and many other…

A recent technique of randomized smoothing has shown that the worst-case (adversarial) $\ell_2$-robustness can be transformed into the average-case Gaussian-robustness by "smoothing" a classifier, i.e., by considering the averaged…

Regularizing neural networks is important for anticipating model behavior in regions of the data space that are not well represented. In this work, we propose a regularization technique for enforcing a level of smoothness in the mapping…

The effects of several nonlinear regularization techniques are discussed in the framework of 3D seismic tomography. Traditional, linear, $\ell_2$ penalties are compared to so-called sparsity promoting $\ell_1$ and $\ell_0$ penalties, and a…