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Stochastic first-order methods for empirical risk minimization employ gradient approximations based on sampled data in lieu of exact gradients. Such constructions introduce noise into the learning dynamics, which can be corrected through…

Denoising of time domain data is a crucial task for many applications such as communication, translation, virtual assistants etc. For this task, a combination of a recurrent neural net (RNNs) with a Denoising Auto-Encoder (DAEs) has shown…

In real-world applications, it is important for machine learning algorithms to be robust against data outliers or corruptions. In this paper, we focus on improving the robustness of a large class of learning algorithms that are formulated…

Recently, several instances of non-Euclidean SGD, including SignSGD, Lion, and Muon, have attracted significant interest from the optimization community due to their practical success in training deep neural networks. Consequently, a number…

Seismic data inevitably suffers from random noise and missing traces in field acquisition. This limits the utilization of seismic data for subsequent imaging or inversion applications. Recently, dictionary learning has gained remarkable…

Gravitational wave astronomy has become a reality after the historical detections accomplished during the first observing run of the two advanced LIGO detectors. In the following years, the number of detections is expected to increase…

Semi-supervised regression (SSR), which aims to predict continuous scores for samples while reducing the reliance on large-scale labeled data, has recently attracted considerable attention across various applications, including computer…

Sparse dictionary learning (SDL) is a fundamental technique that is useful for many image processing tasks. As an example we consider here image recovery, where SDL can be cast as a nonsmooth optimization problem. For this kind of problems,…

Ground penetrating radar (GPR) target detection and classification is a challenging task. Here, we consider online dictionary learning (DL) methods to obtain sparse representations (SR) of the GPR data to enhance feature extraction for…

A recent trend in Natural Language Processing is the exponential growth in Language Model (LM) size, which prevents research groups without a necessary hardware infrastructure from participating in the development process. This study…

Denoising diffusion models have recently shown impressive results in generative tasks. By learning powerful priors from huge collections of training images, such models are able to gradually modify complete noise to a clean natural image…

We study the robustness properties of $\ell_1$ norm minimization for the classical linear regression problem with a given design matrix and contamination restricted to the dependent variable. We perform a fine error analysis of the $\ell_1$…

We propose robust methods to identify underlying Partial Differential Equation (PDE) from a given set of noisy time dependent data. We assume that the governing equation is a linear combination of a few linear and nonlinear differential…

The recovery of signals that are sparse not in a basis, but rather sparse with respect to an over-complete dictionary is one of the most flexible settings in the field of compressed sensing with numerous applications. As in the standard…

Denoising score matching (DSM) provides a way to learn data distributions by training a neural network to recover the score function, defined as the gradient of the log density, from noise-corrupted samples. Once trained, the score…

AI-powered Medical Imaging has recently achieved enormous attention due to its ability to provide fast-paced healthcare diagnoses. However, it usually suffers from a lack of high-quality datasets due to high annotation cost, inter-observer…

We propose a novel sparse representation for heavily underdetermined multichannel sound mixtures, i.e., with much more sources than microphones. The proposed approach operates in the complex Fourier domain, thus preserving spatial…

Discriminative dictionary learning (DDL) has recently gained significant attention due to its impressive performance in various pattern classification tasks. However, the locality of atoms is not fully explored in conventional DDL…

Continual learning in large language models (LLMs) is prone to catastrophic forgetting, where adapting to new tasks significantly degrades performance on previously learned ones. Existing methods typically rely on low-rank,…

Sparsity driven signal processing has gained tremendous popularity in the last decade. At its core, the assumption is that the signal of interest is sparse with respect to either a fixed transformation or a signal dependent dictionary. To…