Related papers: Robust Recovery via Implicit Bias of Discrepant Le…

Empirical evidence suggests that for a variety of overparameterized nonlinear models, most notably in neural network training, the growth of the loss around a minimizer strongly impacts its performance. Flat minima -- those around which the…

We establish theoretical recovery guarantees of a family of Riemannian optimization algorithms for low rank matrix recovery, which is about recovering an $m\times n$ rank $r$ matrix from $p < mn$ number of linear measurements. The…

Un-trained convolutional neural networks have emerged as highly successful tools for image recovery and restoration. They are capable of solving standard inverse problems such as denoising and compressive sensing with excellent results by…

Reconstructing high dynamic range (HDR) images from low dynamic range (LDR) bursts plays an essential role in the computational photography. Impressive progress has been achieved by learning-based algorithms which require LDR-HDR image…

Low-rank adapters enable fine-tuning of large models with only a small number of parameters, thus reducing storage costs and minimizing the risk of catastrophic forgetting. However, they often pose optimization challenges, with poor…

We consider the problem of learning from data corrupted by underrepresentation bias, where positive examples are filtered from the data at different, unknown rates for a fixed number of sensitive groups. We show that with a small amount of…

This paper proposes a straightforward and cost-effective approach to assess whether a deep neural network (DNN) relies on the primary concepts of training samples or simply learns discriminative, yet simple and irrelevant features that can…

The low-rank matrix recovery problem often arises in various fields, including signal processing, machine learning, and imaging science. The Riemannian gradient descent (RGD) algorithm has proven to be an efficient algorithm for solving…

The ability of overparameterized deep networks to interpolate noisy data, while at the same time showing good generalization performance, has been recently characterized in terms of the double descent curve for the test error. Common…

We consider the problem of denoising with the help of prior information taken from a database of clean signals or images. Denoising with variational methods is very efficient if a regularizer well adapted to the nature of the data is…

In recent years, deep neural networks have emerged as a solution for inverse imaging problems. These networks are generally trained using pairs of images: one degraded and the other of high quality, the latter being called 'ground truth'.…

Neural implicit representations have become a popular choice for modeling surfaces due to their adaptability in resolution and support for complex topology. While previous works have achieved impressive reconstruction quality by training on…

In the context of over-parameterization, there is a line of work demonstrating that randomly initialized (stochastic) gradient descent (GD) converges to a globally optimal solution at a linear convergence rate for the quadratic loss…

Implicit deep learning has received increasing attention recently due to the fact that it generalizes the recursive prediction rules of many commonly used neural network architectures. Its prediction rule is provided implicitly based on the…

Images suffer from heavy spatial redundancy because pixels in neighboring regions are spatially correlated. Existing approaches strive to overcome this limitation by reducing less meaningful image regions. However, current leading methods…

We introduce a novel optimization algorithm for image recovery under learned sparse and low-rank constraints, which we parameterize as weighted extensions of the $\ell_p^p$-vector and $\mathcal S_p^p$ Schatten-matrix quasi-norms for…

Common ISAR radar images and signals can be reconstructed from much fewer samples than the sampling theorem requires since they are usually sparse. Unavailable randomly positioned samples can result from heavily corrupted parts of the…

We propose a low-rank transformation-learning framework to robustify subspace clustering. Many high-dimensional data, such as face images and motion sequences, lie in a union of low-dimensional subspaces. The subspace clustering problem has…

Although deep learning has shown its powerful performance in many applications, the mathematical principles behind neural networks are still mysterious. In this paper, we consider the problem of learning a one-hidden-layer neural network…

Deep neural networks can achieve remarkable generalization performances while interpolating the training data perfectly. Rather than the U-curve emblematic of the bias-variance trade-off, their test error often follows a "double descent" -…