Related papers: Learning $\ell_1$-based analysis and synthesis spa…

In this paper we look at a well known linear inverse problem that is one of the mathematical cornerstones of the compressed sensing field. In seminal works \cite{CRT,DOnoho06CS} $\ell_1$ optimization and its success when used for recovering…

Bi-Level Optimization (BLO) is originated from the area of economic game theory and then introduced into the optimization community. BLO is able to handle problems with a hierarchical structure, involving two levels of optimization tasks,…

Bilevel optimization has emerged as a technique for addressing a wide range of machine learning problems that involve an outer objective implicitly determined by the minimizer of an inner problem. While prior works have primarily focused on…

Sparse coding--that is, modelling data vectors as sparse linear combinations of basis elements--is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the large-scale matrix factorization…

This work considers recovery of signals that are sparse over two bases. For instance, a signal might be sparse in both time and frequency, or a matrix can be low rank and sparse simultaneously. To facilitate recovery, we consider minimizing…

The sparse optimization problems arise in many areas of science and engineering, such as compressed sensing, image processing, statistical and machine learning. The $\ell_{0}$-minimization problem is one of such optimization problems, which…

Regularization of ill-posed linear inverse problems via $\ell_1$ penalization has been proposed for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer of such an $\ell_1$ penalized functional is via an…

We consider a bilevel learning framework for learning linear operators. In this framework, the learnable parameters are optimized via a loss function that also depends on the minimizer of a convex optimization problem (denoted lower-level…

Sparse Autoencoders (SAEs) have proven to be powerful tools for interpreting neural networks by decomposing hidden representations into disentangled, interpretable features via sparsity constraints. However, conventional SAEs are…

Semantic parsing aims to map natural language utterances onto machine interpretable meaning representations, aka programs whose execution against a real-world environment produces a denotation. Weakly-supervised semantic parsers are trained…

It was recently established that for convex optimization problems with sparse optimal solutions (be it entry-wise sparsity or matrix rank-wise sparsity) it is possible to design first-order methods with linear convergence rates that depend…

Over the past years, there are increasing interests in recovering the signals from undersampling data where such signals are sparse under some orthogonal dictionary or tight framework, which is referred to be sparse synthetic model. More…

End-to-end deep learning has achieved impressive results but remains limited by its reliance on large labeled datasets, poor generalization to unseen scenarios, and growing computational demands. In contrast, classical optimization methods…

We present a novel algorithm that allows us to gain detailed insight into the effects of sparsity in linear and nonlinear optimization, which is of great importance in many scientific areas such as image and signal processing, medical…

In this paper, we propose an analysis mechanism based structured Analysis Discriminative Dictionary Learning (ADDL) framework. ADDL seamlessly integrates the analysis discriminative dictionary learning, analysis representation and analysis…

It is well known that $\ell_1$ minimization can be used to recover sufficiently sparse unknown signals from compressed linear measurements. In fact, exact thresholds on the sparsity, as a function of the ratio between the system dimensions,…

An effective approach to solving long-horizon tasks in robotics domains with continuous state and action spaces is bilevel planning, wherein a high-level search over an abstraction of an environment is used to guide low-level…

In this paper we propose a bilevel optimization approach for the placement of space and time observations in variational data assimilation problems. Within the framework of supervised learning, we consider a bilevel problem where the…

The task of dataset distillation aims to find a small set of synthetic images such that training a model on them reproduces the performance of the same model trained on a much larger dataset of real samples. Existing distillation methods…

How to extract more and useful information for single image super resolution is an imperative and difficult problem. Learning-based method is a representative method for such task. However, the results are not so stable as there may exist…