相关论文: Learning Deep $\ell_0$ Encoders

We propose a sparse reconstruction framework (aNETT) for solving inverse problems. Opposed to existing sparse reconstruction techniques that are based on linear sparsifying transforms, we train an autoencoder network $D \circ E$ with $E$…

Deep learning has gained great popularity due to its widespread success on many inference problems. We consider the application of deep learning to the sparse linear inverse problem encountered in compressive sensing, where one seeks 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…

Experimental evidence indicates that simple models outperform complex deep networks on many unsupervised similarity tasks. We provide a simple yet rigorous explanation for this behaviour by introducing the concept of an optimal…

Sparse regularization such as $\ell_1$ regularization is a quite powerful and widely used strategy for high dimensional learning problems. The effectiveness of sparse regularization has been supported practically and theoretically by…

Recovering corrupted images is one of the most challenging problems in image processing. Among various restoration tasks, blind image deblurring has been extensively studied due to its practical importance and inherent difficulty. In this…

We present and analyze a novel sparse polynomial technique for approximating high-dimensional Hilbert-valued functions, with application to parameterized partial differential equations (PDEs) with deterministic and stochastic inputs. Our…

Imaging is a standard example of an inverse problem, where the task of reconstructing a ground truth from a noisy measurement is ill-posed. Recent state-of-the-art approaches for imaging use deep learning, spearheaded by unrolled and…

Many approaches to transform classification problems from non-linear to linear by feature transformation have been recently presented in the literature. These notably include sparse coding methods and deep neural networks. However, many of…

Motivated by the question of optimal functional approximation via compressed sensing, we propose generalizations of the Iterative Hard Thresholding and the Compressive Sampling Matching Pursuit algorithms able to promote sparse in levels…

The goal of predictive sparse coding is to learn a representation of examples as sparse linear combinations of elements from a dictionary, such that a learned hypothesis linear in the new representation performs well on a predictive task.…

In this work, we explore the intersection of sparse coding theory and deep learning to enhance our understanding of feature extraction capabilities in advanced neural network architectures. We begin by introducing a novel class of Deep…

We know that compressive sensing can establish stable sparse recovery results from highly undersampled data under a restricted isometry property condition. In reality, however, numerous problems are coherent, and vast majority conventional…

Performance of distributed optimization and learning systems is bottlenecked by "straggler" nodes and slow communication links, which significantly delay computation. We propose a distributed optimization framework where the dataset is…

Pretrained encoders for mathematical texts have achieved significant improvements on various tasks such as formula classification and information retrieval. Yet they remain limited in representing and capturing student strategies for entire…

We consider a class of learning problems that involve a structured sparsity-inducing norm defined as the sum of $\ell_\infty$-norms over groups of variables. Whereas a lot of effort has been put in developing fast optimization methods when…

Sparse tensor best rank-1 approximation (BR1Approx), which is a sparsity generalization of the dense tensor BR1Approx, and is a higher-order extension of the sparse matrix BR1Approx, is one of the most important problems in sparse tensor…

Deep Learning (DL) is a machine learning procedure for artificial intelligence that analyzes the input data in detail by increasing neuron sizes and number of the hidden layers. DL has a popularity with the common improvements on the…

Understanding how the brain responds to sensory inputs is challenging: brain recordings are partial, noisy, and high dimensional; they vary across sessions and subjects and they capture highly nonlinear dynamics. These challenges have led…

Static sparse training aims to train sparse models from scratch, achieving remarkable results in recent years. A key design choice is given by the sparse initialization, which determines the trainable sub-network through a binary mask.…