相关论文: Learning Deep $\ell_0$ Encoders

Sparse auto-encoders are useful for extracting low-dimensional representations from high-dimensional data. However, their performance degrades sharply when the input noise at test time differs from the noise employed during training. This…

The sparse linear reconstruction problem is a core problem in signal processing which aims to recover sparse solutions to linear systems. The original problem regularized by the total number of nonzero components (also known as $L_0$…

In its most elementary form, compressed sensing studies the design of decoding algorithms to recover a sufficiently sparse vector or code from a lower dimensional linear measurement vector. Typically it is assumed that the decoder has…

We propose a novel, efficient approach for distributed sparse learning in high-dimensions, where observations are randomly partitioned across machines. Computationally, at each round our method only requires the master machine to solve a…

The explicit regularization and optimality of deep neural networks estimators from independent data have made considerable progress recently. The study of such properties on dependent data is still a challenge. In this paper, we carry out…

Image smoothing is a fundamental image processing operation that preserves the underlying structure, such as strong edges and contours, and removes minor details and textures in an image. Many image smoothing algorithms rely on computing…

We consider a minimization problem whose objective function is the sum of a fidelity term, not necessarily convex, and a regularization term defined by a positive regularization parameter $\lambda$ multiple of the $\ell_0$ norm composed…

An algorithmic framework, based on the difference of convex functions algorithm (DCA), is proposed for minimizing a class of concave sparse metrics for compressed sensing problems. The resulting algorithm iterates a sequence of $\ell_1$…

This paper presents a novel approach at the intersection of machine learning and number theory, focusing on the classification of prime and non-prime numbers. At the core of our research is the development of a highly sparse encoding…

Recently, considerable research efforts have been devoted to the design of methods to learn from data overcomplete dictionaries for sparse coding. However, learned dictionaries require the solution of an optimization problem for coding new…

In dense retrieval, deep encoders provide embeddings for both inputs and targets, and the softmax function is used to parameterize a distribution over a large number of candidate targets (e.g., textual passages for information retrieval).…

This paper introduces a new method for learning and inferring sparse representations of depth (disparity) maps. The proposed algorithm relaxes the usual assumption of the stationary noise model in sparse coding. This enables learning from…

We propose a sparse regularization model for inversion of incomplete Fourier transforms and apply it to seismic wavefield modeling. The objective function of the proposed model employs the Moreau envelope of the $\ell_0$ norm under a tight…

We propose a continuous non-convex variational model for Single Molecule Localisation Microscopy (SMLM) super-resolution in order to overcome light diffraction barriers. Namely, we consider a variation of the Continuous Exact $\ell_0$…

With increasing demands for efficiency, information retrieval has developed a branch of sparse retrieval, further advancing towards inference-free retrieval where the documents are encoded during indexing time and there is no…

Information processing techniques based on sparseness have been actively studied in several disciplines. Among them, a mathematical framework to approximately express a given dataset by a combination of a small number of basis vectors of an…

For the problem of high-dimensional sparse linear regression, it is known that an $\ell_0$-based estimator can achieve a $1/n$ "fast" rate on the prediction error without any conditions on the design matrix, whereas in absence of…

Motivated by the need to better understand the properties of sparse cutting-planes used in mixed integer programming solvers, the paper [2] studied the idealized problem of how well a polytope is approximated by the use of sparse valid…

We define and discuss the first sparse coding algorithm based on closed-form EM updates and continuous latent variables. The underlying generative model consists of a standard `spike-and-slab' prior and a Gaussian noise model. Closed-form…

In seeking for sparse and efficient neural network models, many previous works investigated on enforcing L1 or L0 regularizers to encourage weight sparsity during training. The L0 regularizer measures the parameter sparsity directly and is…