Related papers: On the sparsity of binary numbers
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…
Binary measurements arise naturally in a variety of statistical and engineering applications. They may be inherent to the problem---e.g., in determining the relationship between genetics and the presence or absence of a disease---or they…
Recovering the digital input of a time-discrete linear system from its (noisy) output is a significant challenge in the fields of data transmission, deconvolution, channel equalization, and inverse modeling. A variety of algorithms have…
Deep neural networks with lots of parameters are typically used for large-scale computer vision tasks such as image classification. This is a result of using dense matrix multiplications and convolutions. However, sparse computations are…
In inverse problems, one attempts to infer spatially variable functions from indirect measurements of a system. To practitioners of inverse problems, the concept of "information" is familiar when discussing key questions such as which parts…
We propose and analyze a novel framework for learning sparse representations, based on two statistical techniques: kernel smoothing and marginal regression. The proposed approach provides a flexible framework for incorporating feature…
We prove an important property of the binomial transform: it converts multiplication by the discrete variable into a certain difference operator. We also consider the case of dividing by the discrete variable. The properties presented here…
A lossy compression algorithm for binary redundant memoryless sources is presented. The proposed scheme is based on sparse graph codes. By introducing a nonlinear function, redundant memoryless sequences can be compressed. We propose a…
This paper describes a recursive estimation procedure for multivariate binary densities (probability distributions of vectors of Bernoulli random variables) using orthogonal expansions. For $d$ covariates, there are $2^d$ basis coefficients…
This work focuses on the reconstruction of sparse signals from their 1-bit measurements. The context is the one of 1-bit compressive sensing where the measurements amount to quantizing (dithered) random projections. Our main contribution…
Spatially-sparse predictors are good models for brain decoding: they give accurate predictions and their weight maps are interpretable as they focus on a small number of regions. However, the state of the art, based on total variation or…
Recovering high-level type information in binaries is a key task in reverse engineering and binary analysis. Binaries contain very little explicit type information. The structure of binary code is incredibly flexible allowing for ad-hoc…
We consider the following "partition and sum" operation on a natural number: Treating the number as a long string of digits insert several plus signs in between some of the digits and carry out the indicated sum. This results in a smaller…
We consider the problem of finding a sparse multiple of a polynomial. Given f in F[x] of degree d over a field F, and a desired sparsity t, our goal is to determine if there exists a multiple h in F[x] of f such that h has at most t…
We provide a new efficient version of the backpropagation algorithm, specialized to the case where the weights of the neural network being trained are sparse. Our algorithm is general, as it applies to arbitrary (unstructured) sparsity and…
Gr{\"o}bner bases is one the most powerful tools in algorithmic non-linear algebra. Their computation is an intrinsically hard problem with a complexity at least single exponential in the number of variables. However, in most of the cases,…
Inversion codes are numerical tools used for the inference of physical properties from the observations. Despite their success, the quality of current spectropolarimetric observations and those expected in the near future presents a…
Compressed sensing is a signal processing scheme that reconstructs high-dimensional sparse signals from a limited number of observations. In recent years, various problems involving signals with a finite number of discrete values have been…
The investigation of the effects of sparsity or sparsity constraints in signal processing problems has received considerable attention recently. Sparsity constraints refer to the a priori information that the object or signal of interest…
This work describes numerical methods that are useful in many areas: examples include statistical modelling (bioinformatics, computational biology), theoretical physics, and even pure mathematics. The methods are primarily useful for the…