Related papers: Correct by construction
Sparse coding is a crucial subroutine in algorithms for various signal processing, deep learning, and other machine learning applications. The central goal is to learn an overcomplete dictionary that can sparsely represent a given input…
Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we…
We formulate explicit predictions concerning the symmetry of optimal codes in compact metric spaces. This motivates the study of optimal codes in various spaces where these predictions can be tested.
The emergence of tools based on artificial intelligence has also led to the need of producing explanations which are understandable by a human being. In most approaches, the system is considered a black box, making it difficult to generate…
Detectability of failures of linear programming (LP) decoding and its potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the LP problem. In this paper, we make a…
Linear codes play a central role in coding theory and have applications in several branches of mathematics. For error correction purposes the minimum Hamming distance should be as large as possible. Linear codes related to applications in…
Since its introduction by Gauss, Matrix Algebra has facilitated understanding of scientific problems, hiding distracting details and finding more elegant and efficient ways of computational solving. Today's largest problems, which often…
In order to achieve fault tolerance, highly reliable system often require the ability to detect errors as soon as they occur and prevent the speared of erroneous information throughout the system. Thus, the need for codes capable of…
In recent years, several algorithms, which approximate matrix decomposition, have been developed. These algorithms are based on metric conservation features for linear spaces of random projection types. We show that an i.i.d sub-Gaussian…
Matching Logic is a framework for specifying programming language semantics and reasoning about programs. Its formulas are called patterns and are built with variables, symbols, connectives and quantifiers. A pattern is a combination of…
We derive exact matrix integral representations for different sums over partitions. The characteristic feature of all obtained matrix models is the presence of logarithmic (or, vice versa, exponential) terms in the potential. Our derivation…
Sparse storage formats are techniques for storing and processing the sparse matrix data efficiently. The performance of these storage formats depend upon the distribution of non-zeros, within the matrix in different dimensions. In order to…
Matrices and more generally multidimensional arrays, form the backbone of computational studies. In this paper we demonstrate increases in computational efficiency by performing partial-tracing/tensor-contractions on sparse-arrays. It was…
Strict linear feasibility or linear separation is usually tackled using efficient approximation/stochastic algorithms (that may even run in sub-linear times in expectation). However, today state of the art for solving…
Matrix completion is the problem of recovering a low rank matrix by observing a small fraction of its entries. A series of recent works [KOM12,JNS13,HW14] have proposed fast non-convex optimization based iterative algorithms to solve this…
Robust Principal Component Analysis (PCA) (Candes et al., 2011) and low-rank matrix completion (Recht et al., 2010) are extensions of PCA to allow for outliers and missing entries respectively. It is well-known that solving these problems…
We present exact mixed-integer linear programming formulations for verifying the performance of first-order methods for parametric quadratic optimization. We formulate the verification problem as a mixed-integer linear program where the…
We analyze the bit complexity of efficient algorithms for fundamental optimization problems, such as linear regression, $p$-norm regression, and linear programming (LP). State-of-the-art algorithms are iterative, and in terms of the number…
Many machine learning applications use latent variable models to explain structure in data, whereby visible variables (= coordinates of the given datapoint) are explained as a probabilistic function of some hidden variables. Finding…
Lattice rules are among the most prominently studied quasi-Monte Carlo methods to approximate multivariate integrals. A rank-1 lattice rule to approximate an $s$-dimensional integral is fully specified by its generating vector $\mathbf{z}…