Related papers: A Representation of Binary Matrices
Consider a binary decision making process where a single machine learning classifier replaces a multitude of humans. We raise questions about the resulting loss of diversity in the decision making process. We study the potential benefits of…
A new initialization method for hidden parameters in a neural network is proposed. Derived from the integral representation of the neural network, a nonparametric probability distribution of hidden parameters is introduced. In this…
Complexity bounds for many problems on matrices with univariate polynomial entries have been improved in the last few years. Still, for most related algorithms, efficient implementations are not available, which leaves open the question of…
Simplification of fractional powers of positive rational numbers and of sums, products and powers of such numbers is taught in beginning algebra. Such numbers can often be expressed in many ways, as this article discusses in some detail.…
We consider optimization problems involving the multiplication of variable matrices to be selected from a given family, which might be a discrete set, a continuous set or a combination of both. Such nonlinear, and possibly discrete,…
Classic cache-oblivious parallel matrix multiplication algorithms achieve optimality either in time or space, but not both, which promotes lots of research on the best possible balance or tradeoff of such algorithms. We study modern…
Nonnegative matrix factorization (NMF) has an established reputation as a useful data analysis technique in numerous applications. However, its usage in practical situations is undergoing challenges in recent years. The fundamental factor…
A new fast algebraic method for obtaining an $\mathcal{H}^2$-approximation of a matrix from its entries is presented. The main idea behind the method is based on the nested representation and the maximum-volume principle to select…
Binary optimization, a representative subclass of discrete optimization, plays an important role in mathematical optimization and has various applications in computer vision and machine learning. Usually, binary optimization problems are…
While almost all existing works which optimally solve just-in-time scheduling problems propose dedicated algorithmic approaches, we propose in this work mixed integer formulations. We consider a single machine scheduling problem that aims…
Succinct data structures give space-efficient representations of large amounts of data without sacrificing performance. They rely one cleverly designed data representations and algorithms. We present here the formalization in Coq/SSReflect…
Single-Instruction, Multiple-Data (SIMD) random number generators (RNGs) take advantage of vector units to offer significant performance gain over non-vectorized libraries, but they often rely on batch production of deviates from…
We discuss a unified approach to stochastic optimization of pseudo-Boolean objective functions based on particle methods, including the cross-entropy method and simulated annealing as special cases. We point out the need for auxiliary…
Unitary matrices are the basis of a large number of signal processing applications. In many of these applications, finding ways to efficiently store, and even transmit these matrices, can significantly reduce memory and throughput…
Binary Neural Network (BNN) represents convolution weights with 1-bit values, which enhances the efficiency of storage and computation. This paper is motivated by a previously revealed phenomenon that the binary kernels in successful BNNs…
We consider a variant of matrix completion where entries are revealed in a biased manner. We wish to understand the extent to which such bias can be exploited in improving predictions. Towards that, we propose a natural model where the…
In this paper we use ternary representation of numbers for compressing text data. We use a binary map for ternary digits and introduce a way to use the binary 11-pair, which has never been use for coding data before, and we futher use…
We observe structure in the sequences of quotients and remainders of the Euclidean algorithm with two families of inputs. Analyzing the remainders, we obtain new algorithms for computing modular inverses and representating prime numbers by…
Two-dimensional patterns are used in many research areas in computer science, ranging from image processing to specification and verification of complex software systems (via scenarios). The contribution of this paper is twofold. First, we…
We propose a method for low-rank semidefinite programming in application to the semidefinite relaxation of unconstrained binary quadratic problems. The method improves an existing solution of the semidefinite programming relaxation to…