相关论文: Hash Property and Coding Theorems for Sparse Matri…
In this paper, we study the dyadic Carleson Embedding Theorem in the matrix weighted setting. We provide two new proofs of this theorem, which highlight connections between the matrix Carleson Embedding Theorem and both maximal functions…
Block encoding of sparse matrices underpins powerful quantum algorithms such as quantum singular value transformation, Hamiltonian simulation, and quantum linear solvers, yet its efficient gate-level realization for general sparse matrices…
We develop a highly scalable optimization method called "hierarchical group-thresholding" for solving a multi-task regression model with complex structured sparsity constraints on both input and output spaces. Despite the recent emergence…
The power of sparse signal modeling with learned over-complete dictionaries has been demonstrated in a variety of applications and fields, from signal processing to statistical inference and machine learning. However, the statistical…
The Harrow-Hassidim-Lloyd (HHL) algorithm is a quantum algorithm for solving systems of linear equations that, in principle, offers an exponential improvement in scaling with the system size compared to classical approaches. In this work,…
We present an algorithm to reduce the computational effort for the multiplication of a given matrix with an unknown column vector. The algorithm decomposes the given matrix into a product of matrices whose entries are either zero or integer…
The performance of maximum-likelihood (ML) decoding on the binary erasure channel for finite-length low-density parity-check (LDPC) codes from two random ensembles is studied. The theoretical average spectrum of the Gallager ensemble is…
In this paper, we introduce the Maximum Matrix Contraction problem, where we aim to contract as much as possible a binary matrix in order to maximize its density. We study the complexity and the polynomial approximability of the problem.…
One of the greatest efforts of computational scientists is to translate the mathematical model describing a class of physical phenomena into large and complex codes. Many of these codes face the difficulty of implementing the mathematical…
In this paper, we introduce an achievability bound on the frame error rate of random tree code ensembles under a sequential decoding algorithm with a hard computational limit and consider the optimization of the random tree code ensembles…
In this paper, we consider the optimization problem of minimizing a continuously differentiable function subject to both convex constraints and sparsity constraints. By exploiting a mixed-integer reformulation from the literature, we define…
The paper introduces new bounds on the asymptotic density of parity-check matrices and the achievable rates under ML decoding of binary linear block codes transmitted over memoryless binary-input output-symmetric channels. The lower bounds…
In this paper, we use linear codes to study zero-error Slepian-Wolf coding of a set of sources with deviation symmetry, where the sources are generalization of the Hamming sources over an arbitrary field. We extend our previous codes,…
Sparse additive models are families of $d$-variate functions that have the additive decomposition $f^* = \sum_{j \in S} f^*_j$, where $S$ is an unknown subset of cardinality $s \ll d$. In this paper, we consider the case where each…
Coded matrix multiplication is a technique to enable straggler-resistant multiplication of large matrices in distributed computing systems. In this paper, we first present a conceptual framework to represent the division of work amongst…
Nowadays sparse systems of equations occur frequently in science and engineering. In this contribution we deal with sparse systems common in cryptanalysis. Given a cipher system, one converts it into a system of sparse equations, and then…
We provide a novel upper-bound on Witsenhausen's rate, the rate required in the zero-error analogue of the Slepian-Wolf problem; our bound is given in terms of a new information-theoretic functional defined on a certain graph. We then use…
Coded distributed computing framework enables large-scale machine learning (ML) models to be trained efficiently in a distributed manner, while mitigating the straggler effect. In this work, we consider a multi-task assignment problem in a…
A novel and efficient neural decoder algorithm is proposed. The proposed decoder is based on the neural Belief Propagation algorithm and the Automorphism Group. By combining neural belief propagation with permutations from the Automorphism…
Transformer-based autoregressive sampling has been the major bottleneck for slowing down large language model inferences. One effective way to accelerate inference is \emph{Speculative Decoding}, which employs a small model to sample a…