Related papers: Beyond Sparsity: Quantum Block Encoding for Dense …

The hierarchical matrix framework partitions matrices into subblocks that are either small or of low numerical rank, enabling linear storage complexity and efficient matrix-vector multiplication. This work focuses on the $H^2$-matrix format…

Solving linear systems of equations plays a fundamental role in numerous computational problems from different fields of science. The widespread use of numerical methods to solve these systems motivates investigating the feasibility of…

Co-clustering simultaneously clusters rows and columns, revealing more fine-grained groups. However, existing co-clustering methods suffer from poor scalability and cannot handle large-scale data. This paper presents a novel and scalable…

Effective quantum computation relies upon making good use of the exponential information capacity of a quantum machine. A large barrier to designing quantum algorithms for execution on real quantum machines is that, in general, it is…

The sparse dictionary coding framework represents signals as a linear combination of a few predefined dictionary atoms. It has been employed for images, time series, graph signals and recently for 2-way (or 2D) spatio-temporal data…

Current quantization methods for LLMs predominantly rely on block-wise structures to maintain efficiency, often at the cost of representational flexibility. In this work, we demonstrate that element-wise quantization can be made as…

We propose an efficient encoding algorithm for the binary and non-binary low-density parity-check codes. This algorithm transforms the parity part of the parity-check matrix into a block triangular matrix with low weight diagonal…

Many problems in information theory can be reduced to optimizations over matrices, where the rank of the matrices is constrained. We establish a link between rank-constrained optimization and the theory of quantum entanglement. More…

This paper contributes to interpretable machine learning via visual knowledge discovery in parallel coordinates. The concepts of hypercubes and hyper-blocks are used as easily understandable by end-users in the visual form in parallel…

Block-encoding is a foundational technique in modern quantum algorithms, enabling the implementation of non-unitary operations by embedding them into larger unitary matrices. While theoretically powerful and essential for advanced protocols…

Probabilistic Circuits (PCs) are tractable representations of probability distributions allowing for exact and efficient computation of likelihoods and marginals. Recent advancements have improved the scalability of PCs either by leveraging…

We present a parallel hierarchical solver for general sparse linear systems on distributed-memory machines. For large-scale problems, this fully algebraic algorithm is faster and more memory-efficient than sparse direct solvers because it…

We give a stochastic optimization algorithm that solves a dense $n\times n$ real-valued linear system $Ax=b$, returning $\tilde x$ such that $\|A\tilde x-b\|\leq \epsilon\|b\|$ in time: $$\tilde O((n^2+nk^{\omega-1})\log1/\epsilon),$$ where…

Recent advances in quantum computers are demonstrating the ability to solve problems at a scale beyond brute force classical simulation. As such, a widespread interest in quantum algorithms has developed in many areas, with optimization…

We present a comprehensive framework for structured sparse coding and modeling extending the recent ideas of using learnable fast regressors to approximate exact sparse codes. For this purpose, we develop a novel block-coordinate proximal…

Building on existing work with Hyperblocks, which classify data using minimum and maximum bounds for each attribute, we focus on enhancing interpretability, decreasing training time, and reducing model complexity without sacrificing…

This work studies quantum algorithms to solve high-dimensional stochastic differential equations (SDEs) $\mathrm{d} \mathbf{X}_t = A(t) \mathbf{X}_t \mathrm{d} t + B(t) \mathrm{d} \mathbf{W}_t$. Aiming for a speed-up in the dimension $N$ of…

Matrices with hierarchical low-rank structure, including HODLR and HSS matrices, constitute a versatile tool to develop fast algorithms for addressing large-scale problems. While existing software packages for such matrices often focus on…

The paper studies optimal coding of hidden Markov sources (HMS), which represent a broad class of practical sources obtained through noisy acquisition processes, beside their explicit modeling use in speech processing and recognition, image…

In this paper, we propose a new coded computing technique called "substitute decoding" for general iterative distributed computation tasks. In the first part of the paper, we use PageRank as a simple example to show that substitute decoding…