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In this short paper we bridge two seemingly unrelated sparse approximation topics: continuous sparse coding and low-rank approximations. We show that for a specific choice of continuous dictionary, linear systems with nuclear-norm…

Matrix multiplication performance has long been the major bottleneck to scaling deep learning workloads, which has stimulated the design of new accelerators that use increasingly low-precision number formats. However, improvements in matrix…

We present algorithmic improvements for fast and memory-efficient use of discrete spatial symmetries in Exact Diagonalization computations of quantum many-body systems. These techniques allow us to work flexibly in the reduced basis of…

The recent development of deep learning methods provides a new approach to optimize the belief propagation (BP) decoding of linear codes. However, the limitation of existing works is that the scale of neural networks increases rapidly with…

A common problem on sequential-type decoding is that at the signal-to-noise ratio (SNR) below the one corresponding to the cutoff rate, the average decoding complexity per information bit and the required stack size grow rapidly with the…

We propose a generalized Lanczos method to generate the many-body basis states of quantum lattice models using tensor-network states (TNS). The ground-state wave function is represented as a linear superposition composed from a set of TNS…

The computation and memory costs of large language models kept increasing over last decade, which reached over the scale of 1T parameters. To address the challenges from the large scale models, model compression techniques such as low-rank…

Semidefinite programming (SDP) with diagonal constraints arise in many optimization problems, such as Max-Cut, community detection and group synchronization. Although SDPs can be solved to arbitrary precision in polynomial time, generic…

A fast algorithm for solving the under-determined 3-D linear gravity inverse problem based on the randomized singular value decomposition (RSVD) is developed. The algorithm combines an iteratively reweighted approach for $L_1$-norm…

In this paper, we introduce a powerful technique based on Leave-one-out analysis to the study of low-rank matrix completion problems. Using this technique, we develop a general approach for obtaining fine-grained, entrywise bounds for…

In this paper we present a novel randomized block coordinate descent method for the minimization of a convex composite objective function. The method uses (approximate) partial second-order (curvature) information, so that the algorithm…

Deep neural networks (DNNs) have made great progress in various fields. In particular, the quantized neural network is a promising technique making DNNs compatible on resource-limited devices for memory and computation saving. In this…

Quantum low-density parity-check (QLDPC) codes are a leading approach to quantum error correction, yet conventional belief propagation (BP) decoders often perform poorly, primarily due to non-convergence exacerbated by stabilizer…

Polynomial optimization problems represent a wide class of optimization problems, with a large number of real-world applications. Current approaches for polynomial optimization, such as the sum of squares (SOS) method, rely on large-scale…

This paper revisits the error analysis of the Stochastic Lanczos Quadrature (SLQ) method for approximating the trace of matrix functions, with a specific focus on asymmetric Lanczos quadrature rules. We reexplain an existing theoretical…

Screening and working set techniques are important approaches to reducing the size of an optimization problem. They have been widely used in accelerating first-order methods for solving large-scale sparse learning problems. In this paper,…

Direct discretization of continuum kinetic equations, like the Vlasov equation, are under-utilized because the distribution function generally exists in a high-dimensional (>3D) space and computational cost increases geometrically with…

Solving constrained nonlinear programs (NLPs) is of great importance in various domains such as power systems, robotics, and wireless communication networks. One widely used approach for addressing NLPs is the interior point method (IPM).…

Verifying multi-step reasoning in large language models is difficult due to imprecise error localization and high token costs. Existing methods either assess entire reasoning chains, suffering attention dilution, or rely on expensive…

The singular value decomposition (SVD) of large-scale matrices is a key tool in data analytics and scientific computing. The rapid growth in the size of matrices further increases the need for developing efficient large-scale SVD…