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In this paper, we consider a well-known sparse optimization problem that aims to find a sparse solution of a possibly noisy underdetermined system of linear equations. Mathematically, it can be modeled in a unified manner by minimizing…
We consider machine learning techniques to develop low-latency approximate solutions to a class of inverse problems. More precisely, we use a probabilistic approach for the problem of recovering sparse stochastic signals that are members of…
In our recent work on iterative computation in hardware, we showed that arbitrary-precision solvers can perform more favorably than their traditional arithmetic equivalents when the latter's precisions are either under- or over-budgeted for…
A key technique for controlling numerical stability in sparse direct solvers is threshold partial pivoting. When selecting a pivot, the entire candidate pivot column below the diagonal must be up-to-date and must be scanned. If the…
Machine learning solvers for partial differential equations (PDEs) have attracted growing interest. However, most existing approaches, such as neural network solvers, rely on stochastic training, which is inefficient and typically requires…
Recent applications in the domain of near-sensor computing require the adoption of floating-point arithmetic to reconcile high precision results with a wide dynamic range. In this paper, we propose a multi-core computing cluster that…
In recent years fused-multiply-add (FMA) units with lower-precision multiplications and higher-precision accumulation have proven useful in machine learning/artificial intelligence applications, most notably in training deep neural networks…
We propose a method for constructing quantum error-correcting codes based on non-binary low-density parity-check codes with Tanner graph girth 16. While conventional constructions using circulant permutation matrices are limited to girth…
The ongoing trend of hardware specialization has led to a growing use of custom data formats when processing sparse workloads, which are typically memory-bound. These formats facilitate optimized software/hardware implementations by…
Sparse matrix-vector multiplication (SpMV) is a fundamental building block for numerous applications. In this paper, we propose CSR5 (Compressed Sparse Row 5), a new storage format, which offers high-throughput SpMV on various platforms…
Large models training is plagued by the intense compute cost and limited hardware memory. A practical solution is low-precision representation but is troubled by loss in numerical accuracy and unstable training rendering the model less…
In this paper we present an efficient active-set method for the solution of convex quadratic programming problems with general piecewise-linear terms in the objective, with applications to sparse approximations and risk-minimization. The…
I present two new methods for exactly summing a set of floating-point numbers, and then correctly rounding to the nearest floating-point number. Higher accuracy than simple summation (rounding after each addition) is important in many…
Characterizing errors on many-qubit quantum computers remains a key challenge to understanding and improving the performance of these devices. Current characterization methods either don't scale beyond a few qubits, or make simplifying…
Sparse matrices have recently played a significant and impactful role in scientific computing, including artificial intelligence-related fields. According to historical studies on sparse matrix--vector multiplication (SpMV), Krylov subspace…
Radial basis functions have become a popular tool for approximation and solution of partial differential equations (PDEs). The recently proposed multilevel sparse interpolation with kernels (MuSIK) algorithm proposed in \cite{Georgoulis}…
The objective of this research was to compute the principal matrix square root with sparse approximation. A new stable iterative scheme avoiding fully matrix inversion (SIAI) is provided. The analysis on the sparsity and error of the…
Decoding of Low-Density Parity Check (LDPC) codes can be viewed as a special case of XOR-SAT problems, for which low-computational complexity bit-flipping algorithms have been proposed in the literature. However, a performance gap exists…
Incomplete LU (ILU) smoothers are effective in the algebraic multigrid (AMG) $V$-cycle for reducing high-frequency components of the error. However, the requisite direct triangular solves are comparatively slow on GPUs. Previous work has…
Positive linear programs (LPs) model many graph and operations research problems. One can solve for a $(1+\epsilon)$-approximation for positive LPs, for any selected $\epsilon$, in polylogarithmic depth and near-linear work via variations…