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We propose a novel stochastic algorithm that randomly samples entire rows and columns of the matrix as a way to approximate an arbitrary matrix function using the power series expansion. This contrasts with existing Monte Carlo methods,…
Machine learning techniques lend themselves as promising decision-making and analytic tools in a wide range of applications. Different ML algorithms have various hyper-parameters. In order to tailor an ML model towards a specific…
The linked cell list algorithm is an essential part of molecular simulation software, both molecular dynamics and Monte Carlo. Though it scales linearly with the number of particles, there has been a constant interest in increasing its…
The lattice Boltzmann method exhibits excellent scalability on current supercomputing systems and has thus increasingly become an alternative method for large-scale non-stationary flow simulations, reaching up to a trillion grid nodes.…
Fast approximations to matrix multiplication have the potential to dramatically reduce the cost of neural network inference. Recent work on approximate matrix multiplication proposed to replace costly multiplications with table-lookups by…
Near-term quantum processors are limited in terms of the number of qubits and gates they can afford. They nevertheless give unprecedented access to programmable quantum systems that can efficiently, although imperfectly, simulate quantum…
Submodular maximization subject to matroid constraints is a central problem with many applications in machine learning. As algorithms are increasingly used in decision-making over datapoints with sensitive attributes such as gender or race,…
We developed a semiclassical approximation method in combination with an adaptive moment estimation optimizer (SCA + ADAM) approach based on the PyTorch plus CUDA library on a the graphics processing unit (GPU). This method was employed to…
Performance optimization is an increasingly challenging but often repetitive task. While each platform has its quirks, the underlying code transformations rely on data movement and computational characteristics that recur across…
Iterative methods based on matrix splittings are useful in solving large sparse linear systems. In this direction, proper splittings and its several extensions are used to deal with singular and rectangular linear systems. In this article,…
We present a matrix-factorization algorithm that scales to input matrices with both huge number of rows and columns. Learned factors may be sparse or dense and/or non-negative, which makes our algorithm suitable for dictionary learning,…
In this paper, we study the $d$-dimensional update-query problem. We provide lower bounds on update and query running times, assuming a long-standing conjecture on min-plus matrix multiplication, as well as algorithms that are close to the…
We introduce fast algorithms for correlation clustering with respect to the Min Max objective that provide constant factor approximations on complete graphs. Our algorithms are the first purely combinatorial approximation algorithms for…
The maximization of submodular functions have found widespread application in areas such as machine learning, combinatorial optimization, and economics, where practitioners often wish to enforce various constraints; the matroid constraint…
We introduce the \emph{submodular objectives chasing problem}, which generalizes many natural and previously-studied problems: a sequence of constrained submodular maximization problems is revealed over time, with both the objective and…
In order to solve large matrix completion problems with practical computational cost, an approximate approach based on matrix factorization has been widely used. Alternating least squares (ALS) and stochastic gradient descent (SGD) are two…
Collaborative filtering (CF) has been proven to be one of the most effective techniques for recommendation. Among all CF approaches, SimpleX is the state-of-the-art method that adopts a novel loss function and a proper number of negative…
Hierarchical matrices can be used to construct efficient preconditioners for partial differential and integral equations by taking advantage of low-rank structures in triangular factorizations and inverses of the corresponding stiffness…
This paper proposes a scalable binary CUR low-rank approximation algorithm that leverages parallel selection of representative rows and columns within a deterministic framework. By employing a blockwise adaptive cross approximation…
Efficient and accurate computational methods for dealing with interacting electron problems on a lattice are of broad interest to the condensed matter community. For interacting Hubbard models, we introduce a cluster slave-particle approach…