Related papers: Matrix Structure Exploitation in Generalized Eigen…
This study proposes the "adaptive flip graph algorithm", which combines adaptive searches with the flip graph algorithm for finding fast and efficient methods for matrix multiplication. The adaptive flip graph algorithm addresses the…
Solving the Kohn-Sham eigenvalue problem constitutes the most computationally expensive part in self-consistent density functional theory (DFT) calculations. In a previous paper, we have proposed a nonlinear Chebyshev-filtered subspace…
The deployment of deep neural networks (DNNs) in privacy-sensitive environments is constrained by computational overheads in fully homomorphic encryption (FHE). This paper explores unstructured sparsity in FHE matrix multiplication schemes…
To understand sparse systems we must account for both strong local atom bonds and weak nonlocal van der Waals forces between atoms separated by empty space. A fully nonlocal functional form [H. Rydberg, B.I. Lundqvist, D.C. Langreth, and M.…
This work focuses on accelerating the multiplication of a dense random matrix with a (fixed) sparse matrix, which is frequently used in sketching algorithms. We develop a novel scheme that takes advantage of blocking and recomputation…
Storing tabular data to balance storage and query efficiency is a long-standing research question in the database community. In this work, we argue and show that a novel DeepMapping abstraction, which relies on the impressive memorization…
Polyhedral compilers can perform complex loop optimizations that improve parallelism and cache behaviour of loops in the input program. These transformations result in significant performance gains on modern processors which have large…
Dense linear layers are the dominant computational bottleneck in foundation models. Identifying more efficient alternatives to dense matrices has enormous potential for building more compute-efficient models, as exemplified by the success…
Density functional theory (DFT) offers a desirable balance between quantitative accuracy and computational efficiency in practical many-electron calculations. Its central component, the exchange-correlation energy functional, has been…
We present a new algorithm, Fractional Decomposition Tree (FDT) for finding a feasible solution for an integer program (IP) where all variables are binary. FDT runs in polynomial time and is guaranteed to find a feasible integer solution…
High fidelity scientific simulations modeling physical phenomena typically require solving large linear systems of equations which result from discretization of a partial differential equation (PDE) by some numerical method. This step often…
Matrix operations such as matrix inversion, eigenvalue decomposition, singular value decomposition are ubiquitous in real-world applications. Unfortunately, many of these matrix operations so time and memory expensive that they are…
Dynamic graph clustering aims to detect and track time-varying clusters in dynamic graphs, revealing the evolutionary mechanisms of complex real-world dynamic systems. Matrix factorization-based methods are promising approaches for this…
Though calculations based on density functional theory (DFT) are used remarkably widely in chemistry, physics, materials science, and biomolecular research and though the modern form of DFT has been studied for almost 60 years, some…
Recently, a class of algorithms combining classical fixed point iterations with repeated random sparsification of approximate solution vectors has been successfully applied to eigenproblems with matrices as large as $10^{108} \times…
One of the most promising techniques used for studying the electronic properties of materials is based on Density Functional Theory (DFT) approach and its extensions. DFT has been widely applied in traditional solid state physics problems…
A recently proposed linear-scaling scheme for density-functional pseudopotential calculations is described in detail. The method is based on a formulation of density functional theory in which the ground state energy is determined by…
We describe a massively parallel implementation of the recently developed discontinuous Galerkin density functional theory (DGDFT) [J. Comput. Phys. 2012, 231, 2140] method, for efficient large-scale Kohn-Sham DFT based electronic structure…
In this paper, we discuss the development of a sublinear sparse Fourier algorithm for high-dimensional data. In ``Adaptive Sublinear Time Fourier Algorithm" by D. Lawlor, Y. Wang and A. Christlieb (2013), an efficient algorithm with…
Discrete transforms such as the discrete Fourier transform (DFT) or the discrete Hartley transform (DHT) furnish an indispensable tool in signal processing. The successful application of transform techniques relies on the existence of the…