Related papers: Effect of Mixed Precision Computing on H-Matrix Ve…
We present a mixed-precision benchmark called HPL-MxP that uses both a lower-precision LU factorization with a non-stationary iterative refinement based on GMRES. We evaluate the numerical stability of one of the methods of generating the…
Many emerging use cases of data mining and machine learning operate on large datasets with data from heterogeneous sources, specifically with both sparse and dense components. For example, dense deep neural network embedding vectors are…
Multiple-precision floating-point branch-free algorithms can significantly accelerate multi-component arithmetic implemented by combining hardware-based binary64 and binary32, particularly for triple- and quadruple-precision computations.…
Matrix-matrix multiplication is a key computational kernel for numerous applications in science and engineering, with ample parallelism and data locality that lends itself well to high-performance implementations. Many matrix…
Support for arithmetic in multiple precisions and number formats is becoming increasingly common in emerging high-performance architectures. From a computational scientist's perspective, our goal is to determine how and where we can safely…
Hierarchical matrix computations have attracted significant attention in the science and engineering community as exploiting data-sparse structures can significantly reduce the computational complexity of many important kernels. One…
There is a growing interest in custom spatial accelerators for machine learning applications. These accelerators employ a spatial array of processing elements (PEs) interacting via custom buffer hierarchies and networks-on-chip. The…
The matrix element method utilizes ab initio calculations of probability densities as powerful discriminants for processes of interest in experimental particle physics. The method has already been used successfully at previous and current…
General matrix-matrix multiplication (GEMM) is a cornerstone of AI computations, making tensor processing engines (TPEs) increasingly critical in GPUs and domain-specific architectures. Existing architectures primarily optimize dataflow or…
Sparse Matrix-Matrix Multiplication (SpMM) is a fundamental operation in graph computing and analytics. However, the irregularity of real-world graphs poses significant challenges to achieving efficient SpMM operation for graph data on…
In science and engineering, intelligent processing of complex signals such as images, sound or language is often performed by a parameterized hierarchy of nonlinear processing layers, sometimes biologically inspired. Hierarchical systems…
Efficient multiple precision linear numerical computation libraries such as MPLAPACK are critical in dealing with ill-conditioned problems. Specifically, there are optimization methods for matrix multiplication, such as the Strassen…
An important linear algebra routine, GEneral Matrix Multiplication (GEMM), is a fundamental operator in deep learning. Compilers need to translate these routines into low-level code optimized for specific hardware. Compiler-level…
We present an efficient numerical method for computing Hamiltonian matrix elements between non-orthogonal Slater determinants, focusing on the most time-consuming component of the calculation that involves a sparse array. In the usual case…
The machine learning explosion has created a prominent trend in modern computer hardware towards low precision floating-point operations. In response, there have been growing efforts to use low and mixed precision in general scientific…
The discretization of non-local operators, e.g., solution operators of partial differential equations or integral operators, leads to large densely populated matrices. $\mathcal{H}^2$-matrices take advantage of local low-rank structures in…
In recent years, deep learning has led to impressive results in many fields. In this paper, we introduce a multi-scale artificial neural network for high-dimensional non-linear maps based on the idea of hierarchical nested bases in the fast…
In this work, we introduce a novel methodology for divisive hierarchical clustering. Our divisive (``top-down'') approach is motivated by the fact that agglomerative hierarchical clustering (``bottom-up''), which is commonly used for…
The Strassen algorithm and Winograd's variant accelerate matrix multiplication by using fewer arithmetic operations than standard matrix multiplication. Although many papers have been published to accelerate single- as well as…
In this paper, we report the results obtained from the acceleration of multi-binary64-type multiple precision matrix multiplication with AVX2. We target double-double (DD), triple-double (TD), and quad-double (QD) precision arithmetic…