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Triangle counting (TC) is a fundamental problem in graph analysis and has found numerous applications, which motivates many TC acceleration solutions in the traditional computing platforms like GPU and FPGA. However, these approaches suffer…
We survey and unify recent results on the existence of accurate algorithms for evaluating multivariate polynomials, and more generally for accurate numerical linear algebra with structured matrices. By "accurate" we mean that the computed…
We propose a new numerical algorithm for computing the tensor rank decomposition or canonical polyadic decomposition of higher-order tensors subject to a rank and genericity constraint. Reformulating this computational problem as a system…
The Fast Fourier Transform (FFT) is one of the most widely used algorithms in high performance computing, with critical applications in spectral analysis for both signal processing and the numerical solution of partial differential…
The continuous shift of computational bottlenecks to the memory access and data transfer, especially for AI applications, poses the urgent needs of re-engineering the computer architecture fundamentals. Many edge computing applications,…
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…
We study the ternary quadratic problem (TQP), a quadratic optimization problem with linear constraints where the variables take values in $\{0, \pm 1\}$. While semidefinite programming (SDP) techniques are well established for $\{0,1\}$-…
The so-called block-term decomposition (BTD) tensor model has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of \emph{blocks} of rank higher than one, a…
Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and…
Networks of coupled nonlinear optical resonators have emerged as an important class of systems in ultrafast optical science, enabling richer and more complex nonlinear dynamics compared to their single-resonator or travelling-wave…
New types of designs called nested space-filling designs have been proposed for conducting multiple computer experiments with different levels of accuracy. In this article, we develop several approaches to constructing such designs. The…
Researchers are increasingly incorporating numeric high-order data, i.e., numeric tensors, within their practice. Just like the matrix/vector (MV) paradigm, the development of multi-purpose, but high-performance, sparse data structures and…
Efficient inference of Deep Neural Networks (DNNs) on resource-constrained edge devices is essential. Quantization and sparsity are key techniques that translate to repetition and sparsity within tensors at the hardware-software interface.…
Recent advances in LLMs have outpaced the computational and memory capacities of edge platforms that primarily employ CPUs, thereby challenging efficient and scalable deployment. While ternary quantization enables significant resource…
The logarithmic number system (LNS) is arguably not broadly used due to exponential circuit overheads for summation tables relative to arithmetic precision. Methods to reduce this overhead have been proposed, yet still yield designs with…
A tapered floating point encoding is proposed which uses the redundant signed radix 2 system and is based on the canonical recoding. By making use of ternary technology, the encoding has a dynamic range exceeding that of the…
Precision tuning or customized precision number representations is emerging, in these recent years, as one of the most promising techniques that has a positive impact on the footprint of programs concerning energy consumption, bandwidth…
Power awareness is fast becoming immensely important in computing, ranging from the traditional High Performance Computing applications, to the new generation of data centric workloads. In this work we describe our efforts towards a power…
In recent times Large Language Models have exhibited tremendous capabilities, especially in the areas of mathematics, code generation and general-purpose reasoning. However for specialized domains especially in applications that require…
Discrete integration is a fundamental problem in computer science that concerns the computation of discrete sums over exponentially large sets. Despite intense interest from researchers for over three decades, the design of scalable…