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We introduce a class of specially structured linear programming (LP) problems, which has favorable modeling capability for important application problems in different areas such as optimal transport, discrete tomography and economics. To…
Alpa automates model-parallel training of large deep learning (DL) models by generating execution plans that unify data, operator, and pipeline parallelism. Existing model-parallel training systems either require users to manually create a…
Among the paradigms for parallel and distributed computing, the one popularized with Linda, and based on tuple spaces, is one of the least used, despite the fact of being intuitive, easy to understand and to use. A tuple space is a…
Fixed-point solvers are ubiquitous in nonlinear PDEs, yet their progress collapses whenever the Jacobian at the solution carries an eigenvalue arbitrarily close to one. We ask whether such stagnation can be removed without storing long…
We report on the implementation of an algorithm for computing the set of all regular triangulations of finitely many points in Euclidean space. This algorithm, which we call down-flip reverse search, can be restricted, e.g., to computing…
Multipoint polynomial evaluation and interpolation are fundamental for modern symbolic and numerical computing. The known algorithms solve both problems over any field of constants in nearly linear arithmetic time, but the cost grows to…
Large pre-trained speech models are widely used as the de-facto paradigm, especially in scenarios when there is a limited amount of labeled data available. However, finetuning all parameters from the self-supervised learned model can be…
This paper studies bilinear saddle point problems $\min_{\bf{x}} \max_{\bf{y}} g(\bf{x}) + \bf{x}^{\top} \bf{A} \bf{y} - h(\bf{y})$, where the functions $g, h$ are smooth and strongly-convex. When the gradient and proximal oracle related to…
Modern GPUs feature specialized hardware units that enable high-performance, asynchronous dataflow execution. However, the conventional SIMT programming model is fundamentally misaligned with this task-parallel hardware, creating a…
In an era where we can not afford to checkpoint frequently, replication is a generic way forward to construct numerical simulations that can continue to run even if hardware parts fail. Yet, replication often is not employed on larger…
We propose a new computational framework that combines the recently developed time-parallel (TP) and the compound wavelet matrix (CWM) methods. The framework, termed tpCWM, offers significant computational acceleration by making…
Recently, the scale of transformers has grown rapidly, which introduces considerable challenges in terms of training overhead and inference efficiency in the scope of task adaptation. Existing works, namely Parameter-Efficient Fine-Tuning…
\textsc{Lara} is a key-value algebra that aims at unifying linear and relational algebra with three types of operation abstraction. The study of \textsc{Lara}'s expressive ability reports that it can represent relational algebra and most…
We describe a new arithmetic system for the Magma computer algebra system for working with $p$-adic numbers exactly, in the sense that numbers are represented lazily to infinite $p$-adic precision. This is the first highly featured such…
We propose a method for conducting algebraic program analysis (APA) incrementally in response to changes of the program under analysis. APA is a program analysis paradigm that consists of two distinct steps: computing a path expression that…
We describe how cross-kernel matrices, that is, kernel matrices between the data and a custom chosen set of `feature spanning points' can be used for learning. The main potential of cross-kernels lies in the fact that (a) only one side of…
We present the Matlab toolbox MacaulayLab, which implements numerical linear algebra algorithms for solving multivariate polynomial systems and rectangular multiparameter eigenvalue problems. Its structure and functionality are the result…
Principal component analysis (PCA) is a statistical technique commonly used in multivariate data analysis. However, PCA can be difficult to interpret and explain since the principal components (PCs) are linear combinations of the original…
Loop compilation for Tightly Coupled Processor Arrays (TCPAs), a class of massively parallel loop accelerators, entails solving NP-hard problems, yet depends on the loop bounds and number of available processing elements (PEs), parameters…
We propose a unified iterative framework for the solution of frictionless mechanical contact problems, which relies exclusively on the solution of standard stiffness systems. The framework is built upon a two-step fixed-point algorithm:…