Related papers: An Optimizing Symbolic Algebra Approach for Genera…
Spectral decomposition of linear operators plays a central role in many areas of machine learning and scientific computing. Recent work has explored training neural networks to approximate eigenfunctions of such operators, enabling scalable…
We consider the problem of minimizing a linear function over an affine section of the cone of positive semidefinite matrices, with the additional constraint that the feasible matrix has prescribed rank. When the rank constraint is active,…
Symbolic execution is a well established method for test input generation. Despite of having achieved tremendous success over numerical domains, existing symbolic execution techniques for heap-based programs are limited due to the lack of a…
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…
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.…
The Fast Multipole Method (FMM) for the Poisson equation is extended to the case of non-axisymmetric problems in an axisymmetric domain, described by cylindrical coordinates. The method is based on a Fourier decomposition of the source into…
Recent advances in robot skill learning have unlocked the potential to construct task-agnostic skill libraries, facilitating the seamless sequencing of multiple simple manipulation primitives (aka. skills) to tackle significantly more…
Mathematical programming is widely employed across various sectors - such as logistics, energy, and workforce planning - to model and solve industrial optimisation problems, but its use requires substantial domain expertise. Large language…
We provide compact algebraic expressions that replace the lengthy symbolic-algebra-generated integrals I6 and I8 in Part I of this series of papers [1]. The MRSE entries of Part I, Table 4.3 are thus updated to simpler algebraic…
In this article we introduce a simple straightforward and powerful method involving symbolic manipulation, Picard iteration, and auxiliary variables for approximating solutions of partial differential boundary value problems. The method is…
We propose a scheme for solving mixed-integer programming problems in which the optimization problem is translated to a ground-state preparation problem on a set of bosonic quantum field modes (qumodes). We perform numerical demonstrations…
Efficient matrix determinant calculations have been studied since the 19th century. Computers expand the range of determinants that are practically calculable to include matrices with symbolic entries. However, the fastest determinant…
One of the greatest efforts of computational scientists is to translate the mathematical model describing a class of physical phenomena into large and complex codes. Many of these codes face the difficulty of implementing the mathematical…
This paper studies the design of programming languages with handlers of higher-order effectful operations -- effectful operations that may take in computations as arguments or return computations as output. We present and analyse a core…
In this paper, we propose a generalized alternating direction method of multipliers (ADMM) with semi-proximal terms for solving a class of convex composite conic optimization problems, of which some are high-dimensional, to moderate…
Automatically generating high-quality step-by-step solutions to math word problems has many applications in education. Recently, combining large language models (LLMs) with external tools to perform complex reasoning and calculation has…
Various kinds of applications take advantage of GPUs through automation tools that attempt to automatically exploit the available performance of the GPU's parallel architecture. Directive-based programming models, such as OpenACC, are one…
This paper introduces a new method of partitioning the solution space of a multi-objective optimisation problem for parallel processing, called Efficient Projection Partitioning. This method projects solutions down into a single dimension,…
We present lightweight and generic symbolic methods to improve the precison of numerical static analyses based on Abstract Interpretation. The main idea is to simplify numerical expressions before they are fed to abstract transfer…
We introduce MOSAIC, a Python program for machine learning models. Our framework is developed with in mind accelerating machine learning studies through making implementing and testing arbitrary network architectures and data sets simpler,…