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Machine learning is driving development across many fields in science and engineering. A simple and efficient programming language could accelerate applications of machine learning in various fields. Currently, the programming languages…
There is a large body of legacy scientific code written in languages like Fortran that is not optimised to get the best performance out of heterogeneous acceleration devices like GPUs and FPGAs, and manually porting such code into parallel…
Natural language to code generation is an important application area of LLMs and has received wide attention from the community. The majority of relevant studies have exclusively concentrated on increasing the quantity and functional…
We propose a new approach to utilize quantum computers for binary linear programming (BLP), which can be extended to general integer linear programs (ILP). Quantum optimization algorithms, hybrid or quantum-only, are currently general…
Integer linear programming (ILP) encompasses a very important class of optimization problems that are of great interest to both academia and industry. Several algorithms are available that attempt to explore the solution space of this class…
Theano is a linear algebra compiler that optimizes a user's symbolically-specified mathematical computations to produce efficient low-level implementations. In this paper, we present new features and efficiency improvements to Theano, and…
We present a library of efficient implementations of deep learning primitives. Deep learning workloads are computationally intensive, and optimizing their kernels is difficult and time-consuming. As parallel architectures evolve, kernels…
Large Language Models (LLMs) have achieved remarkable performance across a wide variety of natural language tasks; however, their large size makes their inference slow and computationally expensive. Focusing on this problem, we propose to…
Algebraic characterization of logic programs has received increasing attention in recent years. Researchers attempt to exploit connections between linear algebraic computation and symbolic computation in order to perform logical inference…
Randomized Numerical Linear Algebra (RandNLA) is a powerful class of methods, widely used in High Performance Computing (HPC). RandNLA provides approximate solutions to linear algebra functions applied to large signals, at reduced…
Large language models (LLMs) are increasingly used for complex tasks that require multiple generation calls, advanced prompting techniques, control flow, and structured inputs/outputs. However, efficient systems are lacking for programming…
Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject…
Kernel methods provide an elegant and principled approach to nonparametric learning, but so far could hardly be used in large scale problems, since na\"ive implementations scale poorly with data size. Recent advances have shown the benefits…
The GEneral Matrix Multiplication (GEMM) is one of the essential algorithms in scientific computing. Single-thread GEMM implementations are well-optimised with techniques like blocking and autotuning. However, due to the complexity of…
Large Language Models (LLMs) can generate code, but can they generate fast code for complex, real-world software systems? In this study, we investigate this question using a dataset of 65 tasks mined from performance-critical open-source…
Designing high-performance kernels requires expert-level tuning and a deep understanding of hardware characteristics. Recent advances in large language models (LLMs) have enabled automated kernel generation, yet most existing systems rely…
Code generation, symbolic math reasoning, and other tasks require LLMs to produce outputs that are both syntactically and semantically correct. Constrained LLM generation is a promising direction to enforce adherence to formal grammar, but…
Educators have started to turn to Generative AI (GenAI) to help create new course content, but little is known about how they should do so. In this project, we investigated the first steps for optimizing content creation for advanced math.…
The solution of linear systems of equations is a very frequent operation and thus important in many fields. The complexity using classical methods increases linearly with the size of equations. The HHL algorithm proposed by Harrow et al.…
We show how to solve a number of problems in numerical linear algebra, such as least squares regression, $\ell_p$-regression for any $p \geq 1$, low rank approximation, and kernel regression, in time $T(A) \poly(\log(nd))$, where for a…