Domain specific abstractions for optimising convolutions and linear algebra
File(s)
Author(s)
Stow, Edward
Type
Thesis
Abstract
This thesis explores the use of domain-specific abstractions in linear algebra and related computations to model data-layouts and algorithm implementations, and to generate optimised programs for them automatically. This is achieved by the development of languages and methods to define semantics, schedules, and data-layouts that can be co-optimised. The work is split, first focusing on discrete convolutions: where a formalisation of filters produces an algebra that captures many arithmetic reducing optimisations, and data-layout choices enable a trade-off between resolution and bit-depth in cellular processing arrays. The focus then shifts to tensor computations: where data-layouts for structures of multiple tensors exploit sparsity, and intermediate representations allow explicitly undefined, composable data-layouts that enable automatic co-optimisations of schedule and storage. The use and range of data-layouts that these abstractions support is evaluated as well as the performance of the resulting compiled programs.
Version
Open Access
Date Issued
2025-04-02
Date Awarded
2026-04-01
Copyright Statement
Attribution-NonCommercial 4.0 International Licence (CC BY-NC)
License URL
Advisor
Kelly, Paul
Sponsor
Engineering and Physical Sciences Research Council
James Dyson Foundation
Publisher Department
Department of Computing
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)