Geometric Machine Learning

Project Description
Geometric Machine Learning concerns the development and understanding of Machine Learning tools
applied to non-euclidean valued data such as graphs, meshes and manifolds. The underlying structure of the data allows us to encode geometric priors into machine learning models which improves
performance. However, the nature of the structure is often more complex than Euclidean data and doesn't always allow for a direct translation of methods between the domains. We aim to draw tools
from topics such as Differential Geometry, Graph Theory and Algebraic Topology to help understand and explain Machine Learning methods on the Geometric Domain. Initially, we will investigate how
a hierarchical structure on a graph may be beneficial in extracting more information in the graph structure and aid the flow of information throughout the graph. Geometric Machine Learning has
many applications such as drug discovery, weather modelling and social networks; the development of theoretically grounded techniques will have a positive impact in many of these application areas.

Aims and Objectives
The aims of the project will be to analyse Machine Learning problems in the Geometric domain from a theoretical perspective, which will help bridge the gap between empirical and theoretical understanding
of Geometric Machine Learning. The objective is to ultimately develop machine learning paradigms whereby the theoretical understanding.

Novelty of the research methodology
A lot of Machine Learning techniques often work well before theoretical or rigorous analysis has been capable of showing why. Whilst there are people in the field of Machine Learning which focus on this
methodology of theoretically grounded models, it is still a small minority. Hence, there are many well grounded tools from Maths and Physics which have yet to be utilised in the understanding of Machine
Learning methods.

Alignment with EPSRC
This project draws connections between the areas of Machine Learning/ Artificial Intelligence and Mathematics in a bid to provide increased understanding of Machine Learning methods. Whilst the
goal is to use this understanding to develop models with increased performance, we get the external benefits of having more explainable and robust methods pushing forward Artificial Intelligence
technologies.

AIMS's impact will be felt across domains of acute need within the UK. We expect AIMS to benefit: UK economic performance, through start-up creation; existing UK firms, both through research and addressing skills needs; UK health, by contributing to cancer research, and quality of life, through the delivery of autonomous vehicles; UK public understanding of and policy related to the transformational societal change engendered by autonomous systems.

Autonomous systems are acknowledged by essentially all stakeholders as important to the future UK economy. PwC claim that there is a £232 billion opportunity offered by AI to the UK economy by 2030 (10% of GDP). AIMS has an excellent track record of leadership in spinout creation, and will continue to foster the commercial projects of its students, through the provision of training in IP, licensing and entrepreneurship. With the help of Oxford Science Innovation (investment fund) and Oxford University Innovation (technology transfer office), student projects will be evaluated for commercial potential.

AIMS will also concretely contribute to UK economic competitiveness by meeting the UK's needs for experts in autonomous systems. To meet this need, AIMS will train cohorts with advanced skills that span the breadth of AI, machine learning, robotics, verification and sensor systems. The relevance of the training to the needs of industry will be ensured by the industrial partnerships at the heart of AIMS. These partnerships will also ensure that AIMS will produce research that directly targets UK industrial needs. Our partners span a wide range of UK sectors, including energy, transport, infrastructure, factory automation, finance, health, space and other extreme environments.

The autonomous systems that AIMS will enable also offer the prospect of epochal change in the UK's quality of life and health. As put by former Digital Secretary Matt Hancock, "whether it's improving travel, making banking easier or helping people live longer, AI is already revolutionising our economy and our society." AIMS will help to realise this potential through its delivery of trained experts and targeted research. In particular, two of the four Grand Challenge missions in the UK Industrial Strategy highlight the positive societal impact underpinned by autonomous systems. The "Artificial Intelligence and data" challenge has as its mission to "Use data, Artificial Intelligence and innovation to transform the prevention, early diagnosis and treatment of chronic diseases by 2030". To this mission, AIMS will contribute the outputs of its research pillar on cancer research. The "Future of mobility" challenge highlights the importance the autonomous vehicles will have in making transport "safer, cleaner and better connected." To this challenge, AIMS offers the world-leading research of its robotic systems research pillar.

AIMS will further promote the positive realisation of autonomous technologies through direct influence on policy. The world-leading academics amongst AIMS's supervisory pool are well-connected to policy formation e.g. Prof Osborne serving as a Commissioner on the Independent Commission on the Future of Work. Further, Dr Dan Mawson, Head of the Economy Unit; Economy and Strategic Analysis Team at BEIS will serve as an advisor to AIMS, ensuring bidirectional influence between policy objectives and AIMS research and training.

Broad understanding of autonomous systems is crucial in making a society robust to the transformations they will engender. AIMS will foster such understanding through its provision of opportunities for AIMS students to directly engage with the public. Given the broad societal importance of getting autonomous systems right, AIMS will deliver core training on the ethical, governance, economic and societal implications of autonomous systems.