In a consortium led by Heriot-Watt with St Andrews, Glasgow, Strathclyde, Edinburgh and Dundee, this proposal for an "EPSRC CDT in Industry-Inspired Photonic Imaging, Sensing and Analysis" responds to the priority area in Imaging, Sensing and Analysis. It recognises the foundational role of photonics in many imaging and sensing technologies, while also noting the exciting opportunities to enhance their performance using emerging computational techniques like machine learning. Photonics' role in sensing and imaging is hard to overstate. Smart and autonomous systems are driving growth in lasers for automotive lidar and smartphone gesture recognition; photonic structural-health monitoring protects our road, rail, air and energy infrastructure; and spectroscopy continues to find new applications from identifying forgeries to detecting chemical-warfare agents. UK photonics companies addressing the sensing and imaging market are vital to our economy (see CfS) but their success is threatened by a lack of doctoral-level researchers with a breadth of knowledge and understanding of photonic imaging, sensing and analysis, coupled with high-level business, management and communication skills. By ensuring a supply of these individuals, our CDT will consolidate the UK industrial knowledge base, driving the high-growth export-led sectors of the economy whose photonics-enabled products and services have far-reaching impacts on society, from consumer technology and mobile computing devices to healthcare and security. Building on the success of our CDT in Applied Photonics, the proposed CDT will be configured with most (40) students pursuing an EngD degree, characterised by a research project originated by a company and hosted on their site. Recognizing that companies' interests span all technology readiness levels, we are introducing a PhD stream where some (15) students will pursue industrially relevant research in university labs, with more flexibility and technical risk than would be possible in an EngD project. Overwhelming industry commitment for over 100 projects represents a nearly 100% industrial oversubscription, with £4.38M cash and £5.56M in-kind support offered by major stakeholders including Fraunhofer UK, NPL, Renishaw, Thales, Gooch and Housego and Leonardo, as well as a number of SMEs. Our request to EPSRC for £4.86M will support 35 students, from a total of 40 EngD and 15 PhD researchers. The remaining students will be funded by industrial (£2.3M) and university (£0.93M) contributions, giving an exceptional 2:3 cash gearing of EPSRC funding, with more students trained and at a lower cost / head to the taxpayer than in our current CDT. For our centre to be reactive to industry's needs a diverse pool of supervisors is required. Across the consortium we have identified 72 core supervisors and a further 58 available for project supervision, whose 1679 papers since 2013 include 154 in Science / Nature / PRL, and whose active RCUK PI funding is £97M. All academics are experienced supervisors, with many current or former CDT supervisors. An 8-month frontloaded residential phase in St Andrews and Edinburgh will ensure the cohort gels strongly, and will equip students with the knowledge and skills they need before beginning their research projects. Business modules (x3) will bring each cohort back to Heriot-Watt for 1-week periods, and weekend skills workshops will be used to regularly reunite the cohort, further consolidating the peer-to-peer network. Core taught courses augmented with specialist options will total 120 credits, and will be supplemented by professional skills and responsible innovation training delivered by our industry partners and external providers. Governance will follow our current model, with a mixed academic-industry Management Committee and an independent International Advisory Board of world-leading experts.

In our work in the current edition of the CMIH we have built up a strong pool of researchers and collaborations across the board from mathematics, statistics, to engineering, medical physics and clinicians. Our work has also confirmed that imaging data is a very important diagnostic biomarker, but also that non-imaging data in the form of health records, memory tests and genomics are precious predictive resources and that when combined in appropriate ways should be the source for AI-based healthcare of the future. Following this philosophy, the new CMIH brings together researchers from mathematics, statistics, computer science and medicine, with clinicians and relevant industrial stakeholder to develop rigorous and clinically practical algorithms for analysing healthcare data in an integrated fashion for personalised diagnosis and treatment, as well as target identification and validation on a population level. We will focus on three medical streams: Cancer, Cardiovascular disease and Dementia, which remain the top 3 causes of death and disability in the UK. Whilst applied mathematics and mathematical statistics are still commonly regarded as separate disciplines there is an increasing understanding that a combined approach, by removing historic disciplinary boundaries, is the only way forward. This is especially the case when addressing methodological challenges in data science using multi-modal data streams, such as the research we will undertake at the Hub. This holistic approach will support the Hub aims to bring AI for healthcare decision making to the clinical end users.

The prospect of an AI-based revolution and its socio-economic benefits is tantalising. We want to live in a world where AI learns effectively with high performance and minimal risks. Such a world is extremely exciting. We tend to believe that AI learns higher level concepts from data, but this is not what happens. Particularly in data such as images, AI extracts rather trivial (low-level) notions from the data even when provided with millions of examples. We often hear that providing more data with high diversity should help improve the information that AI can extract. This data amassing does have though privacy and cost implications. Indeed, considerable cost comes also by the need to pre-process and to sanitise data (i.e. remove unwanted information). More critically, though, in several key applications (e.g. healthcare) some events (e.g. disease) can be rare or truly unique. Collecting more and more data will not change the relative frequency of such rare data. It appears that current AI is not data efficient: it poorly leverages the goldmine of information present in unique and rare data. This project aims to answer a key research question: **Why does AI struggle with concepts, and what is the role of unique data? ** We suspect there are several reasons why AI struggles with concepts: A) The mechanisms we use to extract information from data (known as representation learning) rely on very simple assumptions that do not reflect how real data exist in the world. For example, we know that data have correlations, and we now make simplified assumptions of no correlation at all. We propose to introduce stronger assumptions of causal relationships in the concepts we want to extract. This should in turn help us extract better information. B) To learn any model, we do have to use optimisation processes to find the parameters of the model. We find a weakness in these processes: data that are unique and rare do not get so much attention, or if they do get some, it happens by chance. This leads to considerable inconsistency in the extraction of information. In addition, sometimes wrong information is extracted, either because we found suboptimal representations or because we latched on some data that escaped from the sanitisation process -since no such perfect process can always be guaranteed. We want to understand why such inconsistency exists and propose to devise methods that can ensure that when we train models, we can consistently extract information even from rare data. There is a tight connection between B and A. Without new methods that better optimise learning functions we cannot extract representations reliably from rare data, and hence we cannot impose the causal relationships we need. There is an additional element about this work that helps answer the second part of the question. Rare and unique data may actually reveal unique causal relationships. This is a very tantalising prospect that the work we propose aims to investigate. There are considerable and broad rewards of the work we propose. We put herein the underpinnings for an AI that, because it is data efficient, should not require blind amassing of data with all the privacy fears this engenders for the general public. Because it learns high-lever concepts it will be more adept to empower decision tools that can support how decisions have been reached. And because we introduce strong causal priors in extracting these concepts, we reduce the risk of learning trivial data associations. Overall, a major goal of the AI research community is to create AI that can generalise to new unseen data beyond what was available during training time. We hope that our AI will bring us closer to this goal, thus further paving the way to broader deployment of AI to the real world.

In a consortium led by Heriot-Watt with St Andrews, Glasgow, Strathclyde, Edinburgh, Dundee, Huddersfield and NPL, the "EPSRC CDT in Use-Inspired Photonic Sensing and Metrology" responds to the focus area of "Meeting a User-Need and/or Supporting Civic Priorities" and aligns to EPSRC's Frontiers in Engineering & Technology priority and its aim to produce "tools and technologies that form the foundation of future UK prosperity". Our theme recognises the key role that photonic sensing and metrology has in addressing 21st century challenges in transport (LiDAR), energy (wind-turbine monitoring), manufacturing (precision measurement), medicine (disease sensors), agri-food (spectroscopy), security (chemical sensing) and net-zero (hydrocarbon and H2 metrology). Building on the success of our earlier centres, the addition of NPL and Huddersfield to our team reflects their international leadership in optical metrology and creates a consortium whose REF standing, UKRI income and industrial connectivity makes us uniquely able to deliver this CDT. Photonics contributes £15.2bn annually to the UK economy and employs 80,000 people--equal to automotive production and 3x more than pharmaceutical manufacturing. By 2035, more than 60% of the UK economy will rely on photonics to stay competitive. UK companies addressing the photonic sensing and metrology market are therefore vital to our economy but are threatened by a lack of doctoral-level researchers with a breadth of knowledge and understanding of photonic sensing and metrology, coupled with high-level business, management and communication skills. By ensuring a supply of these individuals, our CDT will consolidate the UK industrial knowledge base, driving this high-growth, export-led sector whose products and services have far-reaching impacts on our society. The proposed CDT will train 55 students. These will comprise at least 40 EngD students, characterised by a research project originated by a company and hosted on their site. A complementary stream of up to 15 PhD students will pursue industrially relevant research in university labs, with more flexibility and technical risk than in an EngD project. In preparing this bid, we invited companies to indicate their support, resulting in £5.5M cash commitments for 102 new students, considerably exceeding our target of 55 students, and highlighting industry's appetite for a CDT in photonic sensing and metrology. Our request to EPSRC for £6.13M will support 35 students, with the remaining students funded by industrial (£2.43M) and university (£1.02M) cash contributions, translating to an exceptional 56% cash leverage of studentship costs. The university partners provide 166 named supervisors, giving the flexibility to identify the most appropriate expertise for industry-led EngD projects. These academics' links to >120 named companies also ensure that the networks exist to co-create university-led PhD projects with industry partners. Our team combines established researchers with considerable supervisory experience (>50 full professors) with many dynamic early-career researchers, including a number of prestigious research fellowship holders. A 9-month frontloaded residential phase in St Andrews and Edinburgh will ensure the cohort gels strongly, equipping students with the knowledge and skills they need before starting their research projects. These core taught courses, augmented with electives from the other universities, will total 120 credits and will be supplemented by accredited MBA courses and training in outreach, IP, communication skills, RRI, EDI, sustainability and trusted-research. Collectively, these training episodes will bring students back to Heriot-Watt a few times each year, consolidating their intra- and inter-cohort networks. Governance will follow our current model, with a mixed academic-industry Management Committee and an International Advisory Committee of world-leading experts.

Developing new health technologies is complicated and often fails to lead to improved patient care. Successfully taking an idea through the necessary research studies and developing it to the point of use in the NHS requires many different areas of expertise. These include; understanding patients' and health professionals' needs, medical and healthcare environments, engineering and digital technologies, design, manufacturing, legal and ethical regulation, business development, how to obtain funding, and many other topics (in our application we refer to these areas the "Innovation Curriculum"). Our Hub covers a region of 1.4 million people in a region that is affected by high levels of disease and health inequalities. Our team includes all regional NHS organisations including GPs, adult and children's hospitals, mental health services and the recently introduced South Yorkshire "Integrated Care System", hundreds of researchers from the University of Sheffield and Sheffield Hallam University, many large and small companies, and patient and public groups. These partners between them have all the necessary expertise and experience in developing new Digital Health technologies to the point of use in the NHS. We will help researchers develop Digital Health technologies by training them in all aspects of the Innovation Curriculum, and by supporting them to work together with the NHS and patients on real ideas and projects. We will hold Citizen's Juries to understand the public and patients' views of Digital Health and to help design our research. We will produce sixty hours of training in Digital Health for researchers, clinicians, patients and the public, freely available and accredited through our partnership with YouTube's authoritative health content programme. We will hold regular "Calls for Ideas" where we support project teams and train them in Digital Health, providing the most promising ideas with initial project funding to help take these towards potential commercialisation.