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.

There is a silent but steady revolution happening in all sectors of the economy, from agriculture through manufacturing to services. In virtually all activities in these sectors, processes are being constantly monitored and improved via data collection and analysis. While there has been tremendous progress in data collection through a panoply of new sensor technologies, data analysis has revealed to be a much more challenging task. Indeed, in many situations, the data generated by sensors often comes in quantities so large that most of it ends up being discarded. Also, many times, sensors collect different types of data about the same phenomenon, the so-called multimodal data. However, it is hard to determine how the different types of data relate to each other or, in particular, what one sensing modality tells about another sensing modality. In this project, we address the challenge of making sensing of multimodal data, that is, data that refers to the same phenomenon, but reveals different aspects from it and is usually presented in different formats. For example, several modalities can be used to diagnose cancer, including blood tests, imaging technologies like magnetic resonance (MR) and computed tomography (CT), genetic data, and family history information. Each of these modalities is typically insufficient to perform an accurate diagnosis but, when considered together, they usually lead to an undeniable conclusion. Our departing point is the realization that different sensing modalities have different costs, where "cost" can be financial, refer to safety or societal issues, or both. For instance, in the above example of cancer diagnosis, CT imaging involves exposing patients to X-ray radiation which, ironically, can provoke cancer. MR imaging, on the other hand, exposes patients to strong magnetics fields, a procedure that is generally safe. A pertinent question is then whether we can perform both MR and CT imaging, but use a lower dose of radiation in CT (obtaining a poor-resolution CT) and, afterward, improve the resolution of CT by leveraging information from MR. This, of course, requires learning what type of information can be transferred between different modalities. Another example scenario is autonomous driving, in which sensors like radar, LiDAR, or infrared cameras, although much more expensive than conventional cameras, collect information that is critical to driving in safe conditions. In this case, is it possible to use cheaper, lower-resolution sensors and enhance them with information from conventional cameras? These examples also demonstrate that many of the scenarios in which we collect multimodal data also have robustness requirements, namely, precision of diagnosis in cancer detection and safety in autonomous driving. Our goal is then to develop data processing algorithms that effectively capture common information across multimodal data, leverage these structures to improve reconstruction, prediction, or classification of the costlier (or all) modalities, and are verifiable and robust. We do this by combining learning-based approaches with model-based approaches. Over the last years, learning-based approaches, namely deep learning methods, have reached unprecedented performance, and work by extracting information from large datasets. Unfortunately, they are vulnerable to so-called generalization errors, which occur when the data to which they are applied differs significantly from the data used in the learning process. On the other hand, model-based methods tend to be more robust, but have poorer performance in general. The approaches we propose to explore use learning-based techniques to determine correspondences across modalities, extracting relevant common information, and integrate that common information into model-based schemes. Their ultimate goal is to compensate cost and quality imbalances across the modalities while, at the same time, providing robustness and verifiability.

Addressing the health needs of a growing and ageing population is a central challenge facing modern society. Technology is enabling the collection of increasingly large and heterogeneous biomedical data sets, yet interpreting such data to gain knowledge about disease mechanisms and clinical and preventative strategies is still a major open problem. Artificial Intelligence (AI) techniques hold huge promise to provide an integrative framework for extracting knowledge from data, with a high potential for fundamental and clinical breakthroughs with significant impact both on public health and on the future of the UK bioeconomy. The ambition of the proposed CDT is to train a cadre of highly skilled interdisciplinary scientists who will spearhead the development and deployment of AI techniques in the biomedical sector. Achieving our long-term aims will require several hurdles to be overcome. The biomedical sector poses unique methodological challenges to AI technology, due to the need of interpretable models which can quantify uncertainties within predictions. It also presents formidable cultural and technical language barriers, requiring honed communication skills to overcome disciplinary boundaries. Perhaps most importantly, it requires researchers and practitioners with a keen awareness of the societal, legal and ethical dimension of their research, who are able to reach out to societal stakeholders, and to anticipate and engage with the potential issues arising from deploying AI technology in the biomedical sector. We will realise our ambition through a structured training programme: students will initially acquire the foundational skills in a Master by Research first year, which includes taught courses on the technical, biomedical and socio-ethical aspects of biomedical AI, and provides multiple opportunities to directly experience interdisciplinary research through rotation projects. Students will then acquire in depth research experience through an interdisciplinary PhD, bridging between the University of Edinburgh's world-leading institutions pursuing informatics and biomedical research. Students will benefit from a large and exceptionally distinguished faculty of potential supervisors: over 60 academics including several fellows of the Royal Society/ Royal Society of Edinburgh, and over forty recipients of prestigious fellowships from the ERC, the research councils, and biomedical charities such as the Wellcome Trust. This training programme will be interleaved with intensive training in interdisciplinary communication and science communication, and will offer multiple opportunities to engage with external stakeholders including industrial and NHS internships.

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.

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.