Artificial intelligence (AI) is on the verge of widespread deployment in ways that will impact our everyday lives. It might do so in the form of self-driving cars or of navigation systems optimising routes on the basis of real-time traffic information. It might do so through smart homes, in which usage of high-power devices is timed intelligently based on real- time forecasts of renewable generation. It might do so by automatically coordinating emergency vehicles in the event of a major incident, natural or man-made, or by coordinating swarms of small robots collectively engaged in some task, such as search-and-rescue. Much of the research on AI to date has focused on optimising the performance of a single agent carrying out a single well-specified task. There has been little work so far on emergent properties of systems in which large numbers of such agents are deployed, and the resulting interactions. Such interactions could end up disturbing the environments for which the agents have been optimised. For instance, if a large number of self-driving cars simultaneously choose the same route based on real-time information, it could overload roads on that route. If a large number of smart homes simultaneously switch devices on in response to an increase in wind energy generation, it could destabilise the power grid. If a large number of stock-trading algorithmic agents respond similarly to new information, it could destabilise financial markets. Thus, the emergent effects of interactions between autonomous agents inevitably modify their operating environment, raising significant concerns about the predictability and robustness of critical infrastructure networks. At the same time, they offer the prospect of optimising distributed AI systems to take advantage of cooperation, information sharing, and collective learning. The key future challenge is therefore to design distributed systems of interacting AIs that can exploit synergies in collective behaviour, while being resilient to unwanted emergent effects. Biological evolution has addressed many such challenges, with social insects such as ants and bees being an example of highly complex and well-adapted responses emerging at the colony level from the actions of very simple individual agents! The goal of this project is to develop the mathematical foundations for understanding and exploiting the emergent features of complex systems composed of relatively simple agents. While there has already been considerable research on such problems, the novelty of this project is in the use of information theory to study fundamental mathematical limits on learning and optimisation in such systems. Information theory is a branch of mathematics that is ideally suited to address such questions. Insights from this study will be used to inform the development of new algorithms for artificial agents operating in environments composed of large numbers of interacting agents. The project will bring together mathematicians working in information theory, network science and complex systems with engineers and computer scientists working on machine learning, AI and robotics. The aim goal is to translate theoretical insights into algorithms that are deployed onreal world applications real systems; lessons learned from deploying and testing the algorithms in interacting systems will be used to refine models and algorithms in a virtuous circle.

Recent reports from the Royal Society, the government Cybersecurity strategy, as well as the National Cyber Security Center highlight the importance of cybersecurity, in ensuring a safe information society. They highlight the challenges faced by the UK in this domain, and in particular the challenges this field poses: from a need for multi-disciplinary expertise and work to address complex challenges, that span from high-level policy to detailed engineering; to the need for an integrated approach between government initiatives, private industry initiatives and wider civil society to tackle both cybercrime and nation state interference into national infrastructures, from power grids to election systems. They conclude that expertise is lacking, particularly when it comes to multi-disciplinary experts with good understanding of effective work both in government and industry. The EPSRC Doctoral Training Center in Cybersecurity addresses this challenge, and aims to train multidisciplinary experts in engineering secure IT systems, tacking and interdicting cybercrime and formulating effective public policy interventions in this domain. The training provided provides expertise in all those areas through a combination of taught modules, and training in conducting original world-class research in those fields. Graduates will be domain experts in more than one of the subfields of cybersecurity, namely Human, Organizational and Regulatory aspects; Attacks, Defences and Cybercrime; Systems security and Cryptography; Program, Software and Platform Security and Infrastructure Security. They will receive training in using techniques from computing, social sciences, crime science and public policy to find appropriate solutions to problems within those domains. Further, they will be trained in responsible research and innovation to ensure both research, but also technology transfer and policy interventions are protective of people's rights, are compatible with democratic institutions, and improve the welfare of the public. Through a program of industrial internships all doctoral students will familiarize themselves with the technologies, polices and also challenges faced by real-world organizations, large and small, trying to tackle cybersecurity challenges. Therefore they will be equipped to assume leadership positions to solve those problems upon graduation.

The CDT will train the next generation of leaders in statistics and statistical machine learning, who will be able to develop widely-applicable novel methodology and theory, as well as create application-specific methods, leading to breakthroughs in real-world problems in government, medicine, industry and science. The research will focus on the development of applicable modern statistical theory and methods as well as on the underpinnings of statistical machine learning. The research will be strongly linked to applications. There is an urgent national need for graduates from this CDT. Large volumes of complicated data are now routinely collected in all sectors of society, encompassing electronic health records, massive scientific datasets, governmental data, and data collected through the advent of the digital economy. The underpinning techniques for exploiting these data come from statistics and machine learning. Exploiting such data is crucial for future UK prosperity. However, several reports from government and learned societies have identified a lack of individuals able to exploit this data. In many situations, existing methodology is insufficient. Off-the-shelf approaches may be misleading due to a lack of reproducibility or sampling biases which they do not correct. Furthermore, understanding the underlying mechanisms is often desired: scientifically valid, interpretable and reproducible results are needed to understand scientific phenomena and to justify decisions, particularly those affecting individuals. Bespoke, model-based statistical methods are needed, that may need to be blended with statistical machine learning approaches to deal with large data. Individuals that can fulfill these more sophisticated demands are doctoral level graduates in statistics who are well versed in the foundations of machine learning. Yet the UK only graduates a small number of statistics PhDs per year, and many of these graduates will not have been exposed to machine learning. The Centre will bring together Imperial and Oxford, two top statistics groups, as equal partners, offering an exceptional training environment and the direct involvement of absolute research leaders in their fields. The supervisor pool will include outstanding researchers in statistical methodology and theory as well as in statistical machine learning. We will use innovative and student-led teaching, focussing on PhD-level training. Teaching cuts across years and thus creates strong cohort cohesion not just within a year group but also between year groups. We will link theoretical advances to application areas through partner interactions as well as through a placement of students with users of statistics. The CDT has a large number of high profile partners that helped shape our application priority areas (digital economy, medicine, engineering, public health, science) and that will co-fund and co-supervise PhD students, as well as co-deliver teaching elements.

A growing consensus identifies autonomous systems as core to future UK prosperity, but only if the present skills shortage is addressed. The AIMS CDT was founded in 2014 to address the training of future leaders in autonomous systems, and has established a strong track record in attracting excellent applicants, building cohorts of research students and taking Oxford's world-leading research on autonomy to achieve industrial impact. We seek the renewal of the CDT to cement its successes in sustainable urban development (including transport and finance), and to extend to applications in extreme and challenging environments and smart health, while strengthening training on the ethical and societal impacts of autonomy. Need for Training: Autonomous systems have been the subject of a recent report from the Royal Society, and an independent review from Professor Dame Wendy Hall and Jérôme Pesenti. Both reports emphatically underline the economic importance of AI to the UK, estimating that "AI could add an additional USD $814 billion (£630bn) to the UK economy by 2035". Both reports also highlight the urgency of training many more skilled experts in autonomy: the summary of the Royal Society's report states "further support is needed to build advanced skills in machine learning. There is already high demand for people with advanced skills, and additional resources to increase this talent pool are critically needed." In contrast with pure Artificial Intelligence CDTs, AIMS places emphasis on the challenges of building end-to-end autonomous systems: such systems require not just Machine Learning, but the disciplines of Robotics and Vision, Cyber-Physical Systems, Control and Verification. Through this cross-disciplinary training, the AIMS CDT is in a unique position to provide positive economic and societal impacts for autonomous systems by 1) growing its existing strengths in sustainable urban development, including autonomous vehicles and quantitative finance, and 2) expanding its scope to the two new application pillars of extreme and challenging environments and smart health. AIMS itself provides evidence for the strong and increasing demand for training in these areas, with an increase in application numbers from 49 to 190 over the last five years. The increase in applications is mirrored by the increase in interest from industrial partners, which has more than doubled since 2014. Our partners span all application areas of AIMS and their contributions, which include training, internships and co-supervision opportunities, will immerse our students in a variety of research challenges linked with real-world problems. Training programme: AIMS has and will provide broad cohort training in autonomous intelligent systems; theoretical foundations, systems research, industry-initiated projects and transferable skills. It covers a comprehensive range of topics centered around a hub of courses in Machine Learning; subsequent spokes provide training in Robotics and Vision, Control and Verification, and Cyber-Physical Systems. The cohort-focused training program will equip our students with both core technical skills via weekly courses, research skills via mini and long projects, as well as transferable skills, opportunities for public engagement, and training on entrepreneurship and IP. The growing societal impacts of autonomous systems demand that future AIMS students receive explicit training in responsible and ethical research and innovation, which will be provided by ORBIT. Additionally, courses on AI ethics, safety, governance and economic impacts will be delivered by Oxford's world-leading Future of Humanity Institute, Oxford Uehiro Centre for Practical Ethics and Oxford Martin Programme on Technology and Employment.

Probabilistic AI involves the embedding of probability models, probabilistic reasoning and measures of uncertainty within AI methods. The ProbAI hub will develop a world leading, diverse and UK-wide research programme in probabilistic AI, that will develop the next generation of mathematically-rigorous, scalable and uncertainty-aware AI algorithms. It will have far-reaching impact across many aspects of AI, including: (1) The sudden and rapid growth of AI systems has led to a new impetus for businesses, governments and creators of AI tools to understand and convey the inherent uncertainties in their systems. A probabilistic approach to AI provides a framework to represent and manipulate uncertainty about models and predictions and already plays a central role in scientific data analysis, robotics and cognitive science. The consequential impact arising from from such developments has the potential to be wide-ranging and substantial: from utilising a probabilistic approach for effective resource allocation (healthcare), prioritisation of actions (infrastructure planning), pattern recognition (cyber security) and the development of robust strategies to mitigate risks (finance). (2) It is possible to gain important theoretical insights into AI models and algorithms through studying their, often probabilistic, limiting behaviour in different asymptotic scenarios. Such results can help with understanding why AI methods work, and how best to choose appropriate architectures - with the potential to substantially reduce the computational cost and carbon footprint of AI. (3) Recent breakthroughs in generative models are based on simulating stochastic processes. There is huge potential to both use these ideas to help develop efficient and scalable probabilistic AI methods more generally; and also to improve and extend current generative models. The latter may lead to more computationally efficient and robust methods, to generative models that use different stochastic processes and are suitable for different types of data, or to novel approaches that can give a level of certainty to the output of a generative model. (4) Models from AI are increasingly being used as emulators. For example, fitting a deep neural network to realisations of a complex computer model for the weather, can lead to more efficient approaches to forecasting the weather. However, in most applications for such methods to be used reliably requires that the emulators report a measure of uncertainty -- so the user can know when the output can be trusted. Also, building on recent generalisations of Bayes updates gives new approaches to incorporate known physical constraints and other structure into these neural network emulators, leading to more robust methods that generalise better outside the training sampler and that have fewer parameters and are easier to fit. Developing these new, practical, general-purpose probabilistic AI methods requires overcoming substantial challenges, and at their heart many of these challenges are mathematical. The hub will unify a fragmented community with interests in Probabilistic AI and bring together UK researchers across the breadth of Applied Mathematics, Computer Science, Probability and Statistics. The hub will promote the area of probabilistic AI widely, encouraging and facilitating cross-disciplinary mathematics research in AI, and has substantial flexibility to fund the involvement of researchers from across the breadth of the UK during its lifetime. ProbAI will draw on and benefit from the well-established world-leading strength in areas relevant to probabilistic AI across different areas of Mathematics and Computer Science, with the aim of making the UK the world-leader in probabilistic AI.