328.77 million terabytes of data are created each day. To put this in perspective, if you were to store all this data on CDs, you would need over 1.5 trillion CDs each day. Modern machine learning (ML), specifically deep learning (DL), works to interpret this massive data, uncover fascinating patterns, and make predictions. DL has been transformative in numerous areas, from healthcare and retail to finance and manufacturing. This rapid advancement, often led by large technology corporations, is evidenced by breakthroughs in conversational AI, like ChatGPT / GPT4, and text-guided image synthesis. Today, one in seven UK businesses have adopted at least one form of ML technology. Despite this success, a challenge lurks in the realm of modern ML. The data we collect from various sources tends to be unstructured and complex. For instance, our Facebook comments are influenced not only by our past conversations, mood, and thoughts but also by the intricate interplay between these factors. Similarly, the interaction between proteins depends on their shape and other interactions. To extract meaningful insights from data and solve real-world problems, we need to consider these complex 'higher-order relationships', which play a key role in areas such as creating accurate 3D models for safer self-driving cars, predicting drug-target interactions for effective drug repurposing during pandemics, and accurately modeling brain neurochemistry for developing life-saving medicine against Alzheimer's disease. Unfortunately, most current machine learning systems focus mainly on modeling pairwise connections and overlook these higher-order relationships. This limits their capability to represent and analyze complex data, especially acquired in scientific areas by X-ray scanners, electron microscopy, or 3D laser scanners. My fellowship aims to harness the potential of big data by developing a new paradigm of deep learning, which encompasses higher order relations at its core and considers the data topology - an important branch of mathematics studying the "shape of data". My proposed research will achieve this in three key objectives: (1) I will develop Unifying Complexes (UCs), novel data representations that simplify working with higher-order relationships while preserving the hierarchical nature of data. At present, the industry standard relies on graphs, which only model pairwise relationships. (2) Existing deep learning models won't readily adapt to the novel UCs I will be developing in Objective 1. I will therefore create a variety of deep learning models tailored to work natively with these UCs. From discriminative to generative, these models will enable learning from rich and complex data. (3) Lastly, I will deploy the UCs and the models developed in Objectives 1 and 2 to address a variety of challenges in multiple applications, including 3D computer vision, drug screening, discovery and design, and in building new and practically relevant theories of deep learning. Thanks to the resources and the uninterrupted time provided by Future Leaders Fellowship (FLF), as a result of UNTOLD, I will be delivering an open-source comprehensive software suite designed to harness the full potential of big, complex data. Beyond scientific dissemination, the widespread adoption of the DL models I develop as part of UNTOLD, will have substantial socioeconomic impacts such as improved augmented and virtual reality, safer self-driving cars, personalized medicine, and better understanding of rare diseases. This will both position the UK as a leader in cutting-edge ML research and will gradually enhance its presence across all sectors using ML to convert complex data into actionable insights.

Over the past decade, deep learning methods have had an enormous impact on the academic and industrial worlds, opening new multi-billion markets ranging from driver-less cars to speech recognition and machine translation. Deep learning has been an emerging technology for decades; it took an orchestrated scientific and engineering effort as well as harnessing of the increasing computational power and large datasets to achieve an overarching technological and societal impact. Most of the successful deep learning methods such as Deep Convolutional Neural Networks (DCNNs) are based on classical signal/image processing models that limit their applicability to data with underlying Euclidean grid-like structure, e.g., 2D/3D images or audio signals. Non-Euclidean (graph-or manifold-structured) data are becoming increasingly abundant; prominent examples include 3D objects (represented as meshes or point clouds) in CV and graphics, as well as social networks, graphs of molecules, and interactomes. Until recently, this has been a significant obstacle precluding the adoption of ML tools in some of the most promising fields. To bridge the gap between Euclidean (e.g., images, videos & speech) and non-Euclidean (e.g., graph and manifolds) ML umbrella terms have recently been coined, such as ''Geometric Deep Learning'' (GDL). Such methods have gained a keen interest in the ML community the past couple of years since graphs can model very abstract systems of relations or interactions, and thus potentially applied across the board. Recent successful examples of the application of non-Euclidean deep learning are as diverse as semantic segmentation on meshes and point clouds, drug-design and event classification in particle physics. Nevertheless, the focus is mainly on discriminative approaches (e.g., classification and segmentation problems) and limited progress has been made towards generative methodologies (i.e., unsupervised methodologies that model the distribution of data) on non-Euclidean spaces. The drawback of discriminative methodologies is that they require a massive amount of labelled, mainly manually, data, which is very expensive, or even impossible to find in many settings. On the other hand, generative approaches can operate in unsupervised scenarios and can even be used to produce data that can be utilised to train discriminative approaches. Currently, available generative frameworks have been developed primarily for Euclidean data (e.g., images, videos) and are not suitable for the non-Euclidean setting. GNoMON aims at bridging this gap by developing a mathematically principled framework for designing and implementing Generative Models for non-Euclidean domains such as graphs or manifolds. We will explore challenging problems in 3D CV and graphics. Nevertheless, the developed techniques will be designed in such a way to be general so that can aid the research in many other fields.

Promoting improved understanding of how children's daily lives are influenced by the digital world that now surrounds them and how they experience family, peer and school life as a result represents a substantial challenge and opportunity relative to facilitating positive mental health and development for children and young people. Historically, researchers have emphasised the role of supportive parenting and positive school experiences (including peer relationships) as primary social environmental influences on children's mental health, with most interventions targeting family and school-based influences aimed at remediating poor mental health outcomes for children and young people. It is increasingly recognised that the digital environment constitutes a new dimension or common denominator to these traditional agencies of socialisation influence on children's mental health. Yet, little progress has been made in equipping parents, teachers and the professional agencies that work with families and schools with new knowledge that harnesses potential strengths while offering protection from substantial risks posed to children by the digital world. How do we equip parents, teachers, practitioners, policy makers and youth themselves with information, support and resources that promotes positive mental health in a contemporary (and future) digital age? Addressing this core challenge represents the primary objective of our multi-disciplinary e-Nurture network. While significant advances have been made in relation to highlighting and understanding the genetic and biological underpinnings of poor mental health and mental health disorders in recent years, it is recognised that the social environments children experience and interact with remain a substantial influence on their positive and negative mental health trajectories (even when genetic factors are considered). Three primary areas of social environmental influence on children's mental health have dominated past research and practice in this area. First, family socialisation processes, specifically parenting practices are recognised as a substantive influence on children's mental health. Second, peer influences are noted as an important influence on children's mental health. Third, school-based factors are recognised as a further influence on children's mental health and development. Increasingly, the digital environment is recognised as a factor that both infuses traditional agencies of socialisation for children and that can influence children directly. Policy makers have recently directed significant attention to the prevalence rates and support needs among children and young people who experience mental health problems. The digital environment and its potential for positive and negative influences on children's well-being, mental health and development has also received substantial research, policy and media attention. Building on this policy platform, the primary objectives of our network are to (1) explore how the digital environment has changed the ways in which children experience and interact with family, school and peer-based influences and what these changes mean for children's mental health, (2) identify how we can recognise and disentangle digital risks from opportunities when working with families, schools and professional agencies in developing intervention programmes to improve mental health outcomes for children and young people, and (3) identify how we effectively incorporate and disseminate this new knowledge to engage present and future practice models and the design and development of digital platforms and interventions aimed at promoting mental health and reducing negative mental health trajectories for young people. The network will engage a collaborative, cross sectoral approach to facilitating impacts by directly engaging academic, charity, industry, policy and front-line beneficiaries (e.g. families, parents, schools, teachers, children and young people).

Promoting improved understanding of how children's daily lives are influenced by the digital world that now surrounds them and how they experience family, peer and school life as a result represents a substantial challenge and opportunity relative to facilitating positive mental health and development for children and young people. Historically, researchers have emphasised the role of supportive parenting and positive school experiences (including peer relationships) as primary social environmental influences on children's mental health, with most interventions targeting family and school-based influences aimed at remediating poor mental health outcomes for children and young people. It is increasingly recognised that the digital environment constitutes a new dimension or common denominator to these traditional agencies of socialisation influence on children's mental health. Yet, little progress has been made in equipping parents, teachers and the professional agencies that work with families and schools with new knowledge that harnesses potential strengths while offering protection from substantial risks posed to children by the digital world. How do we equip parents, teachers, practitioners, policy makers and youth themselves with information, support and resources that promotes positive mental health in a contemporary (and future) digital age? Addressing this core challenge represents the primary objective of our multi-disciplinary e-Nurture network. While significant advances have been made in relation to highlighting and understanding the genetic and biological underpinnings of poor mental health and mental health disorders in recent years, it is recognised that the social environments children experience and interact with remain a substantial influence on their positive and negative mental health trajectories (even when genetic factors are considered). Three primary areas of social environmental influence on children's mental health have dominated past research and practice in this area. First, family socialisation processes, specifically parenting practices are recognised as a substantive influence on children's mental health. Second, peer influences are noted as an important influence on children's mental health. Third, school-based factors are recognised as a further influence on children's mental health and development. Increasingly, the digital environment is recognised as a factor that both infuses traditional agencies of socialisation for children and that can influence children directly. Policy makers have recently directed significant attention to the prevalence rates and support needs among children and young people who experience mental health problems. The digital environment and its potential for positive and negative influences on children's well-being, mental health and development has also received substantial research, policy and media attention. Building on this policy platform, the primary objectives of our network are to (1) explore how the digital environment has changed the ways in which children experience and interact with family, school and peer-based influences and what these changes mean for children's mental health, (2) identify how we can recognise and disentangle digital risks from opportunities when working with families, schools and professional agencies in developing intervention programmes to improve mental health outcomes for children and young people, and (3) identify how we effectively incorporate and disseminate this new knowledge to engage present and future practice models and the design and development of digital platforms and interventions aimed at promoting mental health and reducing negative mental health trajectories for young people. The network will engage a collaborative, cross sectoral approach to facilitating impacts by directly engaging academic, charity, industry, policy and front-line beneficiaries (e.g. families, parents, schools, teachers, children and young people).