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The search for drug molecules which bind strongly to specific proteins is an integral part of the drug discovery process. To this end, virtual screening algorithms which aim to screen a large number of potential binders in silico have been developed. These use scoring functions to assess the probability that a computationally predicted binding pose is correct, and to predict the binding affinity. More recently, research has turned to deep learning-based scoring functions which use binding data to build a model of binding behaviour; this is the main subject of this thesis. The first chapter is an introduction to the concepts and literature which are relevant to the subsequent chapters. This includes fragment-based drug discovery, virtual screening, and machine learning methods in virtual screening. It also touches on the problem of input attribution, where importance is assigned to the atoms or bonds in the input to deep learning- based scoring functions, as well as the problem of machine learning algorithms learning to classify based on dataset biases rather than learning the physical interactions which govern protein-ligand binding. A publication on convolutional neural networks for virtual screening makes up most of the second chapter. The problem of learning training set biases rather than physical interactions is explored using several experiments, and a method of dataset augmentation to combat this effect is proposed. A carefully curated validation set, constructed separately from any training data, is used to show increased use of protein information in classification decisions; input attribution is used on several case studies to show the same. The third chapter concerns the design and engineering decisions involved in PointVS. This is a software package for rapid prototyping and testing of graph neural networks for pose classification and affinity prediction. It includes a variety of scripts for auxiliary tasks such as dataset generation, input attribution visualisation and logging, and has been used by another member of the Oxford Protein Informatics Group for a paper which is briefly described. PointVS forms the basis of another publication, under review at the time of writing; this makes up the fourth chapter. In collaboration with another student, graph neural networks are used for pose classification and affinity prediction, with training and testing sets set up carefully to avoid information leakage. PointVS is compared to several other methods, achieving competitive performance. Attribution scores from PointVS are converted to protein hotspot maps, which are used as input into a generative model for fragment elaboration. This out-performs the results using standard physics-derived hotspot maps, which is evidence that the graph neural networks can pick out important protein-ligand interactions. Finally, we take a more macroscopic view of the field of machine learning- based scoring functions. We conclude that while promising, there are several obstacles that must be overcome in order to train models which truly 'understand' the universe of protein-ligand binding. We propose that an input attribution ground truth test set as an area for possible further study, and identify a possible method to generate one. We conclude that many reported improvements of machine learning-based scoring functions over their physics-inspired predecessors are over-estimated, and that a more dynamic view of binding which takes water into account explicitly is required.

Statistical models which allow generating simulations without providing access to the density of the distribution are called simulator models. They are commonly developed by scientists to represent natural phenomena and depend on physically meaningful parameters. Analogously, generative networks produce samples from a probability distribution by transforming draws from a noise (or latent) distribution via a neural network; as for simulator models, the density is unavailable. These two frameworks, developed independently from different communities, can be grouped into the class of 'generative models'; compared to statistical models that explicitly specify the density, they are more powerful and flexible. For generative networks, typically, a single point estimate for the parameters (or weights) is obtained by minimizing an objective function through gradient descent enabled by automatic differentiation. In contrast, for simulator models, samples from a probability distribution for the parameters are usually obtained via some statistical algorithm. Nevertheless, in both cases, the inference methods rely on common principles that exploit simulations. In this thesis, I follow the principle of assessing how a probabilistic model matches an observation by Scoring Rules. This generalises common statistical practices based on the density function and, with specific 'Scoring Rules', allows tackling generative models. After a detailed introduction and literature review in Chapter 1, the first part of this thesis (Chapters 2 and 3) is concerned with methods to infer probability distributions for the parameters of simulator models. Specifically, Chapter 2 contributes to the traditional 'Bayesian Likelihood-Free Inference' literature with a new way to learn summary statistics, defined as the sufficient statistics of the best exponential family approximation to the simulator model. In contrast, Chapter 3 departs from tradition by defining a new posterior distribution based on the generalised 'Bayesian inference framework', rather than motivated as an approximation to thestandard posterior. The posterior is defined through Scoring Rules computable for simulator models and is robust to outliers. In the second part of the thesis (Chapters 4 and 5), I study 'Scoring Rule Minimization' to determine the weights of generative networks; for specific choices of Scoring Rules, this approach better captures the variability of the data than popular alternatives. I apply generative networks trained in this way to uncertainty-sensitive tasks: in Chapter 4 I use them to provide a probability distribution over the parameters of simulator models, thus falling back to the theme of Chapters 2 and 3; instead, in Chapter 5, I consider probabilistic forecasting, also establishing consistency of the training objective with dependent training data. Finally, I conclude in Chapter 6 with some final thoughts and directions for future work.

Multi-task learning is critical for real-life applications of machine learning. Modern approaches are characterised by algorithmic complexity, often unjustified, leading to impractical solutions. In contrast, this thesis demonstrates that a minimalistic alternative is possible, showing the attractiveness of simple methods. 'In defence of the Unitary Scalarisation for Deep Multi-task Learning' motivates the rest of the thesis, showing that none of the more complex multi-task optimisers outperforms the simple per-task gradient summation when compared on fair grounds. Furthermore, it proposes a novel look at multi-task optimisers from the regularisation standpoint. The rest of this thesis focuses on deep reinforcement learning, a general framework for sequential decision-making. In particular, we look at the setting when observations (inputs to the model) are represented as graphs, i.e., collections of interconnected nodes. In 'Scaling GNNs to High-Dimensional Continuous Control' and 'The Role of Morphology in Graph-Based Incompatible Control', we learn a single control policy for agents of different morphology by representing the observation set elements as graphs and deploy graph neural networks (including transformers). In the former chapter, we devise a simple method to scale graph networks by freezing some parts of the network to stabilise learning and prevent overfitting. In the latter chapter, we show that graph connectivity might be suboptimal for the downstream task demonstrating that less-constrained transformers perform significantly better without having the graph connectivity information. Finally, in the 'Generalisable Branching Heuristic for a SAT Solver', we apply multi-task reinforcement learning to Boolean satisfiability, a fundamental problem in academia and industrial applications. We demonstrate that Q-learning, a staple reinforcement learning algorithm equipped with graph neural networks for function approximation, can learn a generalisable branching heuristic. We hope our findings will steer the further development of the field: creating more complex benchmarks, adding assumptions on task similarities and a model capacity, and exploring other objective functions rather than focusing on the average performance across the tasks.

We face many challenges in deploying high-performance neural networks in practice. These challenges are predominantly due to the size of neural networks and apply to both training and inference. Compressing neural networks to make them train and run more efficiently is therefore crucial and has been a parallel line of research from the early days of neural networks development. The two main compression techniques in deep learning, which are the focus of this thesis, are pruning and quantization. This thesis explores how the information from higher-order gradients (meta-gradients) be used to improve deep learning compression. We start by identifying a fundamental limitation in the formulation of pruning: Although many methods, such as saliency-based pruning, follow pruning by a training or fine-tuning stage, parameter saliencies only look at a snapshot of parameters without taking into account the "trainability" of the parameters. We show how meta-gradients can be used as a more informative signal to find better trainable subnetworks at initialization. We then look at quantized neural networks and show how meta-gradients can be used in a regularization scheme to "learn" models with inherent robustness against post-training quantization. Finally, we look at the dual compression problem, i.e. using neural networks to compress data sources. We start with images and propose a simple autoencoder-free architecture where we store weights of a neural network instead of RGB values of image pixels. We then use meta-gradients to meta-learn a base network to amortize the cost of training one network per input. A significant advantage of our learning compression is that it becomes agnostic to the data type, and we present results on various data types beyond 2D images. Importantly, we evaluate the usefulness of standard DNN compression techniques, e.g., quantization, for this new type of neural network.

Although deep neural networks (DNNs) attain excellent performance on the specific tasks they are trained for, this often seems to be obtained using easier-to-learn proxies for the truly relevant concepts. The problem with proxies is that they cannot be relied on in new situations - the proxy departs from the true concept. And DNNs will very likely be deployed in new situations because the world is always changing, and training data are never exhaustive. Unfortunately, existing approaches are limited in their ability to diagnose the bad proxies being relied on by a DNN. We also cannot accurately characterise a model's generalisation performance on different kinds of data beyond its training task. These limitations additionally prevent us from developing systems that do not rely on bad proxies. To improve this situation, this thesis introduces two new test generation procedures for image classification DNNs. These improve on existing approaches by identifying more kinds of inputs for which a particular DNN gives incorrect outputs. This is achieved by exploiting generative machine learning to solve the test oracle problem in new ways. The first new procedure trains a generative network to directly output test cases that identify failures. The second dynamically perturbs the activation values of a pretrained generative network as it generates new examples - the perturbations adjust the features of the generated data so that they also induce failures in the DNN being evaluated. Besides the primary contribution of these algorithms, this thesis also presents an empirical finding: standard adversarial training that aims to increase model robustness surprisingly decreases DNNs' ability to generalise correctly to changes in high-level features such as object position, orientation, shape or colour.

Machine learning (ML) has caused a fundamental shift in how we practice science, with many now placing learning from data at the focal point of their research. As the complexity of the scientific problems we want to study increases, and the amount of data generated by today's scientific experiments grows, ML is helping to automate, accelerate and enhance traditional workflows. Emerging at the forefront of this revolution is a field called scientific machine learning (SciML). The central goal of SciML is to more tightly combine existing scientific understanding with ML, generating powerful ML algorithms which are informed by our prior knowledge. A plethora of approaches exist for incorporating scientific principles into ML and expectations are rising for SciML to address some of the biggest challenges in science. However, the field is burgeoning and many questions are still arising. A major one is whether SciML approaches can scale to more complex, real-world problems. Much SciML research is at a proof-of-concept stage, where techniques are validated on simplified, toy problems. Yet, understanding how well they scale to more complex problems is essential for them to become widely applicable. This question is of central focus in this thesis. Firstly, multiple different physics-informed ML approaches are designed for three complex, real-world, domain-specific case studies taken from the fields of lunar science and geophysics, and their performance and scalability is assessed. Secondly, the scalability of physics-informed neural networks, a popular and general SciML approach, for solving differential equations with large domains and high frequency solutions is evaluated and improved. Common observations across these studies are discussed, and significant advantages and underlying limitations are identified, highlighting the importance of designing scalable SciML techniques.

Deep learning, and in particular neural networks (NNs), have seen a surge in popularity over the past decade. Their use has increased in, often safety-critical, decision-making systems such as self-driving, medical diagnosis and natural language processing. Thus, there is an urgent need for methodologies to aid the development of AI-based systems. In this thesis, we investigate the role that explainability and uncertainty can play in providing safety assurance for AI applications based on neural networks. Our first contribution, studied primarily for decisions based on neural network models, is a method to derive local explanations with provable robustness and optimality guarantees called Optimal Robust Explanations (OREs). OREs imply the model prediction and thus provide sufficient reason for the model decision. We develop an algorithm to extract OREs that uses a neural network verification tool Marabou or Neurify as a black-box solver. We demonstrate the usefulness of OREs in model development and safety assurance tasks such as model debugging, bias evaluation and repair of explanations provided by non-formal explainers such as Anchors. Our second contribution focuses on an autonomous driving scenario enabled by an end-to-end Bayesian neural network (BNN) controller trained on data from the Carla simulator. BNNs have the ability to capture the uncertainty within the learning model, while retaining the main advantages intrinsic to neural networks. We propose two methods to evaluate the safety of decisions of BNN controllers in the presence of uncertainty in offline and online settings. We develop techniques to approximate bounds on the safety of the entire system with respect to given criteria, with high probability and a priori statistical guarantees. Our final contribution a collection of methods that combine the uncertainty information available from Bayesian neural networks with local explanation methods. We show how to formulate Bayesian versions of existing feature scoring explanation methods, as well as a Bayesian version of our OREs, called Bayes-optimal robust explanations (B-OREs). We define a covering explanation, which condenses the information produced from a number of BNN posterior samples into a single explanation, with a probability of the likelihood that this explanation is an explanation of a random sample. In the case of Bayes-optimal robust covering explanations, we obtain a probability for how likely the explanation is to imply the prediction. We combine Bayesian covering explanations with a notion of feature uncertainty, to give an ordering of importance to each feature that appears in the covering explanation, and we show that feature uncertainty can be used to provide a global overview of the input features that the model most associates with each class.

This thesis concerns sample-efficient embodied machine learning. Machine learning success in sequential decision problems has been limited to domains with a narrow range of goals, requiring orders more experience than humans. Additionally, they lack the ability to generalise to new related goals. In contrast, humans are continual learners. Given their embodiment and computational constraints, humans are forced to reuse knowledge (compressed abstractions of repeated structures present across their lifetime) to tackle novel scenarios in as sample-efficient and safe manner as possible. In robotics, similar traits are desired, given they are also embodied learners. Taking inspiration from humans, the central claim of this thesis is that knowledge abstractions acquired from prior experience can be used to design domain-independent sample-efficient algorithms that improve generalisation across modular domains. We refer to modular domains as Markov decision processes (MDPs) whose optimal policies can be obtained when reasoning and acting occurs over compressed abstractions shared across them. The challenge is how to discover these abstractions with minimal supervision and sample-efficiently. Additionally, for embodied machine learning it is important the approach supports continuous, potentially unbounded, state-action spaces. Adhering to these constraints, we first develop novel self- (Chapter 3) and weakly-supervised (Chapter 4) knowledge abstraction, domain adaptation, methods for zero-shot generalisation to unseen domains. We demonstrate their potential on robotic applications including sim2real transfer (Chapter 3) and generalisation using a human-robot command interface (Chapter 4). We continue by developing novel unsupervised knowledge abstraction, transfer learning, methods for sample-efficient adaptation to unseen domains (Chapters 5 and 6). We highlight their relevance in robotics and continual learning. We introduce a hierarchical KL-regularised RL approach based on novel theory behind the transferability-expressivity trade-off of abstractions (Chapter 5) and develop the first, to our knowledge, bottleneck-options approach adhering to the aforementioned embodied machine learning constraints (Chapter 6).