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Neural networks are used extensively in classification problems in particle physics research. Since the training of neural networks can be viewed as a problem of inference, Bayesian learning of neural networks can provide more optimal and…
Neural operators generalize neural networks to learn mappings between function spaces from data. They are commonly used to learn solution operators of parametric partial differential equations (PDEs) or propagators of time-dependent PDEs.…
This paper introduces a new neural network based prior for real valued functions on $\mathbb R^d$ which, by construction, is more easily and cheaply scaled up in the domain dimension $d$ compared to the usual Karhunen-Lo\`eve function space…
Deep learning has revolutionized the last decade, being at the forefront of extraordinary advances in a wide range of tasks including computer vision, natural language processing, and reinforcement learning, to name but a few. However, it…
Whilst deep neural networks have shown great empirical success, there is still much work to be done to understand their theoretical properties. In this paper, we study the relationship between random, wide, fully connected, feedforward…
The Bayesian approach for the feed-forward neural networks is reviewed. Its potential for usage in hadron physics is discussed. As an example of the application the study of the the two-photon exchange effect is presented. We focus on the…
Recently developed techniques have made it possible to quickly learn accurate probability density functions from data in low-dimensional continuous space. In particular, mixtures of Gaussians can be fitted to data very quickly using an…
Bayesian inference has theoretical attractions as a principled framework for reasoning about beliefs. However, the motivations of Bayesian inference which claim it to be the only 'rational' kind of reasoning do not apply in practice. They…
Modern deep learning models have achieved great success in predictive accuracy for many data modalities. However, their application to many real-world tasks is restricted by poor uncertainty estimates, such as overconfidence on…
Deep neural networks (NNs) are powerful black box predictors that have recently achieved impressive performance on a wide spectrum of tasks. Quantifying predictive uncertainty in NNs is a challenging and yet unsolved problem. Bayesian NNs,…
From the classical and influential works of Neal (1996), it is known that the infinite width scaling limit of a Bayesian neural network with one hidden layer is a Gaussian process, when the network weights have bounded prior variance.…
To adopt neural networks in safety critical domains, knowing whether we can trust their predictions is crucial. Bayesian neural networks (BNNs) provide uncertainty estimates by averaging predictions with respect to the posterior weight…
Normative and task-driven theories offer powerful top-down explanations for biological systems, yet the goals of quantitatively arbitrating between competing theories, and utilizing them as inductive biases to improve data-driven fits of…
While frame-independent predictions with deep neural networks have become the prominent solutions to many computer vision tasks, the potential benefits of utilizing correlations between frames have received less attention. Even though…
Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…
Near-term noisy intermediate-scale quantum circuits can efficiently implement implicit probabilistic models in discrete spaces, supporting distributions that are practically infeasible to sample from using classical means. One of the…
We consider a Gaussian process formulation of the multiple kernel learning problem. The goal is to select the convex combination of kernel matrices that best explains the data and by doing so improve the generalisation on unseen data.…
Physics-informed deep learning have recently emerged as an effective tool for leveraging both observational data and available physical laws. Physics-informed neural networks (PINNs) and deep operator networks (DeepONets) are two such…
We propose Radial Bayesian Neural Networks (BNNs): a variational approximate posterior for BNNs which scales well to large models while maintaining a distribution over weight-space with full support. Other scalable Bayesian deep learning…
The inability of artificial neural networks to assess the uncertainty of their predictions is an impediment to their widespread use. We distinguish two types of learnable uncertainty: model uncertainty due to a lack of training data and…