Related papers: Lecture notes on rough paths and applications to m…

Machine learning algorithms learn a desired input-output relation from examples in order to interpret new inputs. This is important for tasks such as image and speech recognition or strategy optimisation, with growing applications in the IT…

Over the past years, machine learning has emerged as a powerful computational tool to tackle complex problems over a broad range of scientific disciplines. In particular, artificial neural networks have been successfully deployed to…

In this work we investigate the use of the Signature Transform in the context of Learning. Under this assumption, we advance a supervised framework that potentially provides state-of-the-art classification accuracy with the use of few…

Machine learning plays a role in many aspects of modern IR systems, and deep learning is applied in all of them. The fast pace of modern-day research has given rise to many different approaches for many different IR problems. The amount of…

This paper presents a new look at the neural network (NN) robustness problem, from the point of view of graph theory analysis, specifically graph curvature. Graph curvature (e.g., Ricci curvature) has been used to analyze system dynamics…

We present a novel framework for kernel learning with sequential data of any kind, such as time series, sequences of graphs, or strings. Our approach is based on signature features which can be seen as an ordered variant of sample…

In this book, we provide a comprehensive introduction to the most recent advances in the application of machine learning methods in quantum sciences. We cover the use of deep learning and kernel methods in supervised, unsupervised, and…

This thesis rigorously studies fundamental reinforcement learning (RL) methods in modern practical considerations, including robust RL, distributional RL, and offline RL with neural function approximation. The thesis first prepares the…

Recent developments in neural networks have shown the potential of estimating drag on irregular rough surfaces. Nevertheless, the difficulty of obtaining a large high-fidelity dataset to train neural networks is deterring their use in…

Parallel transport, or path development, provides a rich characterization of paths which preserves the underlying algebraic structure of concatenation. The path signature is universal among such maps: any (translation-invariant) parallel…

Learning representations of nodes in a low dimensional space is a crucial task with numerous interesting applications in network analysis, including link prediction, node classification, and visualization. Two popular approaches for this…

The signature is a representation of a path as an infinite sequence of its iterated integrals. Under certain assumptions, the signature characterizes the path, up to translation and reparameterization. Therefore, a crucial question of…

Deep learning has transformed the way we think of software and what it can do. But deep neural networks are fragile and their behaviors are often surprising. In many settings, we need to provide formal guarantees on the safety, security,…

Motivated by recent applications in rough volatility and regularity structures, notably the notion of singular modelled distribution, we study paths, rough paths and related objects with a quantified singularity at zero. In a pure path…

Neural network models are one of the most successful approaches to machine learning, enjoying an enormous amount of development and research over recent years and finding concrete real-world applications in almost any conceivable area of…

Learning representations of nodes in a low dimensional space is a crucial task with many interesting applications in network analysis, including link prediction and node classification. Two popular approaches for this problem include matrix…

These notes cover background material on trees which are used in the paper `On uniqueness of the signature of a path of variation and the reduced path group'.

The availability of large amounts of computer-readable textual data and hardware that can process the data has shifted the focus of knowledge projects towards deep learning architecture. Natural Language Processing, particularly the task of…

Machine learning plays a role in many aspects of modern IR systems, and deep learning is applied in all of them. The fast pace of modern-day research has given rise to many approaches to many IR problems. The amount of information available…

Path signatures have been proposed as a powerful representation of paths that efficiently captures the path's analytic and geometric characteristics, having useful algebraic properties including fast concatenation of paths through tensor…