Related papers: New directions in the applications of rough path t…

The path signature, having enjoyed recent success in the machine learning community, is a theoretically-driven method for engineering features from irregular paths. On the other hand, graph neural networks (GNN), neural architectures for…

Deep hedging is a promising direction in quantitative finance, incorporating models and techniques from deep learning research. While giving excellent hedging strategies, models inherently requires careful treatment in designing…

Signature-based techniques give mathematical insight into the interactions between complex streams of evolving data. These insights can be quite naturally translated into numerical approaches to understanding streamed data, and perhaps…

Combining data-driven applications with control systems plays a key role in recent Autonomous Car research. This thesis offers a structured review of the latest literature on Deep Reinforcement Learning (DRL) within the realm of autonomous…

In this paper, we propose a novel deep coherence model (DCM) using a convolutional neural network architecture to capture the text coherence. The text coherence problem is investigated with a new perspective of learning sentence…

The signature of a path is a sequence of tensors which allows to uniquely reconstruct the path. By employing the geometric theory of nonlinear systems of ordinary differential equations, we find necessary and sufficient algebraic conditions…

Many large scale problems in computational fluid dynamics such as uncertainty quantification, Bayesian inversion, data assimilation and PDE constrained optimization are considered very challenging computationally as they require a large…

Deep learning has arguably achieved tremendous success in recent years. In simple words, deep learning uses the composition of many nonlinear functions to model the complex dependency between input features and labels. While neural networks…

The signature is an infinite graded sequence of statistics known to characterise a stream of data up to a negligible equivalence class. It is a transform which has previously been treated as a fixed feature transformation, on top of which a…

Deep learning is a topic of considerable current interest. The availability of massive data collections and powerful software resources has led to an impressive amount of results in many application areas that reveal essential but hidden…

The increasing demand for autonomous systems in complex and dynamic environments has driven significant research into intelligent path planning methodologies. For decades, graph-based search algorithms, linear programming techniques, and…

Persistence diagrams (PDs), often characterized as sets of death and birth of homology class, have been known for providing a topological representation of a graph structure, which is often useful in machine learning tasks. Prior works rely…

This paper proposes to parameterize open loop controls in stochastic optimal control problems via suitable classes of functionals depending on the driver's path signature, a concept adopted from rough path integration theory. We rigorously…

Signed networks are mathematical structures that encode positive and negative relations between entities such as friend/foe or trust/distrust. Recently, several papers studied the construction of useful low-dimensional representations…

This paper establishes a comprehensive concentration theory for truncated signatures of Gaussian rough paths. The signature of a path, defined as the collection of all iterated integrals, provides a complete description of its geometric…

In recent years, a specific machine learning method called deep learning has gained huge attraction, as it has obtained astonishing results in broad applications such as pattern recognition, speech recognition, computer vision, and natural…

A profile from the Argo ocean observation array is a sequence of three-dimensional vectors composed of pressure, salinity, and temperature, appearing as a continuous curve in three-dimensional space. The shape of this curve is faithfully…

The conjoining of dynamical systems and deep learning has become a topic of great interest. In particular, neural differential equations (NDEs) demonstrate that neural networks and differential equation are two sides of the same coin.…

Control problems frequently arise in scientific and industrial applications, where the objective is to steer a dynamical system from an initial state to a desired target state. Recent advances in deep learning and automatic differentiation…

Registration is the process that computes the transformation that aligns sets of data. Commonly, a registration process can be divided into four main steps: target selection, feature extraction, feature matching, and transform computation…