Related papers: Lecture notes on rough paths and applications to m…
These lecture notes are a personal introduction to signed graphs, concentrating on the aspects that have been most persistently interesting to me. They are just a few corners of signed graph theory; I am leaving out a great deal. The…
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…
These brief lecture notes cover the basics of neural networks and deep learning as well as their applications in the quantum domain, for physicists without prior knowledge. In the first part, we describe training using backpropagation,…
Deep learning has been the most popular machine learning method in the last few years. In this chapter, we present the application of deep learning and physics-informed neural networks concerning structural mechanics and vibration problems.…
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…
Deep Neural Networks have shown tremendous success in the area of object recognition, image classification and natural language processing. However, designing optimal Neural Network architectures that can learn and output arbitrary graphs…
Inferring topological and geometrical information from data can offer an alternative perspective on machine learning problems. Methods from topological data analysis, e.g., persistent homology, enable us to obtain such information,…
Recently, there has been an increased interest in the development of kernel methods for learning with sequential data. The signature kernel is a learning tool with potential to handle irregularly sampled, multivariate time series. In…
Modern deep learning for asset allocation typically separates forecasting from optimization. We argue this creates a fundamental mismatch where minimizing prediction errors fails to yield robust portfolios. We propose the Signature Informed…
In this paper, we introduce the branched signature model, motivated by the branched rough path framework of [Gubinelli, Journal of Differential Equations, 248(4), 2010], which generalizes the classical geometric rough path. We establish a…
Rough sheets are two-parameter analogs of rough paths. In this work the theory of integration over functions of two parameters is extended to cover the case of irregular functions by developing an appropriate notion of rough sheet. The main…
Lecture notes from the course given by Professor Julia Kempe at the summer school "Statistical physics of Machine Learning" in Les Houches. The notes discuss the so-called NTK approach to problems in machine learning, which consists of…
The expected signature kernel arises in statistical learning tasks as a similarity measure of probability measures on path space. Computing this kernel for known classes of stochastic processes is an important problem that, in particular,…
These lecture notes develop the theory of learning in deep and recurrent neuronal networks from the point of view of Bayesian inference. The aim is to enable the reader to understand typical computations found in the literature in this…
In this discussion paper, we survey recent research surrounding robustness of machine learning models. As learning algorithms become increasingly more popular in data-driven control systems, their robustness to data uncertainty must be…
The large amount of online data and vast array of computing resources enable current researchers in both industry and academia to employ the power of deep learning with neural networks. While deep models trained with massive amounts of data…
Draft of textbook chapter on neural machine translation. a comprehensive treatment of the topic, ranging from introduction to neural networks, computation graphs, description of the currently dominant attentional sequence-to-sequence model,…
Neural compression is the application of neural networks and other machine learning methods to data compression. Recent advances in statistical machine learning have opened up new possibilities for data compression, allowing compression…
Signed graphs are powerful models for representing complex relations with both positive and negative connections. Recently, Signed Graph Neural Networks (SGNNs) have emerged as potent tools for analyzing such graphs. To our knowledge, no…
The functional characterization of different neuronal types has been a longstanding and crucial challenge. With the advent of physical quantum computers, it has become possible to apply quantum machine learning algorithms to translate…