Related papers: Deep Learning and Geometric Deep Learning: an intr…
We propose a categorical semantics for machine learning algorithms in terms of lenses, parametric maps, and reverse derivative categories. This foundation provides a powerful explanatory and unifying framework: it encompasses a variety of…
Machine learning is finding increasingly broad application in the physical sciences. This most often involves building a model relationship between a dependent, measurable output and an associated set of controllable, but complicated,…
Applying deep-learning models to geophysical applications has attracted special attentions during the past a couple of years. There are several papers published in this domain involving with different topics primarily focusing on synthetic…
This paper presents a comprehensive review of loss functions and performance metrics in deep learning, highlighting key developments and practical insights across diverse application areas. We begin by outlining fundamental considerations…
Deep learning has become a popular tool across many scientific fields, including the study of differential equations, particularly partial differential equations. This work introduces the basic principles of deep learning and the Deep…
This book provides an introduction to the mathematical analysis of deep learning. It covers fundamental results in approximation theory, optimization theory, and statistical learning theory, which are the three main pillars of deep neural…
A fundamental question in deep learning concerns the role played by individual layers in a deep neural network (DNN) and the transferable properties of the data representations which they learn. To the extent that layers have clear roles,…
Deep learning is a group of exciting new technologies for neural networks. Through a combination of advanced training techniques and neural network architectural components, it is now possible to create neural networks that can handle…
Classical linear metric learning methods have recently been extended along two distinct lines: deep metric learning methods for learning embeddings of the data using neural networks, and Bregman divergence learning approaches for extending…
These notes were compiled as lecture notes for a course developed and taught at the University of the Southern California. They should be accessible to a typical engineering graduate student with a strong background in Applied Mathematics.…
In the last decade or so, we have witnessed deep learning reinvigorating the machine learning field. It has solved many problems in the domains of computer vision, speech recognition, natural language processing, and various other tasks…
Deep learning's performance has been extensively recognized recently. Graph neural networks (GNNs) are designed to deal with graph-structural data that classical deep learning does not easily manage. Since most GNNs were created using…
The success of deep learning has revolutionized many fields of research including areas of computer vision, text and speech processing. Enormous research efforts have led to numerous methods that are capable of efficiently analyzing data,…
Deep learning has been shown to be successful in a number of domains, ranging from acoustics, images, to natural language processing. However, applying deep learning to the ubiquitous graph data is non-trivial because of the unique…
One of the most important parts of Artificial Neural Networks is minimizing the loss functions which tells us how good or bad our model is. To minimize these losses we need to tune the weights and biases. Also to calculate the minimum value…
Deep learning has recently become one of the most popular sub-fields of machine learning owing to its distributed data representation with multiple levels of abstraction. A diverse range of deep learning algorithms are being employed to…
Understanding what graph neural networks can learn, especially their ability to learn to execute algorithms, remains a central theoretical challenge. In this work, we prove exact learnability results for graph algorithms under…
In this paper, we introduce a novel way to use geometric deep learning for knot data by constructing a functor that takes knots to graphs and using graph neural networks. We will attempt to predict several knot invariants with this…
Deep learning methods are increasingly being applied to problems in medicine and healthcare. However, few epidemiologists have received formal training in these methods. To bridge this gap, this article introduces to the fundamentals of…
We propose a paradigm to deep-learn the ever-expanding databases which have emerged in mathematical physics and particle phenomenology, as diverse as the statistics of string vacua or combinatorial and algebraic geometry. As concrete…