Related papers: Information theory, Signal Analysis and Inverse Pr…
Professor Pierre Sabatier contributed much to the study of inverse problems in theory and practice. Two of these contributions were a focus on theory that actually supports practice, and the identification of well-posed aspects of inverse…
Language Models (LMs) exhibit two distinct mechanisms for knowledge acquisition: in-weights learning (i.e., encoding information within the model weights) and in-context learning (ICL). Although these two modes offer complementary…
Information theory is a statistical theory concerned with the relative state of detectors and physical systems. As a consequence, the classical framework of Shannon needs to be extended to deal with quantum detectors, possibly moving at…
For the last few years, the amount of data has significantly increased in the companies. It is the reason why data analysis methods have to evolve to meet new demands. In this article, we introduce a practical analysis of a large database…
Information Theory (IT) has been used in Machine Learning (ML) from early days of this field. In the last decade, advances in Deep Neural Networks (DNNs) have led to surprising improvements in many applications of ML. The result has been a…
Recovering microscopic couplings directly from data provides a route to solving the inverse problem in statistical field theories, one that complements the traditional-often computationally intractable-forward approach of predicting…
This book provides a comprehensive and accessible introduction to the emerging field of AI for mathematics. It covers the core principles and diverse applications of using artificial intelligence to advance mathematical research. Through…
Studying human behaviour through lifelogging has seen an increase in attention from researchers over the past decade. The opportunities that lifelogging offers are based on the fact that a lifelog, as a "black box" of our lives, offers rich…
Microwave Imaging is an essential technique for reconstructing the electrical properties of an inaccessible medium. Many approaches have been proposed employing algorithms to solve the Electromagnetic Inverse Scattering Problem associated…
Information geometry is a study of statistical manifolds, that is, spaces of probability distributions from a geometric perspective. Its classical information-theoretic applications relate to statistical concepts such as Fisher information,…
This book is written to offer a humble, but unified, treatment of e-values in hypothesis testing. It is organized into three parts: Fundamental Concepts, Core Ideas, and Advanced Topics. The first part includes four chapters that introduce…
How can we enable machines to make sense of the world, and become better at learning? To approach this goal, I believe viewing intelligence in terms of many integral aspects, and also a universal two-term tradeoff between task performance…
A new sampling method for inverse scattering problems is proposed to process far field data of one incident wave. As the linear sampling method, the method sets up ill-posed integral equations and uses the (approximate) solutions to…
Since its original publication in 1916 under the title "The Algebraic Theory of Modular Systems", the book by F. S. Macaulay has attracted a lot of scientists with a view towards pure mathematics (D. Eisenbud,...) or applications to control…
The aim of this textbook is to provide students with basic knowledge of stochastic models that may apply to telecommunications research areas, such as traffic modelling, resource provisioning and traffic management. These study areas are…
In this paper we present tools for applied researchers that re-purpose off-the-shelf methods from the computer-science field of machine learning to create a "discovery engine" for data from randomized controlled trials (RCTs). The applied…
In this essay, a general case of information systems contains quantum information systems is considered. By presenting an algorithmic method a new kind of information topology is defined and considered. Continuous maps between two…
We introduce GraphSL, a new library for studying the graph source localization problem. graph diffusion and graph source localization are inverse problems in nature: graph diffusion predicts information diffusions from information sources,…
Science is facing a reproducibility crisis. Previous work has proposed incorporating data analysis replications into classrooms as a potential solution. However, despite the potential benefits, it is unclear whether this approach is…
At the 2023 Les Houches Summer School on Theoretical Biological Physics, several students asked for some background on information theory, and so we added a tutorial to the scheduled lectures. This is largely a transcript of that tutorial,…