Related papers: Strong approximation methods in group theory, an L…

This is a lecture notes for a mini-course in Department of Mathematics, Ghent University, 14 Mar.-25 Mar. 2023.

The purpose of this article is to present a survey of our recent results on length commensurable and isospectral locally symmetric spaces. The geometric questions led us to the notion of "weak commensurability" of two Zariski-dense…

In an era where digital text is proliferating at an unprecedented rate, efficient summarization tools are becoming indispensable. While Large Language Models (LLMs) have been successfully applied in various NLP tasks, their role in…

Sequence-to-sequence models are a powerful workhorse of NLP. Most variants employ a softmax transformation in both their attention mechanism and output layer, leading to dense alignments and strictly positive output probabilities. This…

These lecture notes in Lie Groups are designed for a 1--semester third year or graduate course in mathematics, physics, engineering, chemistry or biology. This landmark theory of the 20th Century mathematics and physics gives a rigorous…

These are informal lecture notes for a three-hour minicourse on Kac-Moody groups, given at the workshop "Kac-Moody geometry" in July 2023 in Kiel. They provide a concise overview of the book "An introduction to Kac-Moody groups over…

These are lecture notes that arose from a representation theory course given by the first author to the remaining six authors in March 2004 within the framework of the Clay Mathematics Institute Research Academy for high school students,…

In this study, we propose a structured methodology that utilizes large language models (LLMs) in a cost-efficient and parsimonious manner, integrating the strengths of scholars and machines while offsetting their respective weaknesses. Our…

The contributions at the DIS2008 workshop in the working group on Diffraction and Vector Mesons are summarised.

In many learning tasks, structural models usually lead to better interpretability and higher generalization performance. In recent years, however, the simple structural models such as lasso are frequently proved to be insufficient.…

Group activities usually involve spatiotemporal dynamics among many interactive individuals, while only a few participants at several key frames essentially define the activity. Therefore, effectively modeling the group-relevant and…

We survey a research program on the strong convergence of unitary and permutation representations of discrete groups. We also take the opportunity to flesh out details that have not appeared elsewhere.

During the last years, low-rank tensor approximation has been established as a new tool in scientific computing to address large-scale linear and multilinear algebra problems, which would be intractable by classical techniques. This survey…

We build on auto-encoding sequential Monte Carlo (AESMC): a method for model and proposal learning based on maximizing the lower bound to the log marginal likelihood in a broad family of structured probabilistic models. Our approach relies…

This paper reports on the "Learning Computational Grammars" (LCG) project, a postdoc network devoted to studying the application of machine learning techniques to grammars suitable for computational use. We were interested in a more…

These are expanded notes from graduate courses about Lie algebras and Chevalley groups held at the University of Stuttgart. In the 1950s Chevalley showed how linear groups over arbitrary fields could be obtained~ -- ~by a uniform procedure~…

We provide a variable metric stochastic approximation theory. In doing so, we provide a convergence theory for a large class of online variable metric methods including the recently introduced online versions of the BFGS algorithm and its…

Self-Attentive Sequential Recommendation (SASRec) effectively captures long-term user preferences by applying attention mechanisms to historical interactions. Concurrently, the rise of Large Language Models (LLMs) has motivated research…

Sepsis remains one of the most complex and heterogeneous syndromes in intensive care, characterized by diverse physiological trajectories and variable responses to treatment. While deep learning models perform well in the early prediction…

The text below was written during two visits that Daniel Segal made at Universit{\'e} Paris 13. Danny stayed at Laboratoire de Physique des Lasers the summers of 2008 and 2009 to participate in the exploration of a novel lead in the field…