Related papers: Strong approximation methods in group theory, an L…
Recent advances in Large Language Models (LLMs) have demonstrated new possibilities for accurate and efficient time series analysis, but prior work often required heavy fine-tuning and/or ignored inter-series correlations. In this work, we…
In data exploration, executing complex non-aggregate queries over large databases can be time-consuming. Our paper introduces a novel approach to address this challenge, focusing on finding an optimized subset of data, referred to as the…
To appear in the proceedings of The Phenomenology of Large N(c) QCD, Tempe, Arizona, 9-11 Jan 2002.
We investigate a slight weakening of the classical property of strong approximation, which we call almost strong approximation, for connected reductive algebraic groups over global fields with respect to special sets of valuations. While…
This note presents an elementary version of Sims's algorithm for computing strong generators of a given perm group, together with a proof of correctness and some notes about appropriate low-level data structures. Upper and lower bounds on…
The aim of this introductory lecture is to review the arguments, according to which the symmetry properties of the strong interaction reveal themselves at low energies. I first discuss the symmetries of QCD, then sketch the method used to…
Large language models (LLMs) have been garnering increasing attention in the recommendation community. Some studies have observed that LLMs, when fine-tuned by the cross-entropy (CE) loss with a full softmax, could achieve…
Lecture notes delivered in Barcellona in the fall of 2003
Extremal Graph Theory is a very deep and wide area of modern combinatorics. It is very fast developing, and in this long but relatively short survey we select some of those results which either we feel very important in this field or which…
Document retrieval is one of the most challenging tasks in Information Retrieval. It requires handling longer contexts, often resulting in higher query latency and increased computational overhead. Recently, Learned Sparse Retrieval (LSR)…
Recently, Large Language Models (LLMs) have been widely employed in Conversational Recommender Systems (CRSs). Unlike traditional language model approaches that focus on training, all existing LLMs-based approaches are mainly centered…
These are notes from talks given at ICMS, Edinburgh, 4/2007 ("Geometry and Algorithms workshop") and at Bernoulli Center, Lausanne 5/2007 ("Limits of graphs in group theory and computer science"). We survey the following type of dichotomies…
An article based on a four-lecture introductory minicourse on minimal surface theory given at the 2013 summer program of the Institute for Advanced Study and the Park City Mathematics Institute.
Despite the rise to fame of incremental variance-reduced methods in recent years, their use in nonsmooth optimization is still limited to few simple cases. This is due to the fact that existing methods require to evaluate the proximity…
This text grew out of my lecture notes for a 4-hours minicourse delivered on October 17 \& 19, 2016 during the research school "Applications of Ergodic Theory in Number Theory" -- an activity related to the Jean-Molet Chair project of…
These are slides for a talk given by the authors at the conference "Current developments and directions in the Langlands program" held in honor of Robert Langlands at the Northwestern University in May of 2008. The slides can be used as a…
This paper is concerned with long-time strong approximations of SDEs with non-globally Lipschitz coefficients.Under certain non-globally Lipschitz conditions, a long-time version of fundamental strong convergence theorem is established for…
Context engineering for large language model (LLM) agents requires distinguishing pragmatically useful information from misleading distractors. We introduce Entropic Context Shaping (ECS), an information-theoretic framework that measures…
Lexicographic Ranking SuperMartingale (LexRSM) is a probabilistic extension of Lexicographic Ranking Function (LexRF), which is a widely accepted technique for verifying program termination. In this paper, we are the first to propose sound…
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.…