Related papers: The Master Thesis of Mosh\'e Flato
The central topic of this thesis is the study of some properties of a class of complex compact manifolds~: Moishezon manifolds. In the first part, we generalize J.-P. Demailly's holomorphic Morse inequalities to the case of a line bundle…
In this article we study motives corresponding to the moduli stacks of G-shtukas and their local models. In particular we deal with the question of describing their motivic fundamental invariants. As an application, we provide a criterion…
Test-Time Scaling (TTS) enhances the reasoning ability of large language models (LLMs) by allocating additional computation during inference. However, existing approaches primarily rely on output-level sampling while overlooking the role of…
A simple framework is presented for unified applications in various fields of colloidal research, with minimal additional concepts & definitions. Several case studies concerning glass transition & crystallization are provided under the…
This talk is dedicated to various aspects of Mirror Symmetry. It summarizes some of the mathematical developments that took place since M. Kontsevich's report at the Z\"urich ICM and provides an extensive, although not exhaustive,…
The sparse Mixture of Experts(MoE) architecture has evolved as a powerful approach for scaling deep learning models to more parameters with comparable computation cost. As an important branch of large language model(LLM), MoE model only…
In this paper we introduce a simple modal logic framework to reason about the expertise of an information source. In the framework, a source is an expert on a proposition $p$ if they are able to correctly determine the truth value of $p$ in…
Mixture-of-experts networks (MoEs) have demonstrated remarkable efficiency in modern deep learning. Despite their empirical success, the theoretical foundations underlying their ability to model complex tasks remain poorly understood. In…
This dissertation gives an overview of Martin Lof's dependant type theory, focusing on its computational content and addressing a question of possibility of fully canonical and computable semantic presentation.
The flavor moonshine hypothesis is formulated to suppose that all particle masses (leptons, quarks, Higgs and gauge particles -- more precisely, their mass ratios) are expressed as coefficients in the Fourier expansion of some modular forms…
Machine learning (ML) has transformed numerous fields, but understanding its foundational research is crucial for its continued progress. This paper presents an overview of the significant classical ML algorithms and examines the…
We present Self-MoE, an approach that transforms a monolithic LLM into a compositional, modular system of self-specialized experts, named MiXSE (MiXture of Self-specialized Experts). Our approach leverages self-specialization, which…
The famous Bloch--Kato conjecture implies that for a field $F$ containing a primitive $p$th root of unity, the cohomology ring of the absolute Galois group $G_F$ of $F$ with $\mathbb{F}_p$ coefficients is generated by degree one elements.…
Configurational analysis can be seen as the adaptation to urban space of complex network approaches already developed in social network analysis (Freeman 1979). Its central idea is that elements of urban form should be analysed with respect…
The distance on a set is a comparative function. The smaller the distance between two elements of that set, the closer, or more similar, those elements are. Fr\'echet axiomatized the distance into what is today known as a metric. In this…
The purpose of this project is to outline various philosophies on the metaphysics of mathematics that have been prominent since the time of Cantor, highlighting some biographical aspects that have influenced these ideas as well. The main…
The paper is proposing a short discussion on the ancient knowledge of Platonic solids, in particular, by Italic people.
This note is based on our recent results on QCD with varying number of flavors of fundamental fermions. Topics include unusual, strong dynamics in the preconformal, confining phase, the physics of the conformal window and the role of…
The topic of the glass transition gives rise to a a wide diversity of views. It is, accordingly, characterized by a lack of agreement on which would be the most profitable theoretical perspective. In this chapter, I provide some elements…
The thesis deals with recognizing diffeomorphisms from fractal properties of discrete orbits, generated by iterations of such diffeomorphisms. The notion of fractal properties of a set refers to the box dimension, the Minkowski content and…