相关论文: Dream resolution and principalization I: enough de…

This is the second paper in a project on dream (or memoryless) principalization and resolution methods. It extends this theory from the case of schemes with enough derivations, which was established in [Tem25], to general excellent schemes…

Theorem 1.2.6 of [ATW20] provides a relatively functorial logarithmic principalization of ideals on relative logarithmic orbifolds $X\to B$ in characteristic 0, relying on a delicate monomialization theorem for Kummer ideals. The paper…

In characteristic zero, we construct relative principalization of ideals for logarithmically regular morphisms of logarithmic schemes, and use it to construct logarithmically regular desingularization of morphisms. These constructions are…

Quantization has gained attention as a promising solution for the cost-effective deployment of large and small language models. However, most prior work has been limited to perplexity or basic knowledge tasks and lacks a comprehensive…

Recently the field of inverse problems has seen a growing usage of mathematically only partially understood learned and non-learned priors. Based on first principles, we develop a projectional approach to inverse problems that addresses the…

Large Language Models (LLMs) have succeeded in a variety of natural language processing tasks [Zha+25]. However, they have notable limitations. LLMs tend to generate hallucinations, a seemingly plausible yet factually unsupported output…

Dimensional regularization of Euclidean momentum space integrals is a highly successful technique in renormalization of quantum field theories. While it yields a straightforward algorithmic method, with which to evaluate diagrams beyond…

In this paper, we study the derivations, central extensions and the automorphisms of the infinite-dimensional Lie algebra W which appeared in [8] and Dong-Zhang's recent work [22] on the classification of some simple vertex operator…

A natural and intuitive idea in model quantization is to approximate each component's quantized output to match its original. Motivated by this idea, most layer-wise post-training quantization (PTQ) methods focus on weight approximation at…

Recently, Greg\'orio and Oliveira developed a proximal point scalarization method (applied to multi-objective optimization problems) for an abstract strict scalar representation with a variant of the logarithmic-quadratic function of…

We present and study approximate notions of dimensional and margin complexity, which correspond to the minimal dimension or norm of an embedding required to approximate, rather then exactly represent, a given hypothesis class. We show that…

This paper considers the problem of minimizing the ordered weighted average (or ordered median) function of finitely many rational functions over compact semi-algebraic sets. Ordered weighted averages of rational functions are not, in…

Despite several algorithmic advances in the training of convolutional neural networks (CNNs) over the years, their generalization capabilities are still subpar across several pertinent domains, particularly within open-set tasks often found…

Let $X$ be a fs logarithmic scheme that is generically logarithmically smooth, and that admits a strict closed embedding into a logarithmically smooth scheme $Y$ over a field $\kk$ of characteristic zero. We construct a simple and fast…

We describe a new algorithm for computing Whitney stratifications of complex projective varieties. The main ingredients are (a) an algebraic criterion, due to L\^e and Teissier, which reformulates Whitney regularity in terms of conormal…

In this paper we present an extension of the classical Root-Locus (RL) method where the points are calculated in the real projective plane instead of the conventional affine real plane; we denominate this extension of the Root-Locus as…

Deep learning models have gained great success in many real-world applications. However, most existing networks are typically designed in heuristic manners, thus lack of rigorous mathematical principles and derivations. Several recent…

The first objective of the paper is to estimate logarithmic partial derivative for meromorphic functions in several complex variables. Our estimations for logarithmic partial derivatives extend the results of Gundersen \cite{GG2} to the…

We present complete realization of irreducible $A_1 ^{(1)}$-modules at the critical level in the principal gradation. Our construction uses vertex algebraic techniques, the theory of twisted modules and representations of Lie conformal…

We extend Jordan's notion of principal angles to work for two subspaces of quaternionic space, and so have a method to analyze two orthogonal projections in M_n(A) for A the real, complex or quaternionic field (or skew field). From this we…