相关论文: Levels of Distribution and the Affine Sieve

Denoising diffusion probabilistic models have recently received much research attention since they outperform alternative approaches, such as GANs, and currently provide state-of-the-art generative performance. The superior performance of…

We present in this article a survey of recent results in value distribution theory for the Gauss maps of several classes of immersed surfaces in space forms, for example, minimal surfaces in Euclidean $n$-space ($n$=3 or 4), improper affine…

This elementary survey article was prepared for a talk at the 2016 Superschool on Derived Categories and D-branes. The goal is to outline an identification of the bounded derived category of coherent sheaves on a Calabi-Yau threefold with…

Semantic segmentation is one of the most challenging tasks in computer vision. However, in many applications, a frequent obstacle is the lack of labeled images, due to the high cost of pixel-level labeling. In this scenario, it makes sense…

Knowledge distillation is considered as a training and compression strategy in which two neural networks, namely a teacher and a student, are coupled together during training. The teacher network is supposed to be a trustworthy predictor…

The complement of a complexified real line arrangement is an affine surface. It is classically known that such a space has a handle decomposition up to $2$-handles. We will describe the handle decomposition induced from Lefschetz hyperplane…

Introducing explicit constraints on the structural predictions has been an effective way to improve the performance of semantic segmentation models. Existing methods are mainly based on insufficient hand-crafted rules that only partially…

In this paper, we overview one promising avenue of progress at the mathematical foundation of deep learning: the connection between deep networks and function approximation by affine splines (continuous piecewise linear functions in…

This paper is based on the first author's lectures at the 2012 University of Regina Workshop "Connections Between Algebra and Geometry". Its aim is to provide an introduction to the theory of higher secant varieties and their applications.…

Identifying robust and accurate correspondences across images is a fundamental problem in computer vision that enables various downstream tasks. Recent semi-dense matching methods emphasize the effectiveness of fusing relevant cross-view…

In this work, we demonstrate yet another approach to tackle the amodal segmentation problem. Specifically, we first introduce a new representation, namely a semantics-aware distance map (sem-dist map), to serve as our target for amodal…

We propose a construction of affine space (or "polynomial rings") over a triangulated category, in the context of stable derivators.

This survey presents in some detail the main advances that have been recently taking place in Computational Linguistics towards the unification of the two prominent semantic paradigms: the compositional formal semantics view and the…

Motivated by control-affine systems in optimal control theory, we introduce the notion of a point-affine distribution on a manifold X - i.e., an affine distribution F together with a distinguished vector field contained in F. We compute…

These are lecture notes expanding upon a set of lectures given by G.M. at the TASI 2023 School. Part I is an introduction to topological field theory, including extended topological field theory. Part II is an introduction to generalized…

Out-of-Distribution (OOD) detection is a cornerstone for the safe deployment of AI systems in the open world. However, existing methods treat OOD detection as a binary classification problem, a cognitive flattening that fails to distinguish…

Intertwiners between \ade lattice models are presented and the general theory developed. The intertwiners are discussed at three levels: at the level of the adjacency matrices, at the level of the cell calculus intertwining the face…

Recently in joint work with E. Sert, we proved sharp boundedness results on discrete fractional integral operators along binary quadratic forms. Present work vastly enhances the scope of those results by extending boundedness to bivariate…

Stable diffusion has demonstrated strong image synthesis ability to given text descriptions, suggesting it to contain strong semantic clue for grouping objects. The researchers have explored employing stable diffusion for training-free…

We give criteria for the existence of a Serre functor on the derived category of a gauged Landau-Ginzburg model. This is used to provide a general theorem on the existence of an admissible (fractional) Calabi-Yau subcategory of a gauged…