Related papers: Virtual global generation in higher dimensions
In the field of computer graphics, the use of vector graphics, particularly Scalable Vector Graphics (SVG), represents a notable development from traditional pixel-based imagery. SVGs, with their XML-based format, are distinct in their…
Visual relation detection (VRD) aims to identify relationships (or interactions) between object pairs in an image. Although recent VRD models have achieved impressive performance, they are all restricted to pre-defined relation categories,…
We introduce a convenient framework for constructing and analyzing orthogonal Thom spectra arising from virtual vector bundles. This framework enables us to set up a theory of orientations and graded Thom isomorphisms with good…
We introduce the concept of a higher algebroid, generalizing the notions of an algebroid and a higher tangent bundle. Our ideas are based on a description of (Lie) algebroids as vector bundle comorphisms - differential relations of a…
Image generation from a single image using generative adversarial networks is quite interesting due to the realism of generated images. However, recent approaches need improvement for such realistic and diverse image generation, when the…
We study the generalization capacity of group convolutional neural networks. We identify precise estimates for the VC dimensions of simple sets of group convolutional neural networks. In particular, we find that for infinite groups and…
Recently, generative adversarial networks have gained a lot of popularity for image generation tasks. However, such models are associated with complex learning mechanisms and demand very large relevant datasets. This work borrows concepts…
Scalable Vector Graphics (SVG) is widely used in front-end development and UI/UX design due to its scalability, editability, and rendering efficiency. However, turning creative ideas into precise vector graphics remains a time-consuming…
Given a vector bundle $E$ of rank $r$ and degree $d$ on a curve $C$ of genus $g$, one can associate to $E$ in a natural way several other vector bundles. For example, one can take wedge powers of $E$. If $E$ is generated by global sections,…
Video-based world models have recently garnered increasing attention for their ability to synthesize diverse and dynamic visual environments. In this paper, we focus on shared world modeling, where a model generates multiple videos from a…
We introduce a collection of convex polytopes associated to a torus-equivariant vector bundle on a smooth complete toric variety. We show that the lattice points in these polytopes correspond to generators for the space of global sections…
We introduce MVDream, a diffusion model that is able to generate consistent multi-view images from a given text prompt. Learning from both 2D and 3D data, a multi-view diffusion model can achieve the generalizability of 2D diffusion models…
Understanding and replicating the real world is a critical challenge in Artificial General Intelligence (AGI) research. To achieve this, many existing approaches, such as world models, aim to capture the fundamental principles governing the…
The notion of a higher bundle gerbe is introduced to give a geometric realization of the higher degree integral cohomology of certain manifolds. We consider examples using the infinite dimensional spaces arising in gauge theories.
Projective spaces for finite-dimensional vector spaces over general fields are considered. The geometry of these spaces and the theory of line bundles over these spaces is presented. Particularly, the space of global regular sections of…
Recent progress in deep generative models has led to tremendous breakthroughs in image generation. However, while existing models can synthesize photorealistic images, they lack an understanding of our underlying 3D world. We present a new…
We classify globally generated vector bundles on the projective n-space with first Chern class = 4. This extends previous results for first Chern class at most 3, namely for 2 of Sierra and Ugaglia [J. Pure Appl. Algebra 213 (2009),…
We exhibit a set of generating relations for the modular invariant ring of a vector and a covector for the two-dimensional general linear group over a finite field.
We ask the question: to what extent can recent large-scale language and image generation models blend visual concepts? Given an arbitrary object, we identify a relevant object and generate a single-sentence description of the blend of the…
Significant progress has been made by the advances in Generative Adversarial Networks (GANs) for image generation. However, there lacks enough understanding of how a realistic image is generated by the deep representations of GANs from a…