Related papers: Virtual global generation in higher dimensions
Vector graphics are widely used in digital art and highly favored by designers due to their scalability and layer-wise properties. However, the process of creating and editing vector graphics requires creativity and design expertise, making…
The field of generative models has recently witnessed significant progress, with diffusion models showing remarkable performance in image generation. In light of this success, there is a growing interest in exploring the application of…
We train deep generative models on datasets of reflexive polytopes. This enables us to compare how well the models have picked up on various global properties of generated samples. Our datasets are complete in the sense that every single…
We show that on a generic curve, a bundle obtained by successive extensions is stable. We compute the dimension of the set of such extensions. We use degeneration methods specializing the curve to a chain of elliptic components
Differential calculi are obtained for quantum homogeneous spaces by extending Woronowicz' approach to the present context. Representation theoretical properties of the differential calculi are investigated. Connections on quantum…
Complex vector light modes with a spatial variant polarization distribution have become topical of late, enabling the development of novel applications in numerous research fields. Key to this is the remarkable similarities they hold with…
Optical vector beam generation based on the superposition technique [Phys. Rev. Lett. 107(5), 053601 (2011)] has attracted significant interest in both fundamental and applied optics due to its simplicity and cost-effectiveness. In this…
We present a generalization of multiview varieties as closures of images obtained by projecting subspaces of a given dimension onto several views, from the photographic and geometric points of view. Motivated by applications in Computer…
With the growing popularity of text-to-image generative models, there has been increasing focus on understanding their risks and biases. Recent work has found that state-of-the-art models struggle to depict everyday objects with the true…
We present VecFusion, a new neural architecture that can generate vector fonts with varying topological structures and precise control point positions. Our approach is a cascaded diffusion model which consists of a raster diffusion model…
A new genus $g=g(X,\ce)$ is defined for the pairs $(X,\ce)$ that consist of $n$-dimensional compact complex manifolds $X$ and ample vector bundles $\ce$ of rank $r$ less than $n$ on $X$. In case $r=n-1$, $g$ is equal to curve genus. Above…
The accelerating advancement of generative models has introduced new challenges for detecting AI-generated images, especially in real-world scenarios where novel generation techniques emerge rapidly. Existing learning paradigms are likely…
Recent advancements in computer vision have highlighted the scalability of Vision Transformers (ViTs) across various tasks, yet challenges remain in balancing adaptability, computational efficiency, and the ability to model higher-order…
Scalable Vector Graphics (SVG) are ubiquitous in modern 2D interfaces due to their ability to scale to different resolutions. However, despite the success of deep learning-based models applied to rasterized images, the problem of vector…
We provide a framework connecting several well known theories related to the linearity of graded modules over graded algebras. In the first part, we pay a particular attention to the tensor products of graded bimodules over graded algebras.…
In real world domains, most graphs naturally exhibit a hierarchical structure. However, data-driven graph generation is yet to effectively capture such structures. To address this, we propose a novel approach that recursively generates…
Vector fields in the expanding Universe are considered within the multidimensional theory of General Relativity. Vector fields in general relativity form a three-parametric variety. Our consideration includes the fields with a nonzero…
We develop an alternative view on the concept of connections over a vector bundle map, which consists of a horizontal lift procedure to a prolonged bundle. We further focus on prolongations to an affine bundle and introduce the concept of…
Generation of photo-realistic images, semantic editing and representation learning are a few of many potential applications of high resolution generative models. Recent progress in GANs have established them as an excellent choice for such…
We obtain effective results for the global generation of pluritheta line bundles on moduli spaces of vector bundles on curves. The main ingredient is an independent result giving an upper bound on the dimension of the Hilbert scheme of…