Related papers: Virtual global generation in higher dimensions
Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new…
We desribe vector bundles over a class of noncommutative curves, namely, over noncommutative nodal curves of string type and of almost string type. We also prove that in other cases the classification of vector bundles over a noncommutative…
The decoder-based machine learning generative algorithms such as Generative Adversarial Networks (GAN), Variational Auto-Encoders (VAE), Transformers show impressive results when constructing objects similar to those in a training ensemble.…
The integration of Vector Quantised Variational AutoEncoder (VQ-VAE) with autoregressive models as generation part has yielded high-quality results on image generation. However, the autoregressive models will strictly follow the progressive…
We prove two results about vector bundles on singular algebraic surfaces. First, on proper surfaces there are vector bundles of rank two with arbitrarily large second Chern number and fixed determinant. Second, on separated normal surfaces…
We address the recently introduced notions of generalized principal bundle and generalized principal connection by keeping track of global geometric properties through local coordinate transformation laws. This approach leads us to…
Hypernetworks are neural networks that generate weights for another neural network. We formulate the hypernetwork training objective as a compromise between accuracy and diversity, where the diversity takes into account trivial symmetry…
Dramatic advances in generative models have resulted in near photographic quality for artificially rendered faces, animals and other objects in the natural world. In spite of such advances, a higher level understanding of vision and imagery…
Vector graphics are widely used to represent fonts, logos, digital artworks, and graphic designs. But, while a vast body of work has focused on generative algorithms for raster images, only a handful of options exists for vector graphics.…
Vector maps are essential in autonomous driving for tasks like localization and planning, yet their creation and maintenance are notably costly. While recent advances in online vector map generation for autonomous vehicles are promising,…
Current image-to-image translation methods formulate the task with conditional generation models, leading to learning only the recolorization or regional changes as being constrained by the rich structural information provided by the…
In this chapter, we discuss normal generators for mapping class groups of surfaces. Especially, we focus on the relation between normal generation of a mapping class with its asymptotic translation lengths on the Teichm\"uller space and the…
In this article, we investigate the instability of syzygy bundles corresponding to globally generated vector bundles on smooth irreducible projective surfaces under change of polarization.
We investigate the existence of globally generated vector bundles of rank 2 with $c_1\leq 3$ on a smooth quadric threefold and determine their Chern classes. As an automatic consequence, every rank 2 globally generated vector bundle on $Q$…
Generative Adversarial Networks (GAN) have motivated a rapid growth of the domain of computer image synthesis. As almost all the existing image synthesis algorithms consider an image as a pixel matrix, the high-resolution image synthesis is…
Generative models based on diffusion have become the state of the art in the last few years, notably for image generation. Here, we analyse them in the high-dimensional limit, where data are formed by a very large number of variables. We…
As academic interest in procedural content generation (PCG) for games has increased, so has the need for methodologies for comparing and contrasting the output spaces of alternative PCG systems. In this paper we introduce and evaluate a…
Generative models have made significant progress in the tasks of modeling complex data distributions such as natural images. The introduction of Generative Adversarial Networks (GANs) and auto-encoders lead to the possibility of training on…
Generative Adversarial Networks (GANs) are machine learning methods that are used in many important and novel applications. For example, in imaging science, GANs are effectively utilized in generating image datasets, photographs of human…
Significant research has been carried out in the past half-century on defining generalised determinants for transformations between (typically real) vector spaces of different dimensions. We review three different generalisations of the…