Related papers: Virtual global generation in higher dimensions
We give a global geometric decomposition of continuously differentiable vector fields on $\mathbb{R}^n$. More precisely, given a vector field of class $\mathcal{C}^{1}$ on $\mathbb{R}^{n}$, and a geometric structure on $\mathbb{R}^n$, we…
Projection matrices are necessary for a large portion of rendering computer graphics. There are primarily two different types of projection matrices -- perspective and orthographic -- which are used frequently, and are traditionally treated…
While the interpretation of high-dimensional datasets has become a necessity in most industries, and is supported by continuous advances in data science and machine learning, the spatial visualization of higher-dimensional geometry has…
We present a geometric interpretation of the integration-by-parts formula on an arbitrary vector bundle. As an application we give a new geometric formulation of higher-order variational calculus.
We show that the core reasons that complex and hypercomplex valued neural networks offer improvements over their real-valued counterparts is the weight sharing mechanism and treating multidimensional data as a single entity. Their algebra…
Creating 3D head avatars is a significant yet challenging task for many applicated scenarios. Previous studies have set out to learn 3D human head generative models using massive 2D image data. Although these models are highly generalizable…
Many codes have been developed to study highly relativistic, magnetized flows around and inside compact objects. Depending on the adopted formalism, some of these codes evolve the vector potential $\mathbf{A}$, and others evolve the…
Large-scale video generative models can synthesize diverse and realistic visual content for dynamic world creation, but they often lack element-wise controllability, hindering their use in editing scenes and training embodied AI agents. We…
In this paper, we introduce a study of prolongations of homogeneous vector bundles. We give an alternative approach for the prolongation. For a given homogeneous vector bundle E, we obtain a new homogeneous vector bundle. The homogeneous…
This paper is a survey on invariants of representations of quivers and their generalizations. We present the description of generating systems for invariants and relations between generators.
Deep neural networks trained with different architectures, objectives, and datasets have been reported to converge on similar visual representations. However, what remains unknown is which visual properties models actually converge on and…
Being the most cutting-edge generative methods, diffusion methods have shown great advances in wide generation tasks. Among them, graph generation attracts significant research attention for its broad application in real life. In our…
Diffusion models have achieved impressive performance in video generation, but their iterative denoising process remains computationally expensive due to the large number of tokens processed at each timestep. Recently, progressive…
World models play a crucial role in understanding and predicting the dynamics of the world, which is essential for video generation. However, existing world models are confined to specific scenarios such as gaming or driving, limiting their…
The measurements performed by particle physics experiments must account for the imperfect response of the detectors used to observe the interactions. One approach, unfolding, statistically adjusts the experimental data for detector effects.…
Multimodal foundation models have demonstrated strong generalization, yet their ability to transfer knowledge to specialized domains such as garment generation remains underexplored. We introduce VLG, a vision-language-garment model that…
Video generation is an interesting problem in computer vision. It is quite popular for data augmentation, special effect in move, AR/VR and so on. With the advances of deep learning, many deep generative models have been proposed to solve…
We study the projective normality of the projective bundle of an Ulrich vector bundle embedded through the complete linear system of its tautological line bundle. The focus will be on Ulrich bundles defined over curves, surfaces with…
Two natural generalizations of knot theory are the study of spatial graphs and virtual knots. Our goal is to unify these two approaches into the study of virtual spatial graphs. This paper is a survey, and does not contain any new results.…
Trained on internet-scale video data, generative world models are increasingly recognized as powerful world simulators that can generate consistent and plausible dynamics over structure, motion, and physics. This raises a natural question:…