Related papers: Geometry encoding for numerical simulations
Simulating complex systems remains an ongoing challenge for classical computers, while being recognised as a task where a quantum computer has a natural advantage. In both digital and analogue quantum simulations the system description is…
Graph encoder embedding, a recent technique for graph data, offers speed and scalability in producing vertex-level representations from binary graphs. In this paper, we extend the applicability of this method to a general graph model, which…
The surface code is a many-body quantum system, and simulating it in generic conditions is computationally hard. While the surface code is believed to have a high threshold, the numerical simulations used to establish this threshold are…
This paper presents a survey of ocean simulation and rendering methods in computer graphics. To model and animate the ocean's surface, these methods mainly rely on two main approaches: on the one hand, those which approximate ocean dynamics…
Text-to-CAD code generation is a long-horizon task that translates textual instructions into long sequences of interdependent operations. Existing methods typically decode text directly into executable code (e.g., bpy) without explicitly…
Learning structured task representations from human demonstrations is essential for understanding long-horizon manipulation behaviors, particularly in bimanual settings where action ordering, object involvement, and interaction geometry can…
A unique decoding algorithm for general AG codes, namely multipoint evaluation codes on algebraic curves, is presented. It is a natural generalization of the previous decoding algorithm which was only for one-point AG codes. As such, it…
Mathematical notation makes up a large portion of STEM literature, yet finding semantic representations for formulae remains a challenging problem. Because mathematical notation is precise, and its meaning changes significantly with small…
Neural radiance fields have achieved remarkable performance in modeling the appearance of 3D scenes. However, existing approaches still struggle with the view-dependent appearance of glossy surfaces, especially under complex lighting of…
Proteins perform much of the work in living organisms, and consequently the development of efficient computational methods for protein representation is essential for advancing large-scale biological research. Most current approaches…
We introduce a Geometry of Interaction model for higher-order quantum computation, and prove its adequacy for a full quantum programming language in which entanglement, duplication, and recursion are all available. Our model comes with a…
Kernel methods are powerful for machine learning, as they can represent data in feature spaces that similarities between samples may be faithfully captured. Recently, it is realized that machine learning enhanced by quantum computing is…
We show that it is possible to represent various descriptions of Quantum Mechanics in geometrical terms. In particular we start with the space of observables and use the momentum map associated with the unitary group to provide an unified…
Like [1], we present an algorithm to compute the simulation of a query pattern in a graph of labeled nodes and unlabeled edges. However, our algorithm works on a compressed graph grammar, instead of on the original graph. The speed-up of…
We consider the problem of image representation for the tasks of unsupervised learning and semi-supervised learning. In those learning tasks, the raw image vectors may not provide enough representation for their intrinsic structures due to…
Computational Intelligence (CI) techniques have shown great potential as a surrogate model of expensive physics simulation, with demonstrated ability to make fast predictions, albeit at the expense of accuracy in some cases. For many…
Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…
Geometry Problem Solving (GPS), which is a classic and challenging math problem, has attracted much attention in recent years. It requires a solver to comprehensively understand both text and diagram, master essential geometry knowledge,…
Different neural networks trained on the same dataset often learn similar input-output mappings with very different weights. Is there some correspondence between these neural network solutions? For linear networks, it has been shown that…
We interpret quantum computing as a geometric evolution process by reformulating finite quantum systems via Connes' noncommutative geometry. In this formulation, quantum states are represented as noncommutative connections, while gauge…