相关论文: Verifying an algorithm computing Discrete Vector F…

Equational Unification is a critical problem in many areas such as automated theorem proving and security protocol analysis. In this paper, we focus on XOR-Unification, that is, unification modulo the theory of exclusive-or. This theory…

Coherent diffraction imaging (CDI) is a promising imaging technique revealing most of the information from diffraction measurements. An ideal CDI should reconstruct complex-valued object from a single-shot far-field diffraction without any…

Scalable Vector Graphics (SVG) is a popular format on the web and in the design industry. However, despite the great strides made in generative modeling, SVG has remained underexplored due to the discrete and complex nature of such data. We…

Artefacts in quantum-mimic Optical Coherence Tomography are considered detrimental because they scramble the images even for the simplest objects. They are a side effect of autocorrelation which is used in the quantum entanglement mimicking…

Computer based recognition and detection of abnormalities in ECG signals is proposed. For this purpose, the Support Vector Machines (SVM) are combined with the advantages of Hermite transform representation. SVM represent a special type of…

The ever-growing complexity of mathematical proofs makes their manual verification by mathematicians very cognitively demanding. Autoformalization seeks to address this by translating proofs written in natural language into a formal…

The study of quantum evolution on graphs for diversified topologies is beneficial to modeling various realistic systems. A systematic method, the dimerized decomposition, is proposed to analyze the dynamics on an arbitrary network. By…

We present a novel diffusion-based framework for synthesizing 2D vector fields from sparse, coherent inputs (i.e., streamlines) while maintaining physical plausibility. Our method employs a conditional denoising diffusion probabilistic…

Formal verification of complex algorithms is challenging. Verifying their implementations goes beyond the state of the art of current automatic verification tools and usually involves intricate mathematical theorems. Certifying algorithms…

Embedding vectors are widely used for representing unstructured data and searching through it for semantically similar items. However, the large size of these vectors, due to their high-dimensionality, creates problems for modern vector…

Using vertex algebra techniques, we determine a set of generators for the cohomology ring of the Hilbert schemes of points on an arbitrary smooth projective surface over the field of complex numbers.

We study ordinary differential equations in the complex domain given by meromorphic vector fields on K\"ahler compact complex surfaces. We prove that if such an equation has a maximal single valued solution with Zariski-dense image (in…

Deep neural networks with discrete latent variables offer the promise of better symbolic reasoning, and learning abstractions that are more useful to new tasks. There has been a surge in interest in discrete latent variable models, however,…

Humans are excellent at perceiving illusory outlines. We are readily able to complete contours, shapes, scenes, and even unseen objects when provided with images that contain broken fragments of a connected appearance. In vision science,…

Vector tomography methods intend to reconstruct and visualize vector fields in restricted domains by measuring line integrals of projections of these vector fields. Here, we deal with the reconstruction of irrotational vector functions from…

Recently, Vector Quantized AutoRegressive (VQ-AR) models have shown remarkable results in text-to-image synthesis by equally predicting discrete image tokens from the top left to bottom right in the latent space. Although the simple…

Image co-segmentation is important for its advantage of alleviating the ill-pose nature of image segmentation through exploring the correlation between related images. Many automatic image co-segmentation algorithms have been developed in…

We propose a flexible algorithm for feature detection and hypothesis testing in images with ultra low signal-to-noise ratio using cubical persistent homology. Our main application is in the identification of atomic columns and other…

Vector quantization (VQ) transforms continuous image features into discrete representations, providing compressed, tokenized inputs for generative models. However, VQ-based frameworks suffer from several issues, such as non-smooth latent…

Variational quantum algorithms (VQAs) are considered as one of the most promising candidates for achieving quantum advantages on quantum devices in the noisy intermediate-scale quantum (NISQ) era. They have been developed for numerous…