相关论文: Verifying an algorithm computing Discrete Vector F…
An active learning algorithm for the classification of high-dimensional images is proposed in which spatially-regularized nonlinear diffusion geometry is used to characterize cluster cores. The proposed method samples from estimated cluster…
Vector Quantization (VQ) techniques face significant challenges in codebook utilization, limiting reconstruction fidelity in image modeling. We introduce a Dual Codebook mechanism that effectively addresses this limitation by partitioning…
We construct the space of vector fields on a generic quantum group. Its elements are products of elements of the quantum group itself with left invariant vector fields. We study the duality between vector fields and 1-forms and generalize…
We show that some hard to detect properties of quadratic ODEs (eg certain preserved integrals and measures) can be deduced more or less algorithmically from their Kahan discretization, using Darboux Polynomials (DPs). Somewhat similar…
Accurate delineation of fine-scale structures is a very important yet challenging problem. Existing methods use topological information as an additional training loss, but are ultimately making pixel-wise predictions. In this paper, we…
We present a newly developed methodology using computer-readable fiducial markers to allow images from multiple imaging modalities to be registered automatically. This methodology makes it possible to correlate images from many surface…
We discuss a Nash-Moser/ KAM algorithm for the construction of invariant tori for {\em tame} vector fields. Similar algorithms have been studied widely both in finite and infinite dimensional contexts: we are particularly interested in the…
Complex vector analysis is widely used to analyze continuous systems in many disciplines, including physics and engineering. In this paper, we present a higher-order-logic formalization of the complex vector space to facilitate conducting…
Vector Quantization (VQ) is a method for discretizing latent representations and has become a major part of the deep learning toolkit. It has been theoretically and empirically shown that discretization of representations leads to improved…
Medical images are characterized by intricate and complex features, requiring interpretation by physicians with medical knowledge and experience. Classical neural networks can reduce the workload of physicians, but can only handle these…
Many learning problems require predicting sets of objects when the number of objects is not known beforehand. Examples include object detection, molecular modeling, and scientific inference tasks such as astrophysical source detection.…
Image compression under ultra-low bitrates remains challenging for both conventional learned image compression (LIC) and generative vector-quantized (VQ) modeling. Conventional LIC suffers from severe artifacts due to heavy quantization,…
Research on image quality assessment (IQA) remains limited mainly due to our incomplete knowledge about human visual perception. Existing IQA algorithms have been designed or trained with insufficient subjective data with a small degree of…
Vector quantization, which discretizes a continuous vector space into a finite set of representative vectors (a codebook), has been widely adopted in modern machine learning. Despite its effectiveness, vector quantization poses a…
The emergence of visual autoregressive (AR) models has revolutionized image generation while presenting new challenges for synthetic image detection. Unlike previous GAN or diffusion-based methods, AR models generate images through discrete…
DisCoPy (Distributional Compositional Python) is an open source toolbox for computing with string diagrams and functors. In particular, the diagram data structure allows to encode various kinds of quantum processes, with functors for…
We explicitly compute the Dolbeault cohomologies of certain domains in complex space generalizing the classical Hartogs figure. The cohomology groups are non-Hausdorff topological vector spaces, and it is possible to identify the reduced…
The interaction between discrete and continuous mathematics lies at the heart of many fundamental problems in applied mathematics and computational sciences. In this paper we discuss the problem of discretizing vector-valued functions…
We consider passive imaging tasks involving discrimination between known candidate objects and investigate the best possible accuracy with which the correct object can be identified. We analytically compute quantum-limited error bounds for…
A method is presented for the distributed computation of persistent homology, based on an extension of the generalized Mayer-Vietoris principle to filtered spaces. Cellular cosheaves and spectral sequences are used to compute global…