相关论文: The Canonical Distortion Measure for Vector Quanti…

In this work, we explore the quantization of diffusion models in extreme compression regimes to reduce model size while maintaining performance. We begin by investigating classical vector quantization but find that diffusion models are…

Multivariate functions encountered in high-dimensional uncertainty quantification problems often vary most strongly along a few dominant directions in the input parameter space. We propose a gradient-based method for detecting these…

We introduce a saliency-based distortion layer for convolutional neural networks that helps to improve the spatial sampling of input data for a given task. Our differentiable layer can be added as a preprocessing block to existing task…

Sampling and quantization are standard practices in signal and image processing, but a theoretical understanding of their impact is incomplete. We consider discrete image registration when the underlying function is a one-dimensional…

We explore the quantization of classical models with position-dependent mass (PDM) terms constrained to a bounded interval in the canonical position. This is achieved through the Weyl-Heisenberg covariant integral quantization by properly…

We aim to analyze the relation between two random vectors that may potentially have both different number of attributes as well as realizations, and which may even not have a joint distribution. This problem arises in many practical…

Quantum classifiers are trainable quantum circuits used as machine learning models. The first part of the circuit implements a quantum feature map that encodes classical inputs into quantum states, embedding the data in a high-dimensional…

While neural representations for static 3D shapes are widely studied, representations for deformable surfaces are limited to be template-dependent or lack efficiency. We introduce Canonical Deformation Coordinate Space (CaDeX), a unified…

The distribution closeness testing (DCT) assesses whether the distance between a distribution pair is at least $\epsilon$-far. Existing DCT methods mainly measure discrepancies between a distribution pair defined on discrete one-dimensional…

Quantizers play a critical role in digital signal processing systems. Recent works have shown that the performance of quantization systems acquiring multiple analog signals using scalar analog-to-digital converters (ADCs) can be…

A canonical transformation is performed on the phase space of a number of homogeneous cosmologies to simplify the form of the scalar (or, Hamiltonian) constraint. Using the new canonical coordinates, it is then easy to obtain explicit…

Convolutional Neural Networks (CNNs) have proven to be a powerful state-of-the-art method for image classification tasks. One drawback however is the high computational complexity and high memory consumption of CNNs which makes them…

In this paper, we propose Complex Diffusion Maps (CDM), a novel diffusion mapping framework that aims to reveal the dominant complex harmonics of high-dimensional data. Inspired by the local Gaussian kernel relevant to the heat equation and…

We consider quantizing an $Ld$-dimensional sample, which is obtained by concatenating $L$ vectors from datasets of $d$-dimensional vectors, to a $d$-dimensional cluster center. The distortion measure is the weighted sum of $r$th powers of…

Representing probability distributions by the gradient of their density functions has proven effective in modeling a wide range of continuous data modalities. However, this representation is not applicable in discrete domains where the…

Contrastive Language-Image Pretraining has emerged as a prominent approach for training vision and text encoders with uncurated image-text pairs from the web. To enhance data-efficiency, recent efforts have introduced additional supervision…

Color quantization represents an image using a fraction of its original number of colors while only minimally losing its visual quality. The $k$-means algorithm is commonly used in this context, but has mostly been applied in the…

The electromagnetic field is canonically quantized in the presence of a linear, dispersive and dissipative medium that is in uniform motion. Specifically we calculate the change in the normal modes of the coupled matter-field system and…

Approximating non-linear kernels using feature maps has gained a lot of interest in recent years due to applications in reducing training and testing times of SVM classifiers and other kernel based learning algorithms. We extend this line…

We introduce a distortion measure for images, Wasserstein distortion, that simultaneously generalizes pixel-level fidelity on the one hand and realism or perceptual quality on the other. We show how Wasserstein distortion reduces to a pure…