Related papers: Comparison-limited Vector Quantization

Consider a problem where 4k given vectors need to be partitioned into k clusters of four vectors each. A cluster of four vectors is called a quad, and the cost of a quad is the sum of the component-wise maxima of the four vectors in the…

Schmidt decomposition of a vector can be understood as writing the singular value decomposition (SVD) in vector form. A vector can be written as a linear combination of tensor product of two dimensional vectors by recursively applying…

It is revealed that there is a link between the quantization approach employed and the dimension of the vector parameter which can be accurately estimated by a quantized estimation system. A critical quantity called inestimable dimension…

We address the problem of indirect quantization of a source subject to a mean-squared error distortion constraint. A well-known result of Wolf and Ziv is that the problem can be reduced to a standard (direct) quantization problem via a…

Vectorization is a technique that replaces a set-valued optimization problem with a vector optimization problem. In this work, by using an extension of Gerstewitz function [1], a vectorizing function is defined to replace a given set-valued…

Quantizing images into discrete representations has been a fundamental problem in unified generative modeling. Predominant approaches learn the discrete representation either in a deterministic manner by selecting the best-matching token or…

We study the witness-counting problem: given a set of vectors $V$ in the $d$-dimensional vector space over $\mathbb{F}_2$, a target vector $t$, and an integer $k$, count all ways to sum-up exactly $k$ different vectors from $V$ to reach…

This paper proposes a parallel approach for the Vector Quantization (VQ) problem in image processing. VQ deals with codebook generation from the input training data set and replacement of any arbitrary data with the nearest codevector. Most…

Motivated by the problem of effectively executing clustering algorithms on very large data sets, we address a model for large scale distributed clustering methods. To this end, we briefly recall some standards on the quantization problem…

Vector quantization via random projection followed by scalar quantization is a fundamental primitive in machine learning, with applications ranging from similarity search to federated learning and KV cache compression. While dense random…

In deep image compression, uniform quantization is applied to latent representations obtained by using an auto-encoder architecture for reducing bits and entropy coding. Quantization is a problem encountered in the end-to-end training of…

One-bit quantization with time-varying sampling thresholds has recently found significant utilization potential in statistical signal processing applications due to its relatively low power consumption and low implementation cost. In…

Quantum annealing is a proposed combinatorial optimization technique meant to exploit quantum mechanical effects such as tunneling and entanglement. Real-world quantum annealing-based solvers require a combination of annealing and classical…

Many modern search domains comprise high-dimensional vectors of floating point numbers derived from neural networks, in the form of embeddings. Typical embeddings range in size from hundreds to thousands of dimensions, making the size of…

When a quantizer input signal is the sum of the desired signal and input white noise, the quantization error is a function of total input signal. Our new equivalent model splits the quantization error into two components: a non-linear…

Low-resolution digital-to-analog and analog-to-digital converters (DACs and ADCs) have attracted considerable attention in efforts to reduce power consumption in millimeter wave (mmWave) and massive MIMO systems. This paper presents an…

The paper deals with the task of optimal design of Analog to Digital Converters (ADCs). A general ADC is modeled as a causal discrete-time dynamical system with outputs taking values in a finite set, and its performance is defined as the…

In a typical online learning scenario, a learner is required to process a large data stream using a small memory buffer. Such a requirement is usually in conflict with a learner's primary pursuit of prediction accuracy. To address this…

Applications such as simulating complicated quantum systems or solving large-scale linear algebra problems are very challenging for classical computers due to the extremely high computational cost. Quantum computers promise a solution,…

All-pairs similarity problem asks to find all vector pairs in a set of vectors the similarities of which surpass a given similarity threshold, and it is a computational kernel in data mining and information retrieval for several tasks. We…