Related papers: Properties of Carry Value Transformation

The quantum Fourier transform for discrete variable (dvQFT) is an efficient algorithm for several applications. It is usually considered for the processing of quantum bits (qubits) and its efficient implementation is obtained with two…

Variable-to-variable length (VV) codes are a class of lossless source coding. As their name implies, VV codes encode a variable-length sequence of source symbols into a variable-length codeword. This paper will give a complete proof of an…

Visual Transformers (VTs) are emerging as an architectural paradigm alternative to Convolutional networks (CNNs). Differently from CNNs, VTs can capture global relations between image elements and they potentially have a larger…

We consider the class of risk measures associated with optimized certainty equivalents. This class includes several popular examples, such as CV@R and monotone mean-variance. Numerical schemes are developed for the computation of these risk…

The design of the optimal inverse discrete cosine transform (IDCT) to compensate the quantization error is proposed for effective lossy image compression in this work. The forward and inverse DCTs are designed in pair in current image/video…

Query-by-Vocal Imitation (QBV) is about searching audio files within databases using vocal imitations created by the user's voice. Since most humans can effectively communicate sound concepts through voice, QBV offers the more intuitive and…

Causal Dynamical Triangulations (CDT) is a proposal for a theory of quantum gravity, which implements a path-integral quantization of gravity as the continuum limit of a sum over piecewise flat spacetime geometries. We use Monte Carlo…

Transformers have emerged as the prevailing standard solution for various AI tasks, including computer vision and natural language processing. The widely adopted Query, Key, and Value formulation (QKV) has played a significant role in this.…

Pre-trained vision-language models (VLMs) have shown impressive results in various visual classification tasks. However, we often fail to fully unleash their potential when adapting them for new concept understanding due to limited…

The Continuous Wavelet Transform (CWT) is an effective tool for feature extraction in acoustic recognition using Convolutional Neural Networks (CNNs), particularly when applied to non-stationary audio. However, its high computational cost…

Vision transformers have been successfully applied to image recognition tasks due to their ability to capture long-range dependencies within an image. However, there are still gaps in both performance and computational cost between…

We show that any subset of the squares of positive relative upper density contains non-trivial solutions to a translation-invariant linear equation in five or more variables, with explicit quantitative bounds. As a consequence, we establish…

Vision Transformers (ViTs) have emerged as state-of-the-art models for various vision tasks recently. However, their heavy computation costs remain daunting for resource-limited devices. To address this, researchers have dedicated…

Vector addition systems are an important model in theoretical computer science and have been used in a variety of areas. In this paper, we consider vector addition systems with states over a parameterized initial configuration. For these…

The famous Hadwiger theorem classifies all rigid motion invariant continuous valuations on convex sets as linear conbinations of quermassintegrals. We prove much more general result. We classify continuous valuations which are invariant…

In this paper, we re-examine the Markov property in the context of neural machine translation. We design a Markov Autoregressive Transformer~(MAT) and undertake a comprehensive assessment of its performance across four WMT benchmarks. Our…

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…

Let R and S be two vectors of real numbers whose entries have the same sum. In the transportation problems one wishes to find a matrix A with row sum vector R and column sum vector S. If, in addition, the two vectors only contain…

Given a combinatorial optimization problem, we aim at characterizing the set of all instances for which every feasible solution has the same objective value. Our central result deals with multi-dimensional assignment problems. We show that…

Vision Transformers (ViT) have achieved remarkable success in large-scale image recognition. They split every 2D image into a fixed number of patches, each of which is treated as a token. Generally, representing an image with more tokens…