Related papers: A Self-contained Analysis of the Lempel-Ziv Compre…
We present a new, simple, and efficient approach for computing the Lempel-Ziv (LZ77) factorization of a string in linear time, based on suffix arrays. Computational experiments on various data sets show that our approach constantly…
Abstract: In this article, we will analyze in detail the coding limit of an individual sequence by introducing the latest developments brought by the Set Shaping Theory. This new theory made us realize that there is a huge difference…
Given the widespread use of lossless compression algorithms to approximate algorithmic (Kolmogorov-Chaitin) complexity, and that lossless compression algorithms fall short at characterizing patterns other than statistical ones not different…
Machine-learning interatomic potentials (MLIPs) have become a mainstay in computationally-guided materials science, surpassing traditional force fields due to their flexible functional form and superior accuracy in reproducing physical…
We derive an algorithm for compression of the currents and varifolds representations of shapes, using ridge leverage score (RLS) sampling, and the theory of Nystrom approximation in Reproducing Kernel Hilbert Spaces. Our method is faster…
We present an algorithm that computes the Lempel-Ziv decomposition in $O(n(\log\sigma + \log\log n))$ time and $n\log\sigma + \epsilon n$ bits of space, where $\epsilon$ is a constant rational parameter, $n$ is the length of the input…
Deep convolutional neural networks contain tens of millions of parameters, making them impossible to work efficiently on embedded devices. We propose iterative approach of applying low-rank approximation to compress deep convolutional…
We consider the computational aspects of lossy data compression problem, where the compression error is determined by a cover of the data space. We propose an algorithm which reduces the number of partitions needed to find the entropy with…
Tries are among the most versatile and widely used data structures on words. They are pertinent to the (internal) structure of (stored) words and several splitting procedures used in diverse contexts ranging from document taxonomy to IP…
In [Haruna, T. and Nakajima, K., 2011. Physica D 240, 1370-1377], the authors introduced the duality between values (words) and orderings (permutations) as a basis to discuss the relationship between information theoretic measures for…
A novel compression scheme for compressing the outcome of $n$ independent Bernoulli trials is introduced and analysed. The resulting algorithm, BernoulliZip, is a fast and near-optimal method to produce prefix codes for a Bernoulli process.…
We investigate symbolic sequences and in particular information carriers as e.g. books and DNA--strings. First the higher order Shannon entropies are calculated, a characteristic root law is detected. Then the algorithmic entropy is…
Key-Value cache (\texttt{KV} \texttt{cache}) compression has emerged as a promising technique to optimize Large Language Model (LLM) serving. It primarily decreases the memory consumption of \texttt{KV} \texttt{cache} to reduce the…
Coded source compression, also known as source compression with helpers, has been a major variant of distributed source compression, but has hitherto received little attention in the quantum regime. This work treats and solves the…
We study and provide exposition to several phenomena that are related to the perceptron's compression. One theme concerns modifications of the perceptron algorithm that yield better guarantees on the margin of the hyperplane it outputs.…
In data storage and transmission, file compression is a common technique for reducing the volume of data, reducing data storage space and transmission time and bandwidth. However, there are significant differences in the compression…
We consider lossy compression of an information source when the decoder has lossless access to a correlated one. This setup, also known as the Wyner-Ziv problem, is a special case of distributed source coding. To this day, practical…
Entropy estimation is a fundamental problem in information theory that has applications in various fields, including physics, biology, and computer science. Estimating the entropy of discrete sequences can be challenging due to limited data…
The amount of data generated and gathered in scientific simulations and data collection applications is continuously growing, putting mounting pressure on storage and bandwidth concerns. A means of reducing such issues is data compression;…
Images are a substantial portion of the internet, making efficient compression important for reducing storage and bandwidth demands. This study investigates the use of Singular Value Decomposition and low-rank matrix approximations for…