Related papers: Finite-State Dimension and Lossy Decompressors

Error-controlled lossy compression has been studied for years because of extremely large volumes of data being produced by today's scientific simulations. None of existing lossy compressors, however, allow users to fix the peak…

As conventional communication systems based on classic information theory have closely approached the limits of Shannon channel capacity, semantic communication has been recognized as a key enabling technology for the further improvement of…

Most data is automatically collected and only ever "seen" by algorithms. Yet, data compressors preserve perceptual fidelity rather than just the information needed by algorithms performing downstream tasks. In this paper, we characterize…

In this paper we introduce a variant of pushdown dimension called bounded pushdown (BPD) dimension, that measures the density of information contained in a sequence, relative to a BPD automata, i.e. a finite state machine equipped with an…

We show how to calculate the finite-state dimension (equivalently, the finite-state compressibility) of a saturated sets $X$ consisting of {\em all} infinite sequences $S$ over a finite alphabet $\Sigma_m$ satisfying some given condition…

We investigate the problem of finding the optimal convex decomposition of a bipartite quantum state into a separable part and a positive remainder, in which the weight of the separable part is maximal. This weight is naturally identified…

In this paper, we propose a new protocol for a data compression task, blind quantum data compression, with finite local approximations. The rate of blind data compression is susceptible to approximations even when the approximations are…

We study a class of filters -- discrete finite-state transition systems employed as incremental stream transducers -- that have application to robotics: e.g., to model combinatorial estimators and also as concise encodings of feedback…

Despite the increasing prevalence of large language models (LLMs), we still have a limited understanding of how their representational spaces are structured. This limits our ability to interpret how and what they learn or relate them to…

The deployment of Large Language Models (LLMs) in long-context scenarios is hindered by computational inefficiency and significant information redundancy. Although recent advancements have widely adopted context compression to address these…

We consider the setting where actions can be used to modify a state sequence before compression. The minimum rate needed to losslessly describe the optimal modified sequence is characterized when the state sequence is either non-causally or…

We study the problem of multi-compression and reconstructing a stochastic signal observed by several independent sensors (or compressors) that transmit compressed information to a fusion center. { The key aspect of this problem is to find…

Lossy compression algorithms aim to compactly encode images in a way which enables to restore them with minimal error. We show that a key limitation of existing algorithms is that they rely on error measures that are extremely sensitive to…

Lossy compression is one of the most effective methods for reducing the size of scientific data containing multiple data fields. It reduces information density through prediction or transformation techniques to compress the data. Previous…

A *dimension extractor* is an algorithm designed to increase the effective dimension -- i.e., the amount of computational randomness -- of an infinite binary sequence, in order to turn a "partially random" sequence into a "more random"…

Error-bounded lossy compression is one of the most efficient solutions to reduce the volume of scientific data. For lossy compression, progressive decompression and random-access decompression are critical features that enable on-demand…

As a fundamental data format representing spatial information, depth map is widely used in signal processing and computer vision fields. Massive amount of high precision depth maps are produced with the rapid development of equipment like…

Data compression is a well-studied (and well-solved) problem in the setup of long coding blocks. But important emerging applications need to compress data to memory words of small fixed widths. This new setup is the subject of this paper.…

This paper is concerned with quantum data compression of asymptotically many independent and identically distributed copies of ensembles of mixed quantum states. The encoder has access to a side information system. The figure of merit is…

Deep neural networks have delivered remarkable performance and have been widely used in various visual tasks. However, their huge size causes significant inconvenience for transmission and storage. Many previous studies have explored model…