Related papers: Partition Reduction for Lossy Data Compression Pro…
In this report, we summarize the set partition enumeration problems and thoroughly explain the algorithms used to solve them. These algorithms iterate through the partitions in lexicographic order and are easy to understand and implement in…
Based on the problem of quantum data compression in a lossless way, we present here an operational interpretation for the family of quantum R\'enyi entropies. In order to do this, we appeal to a very general quantum encoding scheme that…
Error-bounded lossy compression is one of the most effective techniques for scientific data reduction. However, the traditional trial-and-error approach used to configure lossy compressors for finding the optimal trade-off between…
With ever-increasing volumes of scientific data produced by HPC applications, significantly reducing data size is critical because of limited capacity of storage space and potential bottlenecks on I/O or networks in writing/reading or…
In edge computing, suppressing data size is a challenge for machine learning models that perform complex tasks such as autonomous driving, in which computational resources (speed, memory size and power) are limited. Efficient lossy…
Reliable data-driven estimation of Shannon entropy from small data sets, where the number of examples is potentially smaller than the number of possible outcomes, is a critical matter in several applications. In this paper, we introduce a…
A randomized algorithm for finding sparse cuts is given which is based on constructing a dual markov chain called multiscale rings process(MRP) and a new concept of entropy. It is shown how the time to absorption of the dual process…
The escalating surge in data generation presents formidable challenges to information technology, necessitating advancements in storage, retrieval, and utilization. With the proliferation of artificial intelligence and big data, the "Data…
Characterizing the entropy of a system is a crucial, and often computationally costly, step in understanding its thermodynamics. It plays a key role in the study of phase transitions, pattern formation, protein folding and more. Current…
Lossy compression, widely used by scientists to reduce data from simulations, experiments, and observations, can distort features of interest even under bounded error. Such distortions may compromise downstream analyses and lead to…
Current discrete randomness and information conservation inequalities are over total recursive functions, i.e. restricted to deterministic processing. This restriction implies that an algorithm can break algorithmic randomness conservation…
The problem of variable-rate lossless data compression is considered, for codes with and without prefix constraints. Sharp bounds are derived for the best achievable compression rate of memoryless sources, when the excess-rate probability…
Graphical data is comprised of a graph with marks on its edges and vertices. The mark indicates the value of some attribute associated to the respective edge or vertex. Examples of such data arise in social networks, molecular and systems…
The entropy bottleneck introduced by Ball\'e et al. is a common component used in many learned compression models. It encodes a transformed latent representation using a static distribution whose parameters are learned during training.…
In this paper, we use entropy functions to characterise the set of rate-capacity tuples achievable with either zero decoding error, or vanishing decoding error, for general network coding problems. We show that when sources are colocated,…
Scientific applications are generating unprecedented volumes of data that overwhelm storage and transmission systems, posing significant challenges for the design of data management tools and scientific databases. Lossy compression has…
Recent advances in capsule endoscopy systems have introduced new methods and capabilities. The capsule endoscopy system, by observing the entire digestive tract, has significantly improved diagnosing gastrointestinal disorders and diseases.…
The area law conjecture states that the entanglement entropy of a region of space in the ground state of a gapped, local Hamiltonian only grows like the surface area of the region. We show that, for any quantum state that fulfills an area…
Bloom filters are widely used data structures that compactly represent sets of elements. Querying a Bloom filter reveals if an element is not included in the underlying set or is included with a certain error rate. This membership testing…
As large language models continue to scale, their growing computational and storage demands pose significant challenges for real-world deployment. In this work, we investigate redundancy within Transformer-based models and propose an…