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We propose a strategy to compress and store large volumes of scientific data represented on unstructured grids. Approaches utilizing tensor decompositions for data compression have already been proposed. Here, data on a structured grid is…

Researchers are increasingly incorporating numeric high-order data, i.e., numeric tensors, within their practice. Just like the matrix/vector (MV) paradigm, the development of multi-purpose, but high-performance, sparse data structures and…

Coresets have emerged as a powerful tool to summarize data by selecting a small subset of the original observations while retaining most of its information. This approach has led to significant computational speedups but the performance of…

Neural networks are widely used for image-related tasks but typically demand considerable computing power. Once a network has been trained, however, its memory- and compute-footprint can be reduced by compression. In this work, we focus on…

Principal component analysis, dictionary learning, and auto-encoders are all unsupervised methods for learning representations from a large amount of training data. In all these methods, the higher the dimensions of the input data, the…

This paper presents evidence for the idea that much of artificial intelligence, human perception and cognition, mainstream computing, and mathematics, may be understood as compression of information via the matching and unification of…

In this paper we present a general method for information extraction that exploits the features of data compression techniques. We first define and focus our attention on the so-called "dictionary" of a sequence. Dictionaries are…

Recently Implicit Neural Representations (INRs) gained attention as a novel and effective representation for various data types. Thus far, prior work mostly focused on optimizing their reconstruction performance. This work investigates INRs…

To cluster, classify and represent are three fundamental objectives of learning from high-dimensional data with intrinsic structure. To this end, this paper introduces three interpretable approaches, i.e., segmentation (clustering) via the…

Neural networks can be compressed to reduce memory and computational requirements, or to increase accuracy by facilitating the use of a larger base architecture. In this paper we focus on pruning individual neurons, which can simultaneously…

Compressed sensing is a signal processing method that acquires data directly in a compressed form. This allows one to make less measurements than what was considered necessary to record a signal, enabling faster or more precise measurement…

A unified combinatorial definition of the information content and entropy of different types of patterns, compatible with the traditional concepts of information and entropy, going beyond the limitations of Shannon information interpretable…

A coreset (or core-set) of a dataset is its semantic compression with respect to a set of queries, such that querying the (small) coreset provably yields an approximate answer to querying the original (full) dataset. In the last decade,…

We consider a popular family of constrained optimization problems arising in machine learning that involve optimizing a non-decomposable evaluation metric with a certain thresholded form, while constraining another metric of interest.…

The basic problem of semantic compression is to minimize the length of a message while preserving its meaning. This differs from classical notions of compression in that the distortion is not measured directly at the level of bits, but…

Modern scientific simulations, observations, and large-scale experiments generate data at volumes that often exceed the limits of storage, processing, and analysis. This challenge drives the development of data reduction methods that…

Developing an understanding of high-dimensional data can be facilitated by visualizing that data using dimensionality reduction. However, the low-dimensional embeddings are often difficult to interpret. To facilitate the exploration and…

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…

While there has been progress in developing non-vacuous generalization bounds for deep neural networks, these bounds tend to be uninformative about why deep learning works. In this paper, we develop a compression approach based on…

Neural networks' expressiveness comes at the cost of complex, black-box models that often extrapolate poorly beyond the domain of the training dataset, conflicting with the goal of finding compact analytic expressions to describe scientific…