Related papers: Mathematics and Logic as Information Compression b…
Image coding for machines (ICM) aims to compress images to support downstream AI analysis instead of human perception. For ICM, developing a unified codec to reduce information redundancy while empowering the compressed features to support…
These notes pose a "proof challenge": a proof, or disproof, of the proposition that "For any given body of information, I, expressed as a one-dimensional sequence of atomic symbols, a multiple alignment concept, described in the document,…
In many areas of applied mathematics, engineering, and social and natural sciences, decentralization of information is a key aspect determining how to approach a problem. In this review article, we study information structures in a…
A steadily growing computational power is employed to perform molecular dynamics simulations of biological macromolecules, which represents at the same time an immense opportunity and a formidable challenge. In fact, large amounts of data…
Over the last decades, a class of important mathematical results have required an ever increasing amount of human effort to carry out. For some, the help of computers is now indispensable. We analyze the implications of this trend towards…
Can machine learning help discover new mathematical structures? In this article we discuss an approach to doing this which one can call "mathematical data science". In this paradigm, one studies mathematical objects collectively rather than…
Large Language Models (LLMs) have demonstrated remarkable performance across a wide range of tasks by understanding input information and predicting corresponding outputs. However, the internal mechanisms by which LLMs comprehend input and…
Numeral systems and units of measurement are two conjoined topics in activities of human beings and have mutual effects with the languages expressing them. Currently, the evaluation of Large Language Models (LLMs) often involves…
Since its existence, the computer tool has often supported mathematicians, whether it is to implement an approximation method (numerical calculation of a root, of an integral, ...) or to simulate a phenomenon (geometric in nature,…
Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…
In contrast to Computer Science, where the fundamental role of Logic is widely recognized, it plays a practically non-existent role in Information Systems curricula. In this paper we argue that instead of Logic's exclusion from the IS…
We conceptualize the process of understanding as information compression, and propose a method for ranking large language models (LLMs) based on lossless data compression. We demonstrate the equivalence of compression length under…
The concept of information has emerged as a language in its own right, bridging several disciplines that analyze natural phenomena and man-made systems. Integrated information has been introduced as a metric to quantify the amount of…
Originally developed as a theory of consciousness, integrated information theory provides a mathematical framework to quantify the causal irreducibility of systems and subsets of units in the system. Specifically, mechanism integrated…
This article presents a re-classification of information seeking (IS) tasks, concepts, and algorithms. The proposed taxonomy provides new dimensions to look into information seeking tasks and methods. The new dimensions include the number…
We survey diverse approaches to the notion of information: from Shannon entropy to Kolmogorov complexity. Two of the main applications of Kolmogorov complexity are presented: randomness and classification. The survey is divided in two parts…
Multivariate information theory provides a general and principled framework for understanding how the components of a complex system are connected. Existing analyses are coarse in nature -- built up from characterizations of discrete…
Computational thinking is a way of reasoning about the world in terms of data. This mindset channels number crunching toward an ambition to discover knowledge through logic, models and simulations. Here we show how computational cognitive…
Questions concerning origin of mathematical knowledge and roles of language and intuition (imagery) in mathematical thoughts are long standing and widely debated. By introspection, mathematicians usually have some beliefs regarding these…
We review the current literature concerned with information plane analyses of neural network classifiers. While the underlying information bottleneck theory and the claim that information-theoretic compression is causally linked to…