Related papers: Information Topology
Finding observing path creating its observer is important problem in physics and information science. In observing processes, each observation is act changing the observing process that generates interactive observation. Each interaction is…
Information theory is introduced in this lecture note with a particular emphasis on its relevance to algebraic coding theory. The document develops the mathematical foundations for quantifying uncertainty and information transmission by…
A new conceptual foundation for the notion of "information" is proposed, based on the concept of a "distinction graph": a graph in which two nodes are connected iff they cannot be distinguished by a particular observer. The "graphtropy" of…
We formalize a minimal setting in which a chronology (a strict partial order on events) is forced by consistency of distributed information under local composability. The system maintains distributed records interpreted as constraints over…
Many branches of theoretical and applied mathematics require a quantifiable notion of complexity. One such circumstance is a topological dynamical system - which involves a continuous self-map on a metric space. There are many notions of…
Conformal Prediction (CP) is a distribution-free uncertainty estimation framework that constructs prediction sets guaranteed to contain the true answer with a user-specified probability. Intuitively, the size of the prediction set encodes a…
The logical basis for information theory is the newly developed logic of partitions that is dual to the usual Boolean logic of subsets. The key concept is a "distinction" of a partition, an ordered pair of elements in distinct blocks of the…
A mathematical framework for information-theoretic analysis is established, with a new viewpoint of describing transmitted messages and communication channels by the nonlinear expectation theory, beyond the framework of classical…
In recent work, Stalnaker proposes a logical framework in which belief is realized as a weakened form of knowledge. Building on Stalnaker's core insights, and using frameworks developed in previous work by Bjorndahl and Baltag et al., we…
This paper introduces time into information theory, gives a more accurate definition of information, and unifies the information in cognition and Shannon information theory. Specially, we consider time as a measure of information, giving a…
Complex systems are difficult to study not only because they are nonlinear, multiscale, and often nonstationary, but because their scientifically relevant organization is often invisible at the level of individual components, pairwise…
The problems of causality, modeling, and control for chaotic, high-dimensional dynamical systems are formulated in the language of information theory. The central quantity of interest is the Shannon entropy, which measures the amount of…
Humans communicate using systems of interconnected stimuli or concepts -- from language and music to literature and science -- yet it remains unclear how, if at all, the structure of these networks supports the communication of information.…
Shannon entropy, a cornerstone of information theory, statistical physics and inference methods, is uniquely identified by the Shannon-Khinchin or Shore-Johnson axioms. Generalizations of Shannon entropy, motivated by the study of…
In this paper we develop a novel mathematical formalism for the modeling of neural information networks endowed with additional structure in the form of assignments of resources, either computational or metabolic or informational. The…
The properties of complex networked systems arise from the interplay between the dynamics of their elements and the underlying topology. Thus, to understand their behaviour, it is crucial to convene as much information as possible about…
Current continuous generative models (e.g., Diffusion Models, Flow Matching) implicitly assume that locally consistent causal mechanisms naturally yield globally coherent counterfactuals. In this paper, we prove that this assumption fails…
Knowledge is a network of interconnected concepts. Yet, precisely how the topological structure of knowledge constrains its acquisition remains unknown, hampering the development of learning enhancement strategies. Here we study the…
We develop an axiomatic reconstruction of thermodynamics based entirely on two primitive components: a description of what aspects of a system are observed and a reference measure that encodes the underlying descriptive convention. These…
A message of any sort can be regarded as a source of information. Claude. E. Shannon showed in the last century that information ("what we don't already know") is equivalent to the entropy as defined in statistical mechanics. A string of…