Related papers: Maximally Informative Observables and Categorical …

We highlight the underlying category-theoretic structure of measures of information flow. We present an axiomatic framework in which communication systems are represented as morphisms, and information flow is characterized by its behavior…

Classification and characterization of variable phenomena and transient phenomena are critical for astrophysics and cosmology. These objects are commonly studied using photometric time series or spectroscopic data. Given that many ongoing…

Inspired by findings of sensorimotor coupling in humans and animals, there has recently been a growing interest in the interaction between action and perception in robotic systems [Bogh et al., 2016]. Here we consider perception and action…

The representation theory for categorical groups is constructed. Each categorical group determines a monoidal bicategory of representations. Typically, these categories contain representations which are indecomposable but not irreducible. A…

We address the practical problems of estimating the information relations that characterize large networks. Building on methods developed for analysis of the neural code, we show that reliable estimates of mutual information can be obtained…

We consider biological individuality in terms of information theoretic and graphical principles. Our purpose is to extract through an algorithmic decomposition system-environment boundaries supporting individuality. We infer or detect…

Shannon information theory provides various measures of so-called "syntactic information", which reflect the amount of statistical correlation between systems. In contrast, the concept of "semantic information" refers to those correlations…

While Kolmogorov complexity is the accepted absolute measure of information content in an individual finite object, a similarly absolute notion is needed for the information distance between two individual objects, for example, two…

Interpretable and explainable machine learning has seen a recent surge of interest. We focus on safety as a key motivation behind the surge and make the relationship between interpretability and safety more quantitative. Toward assessing…

Informational bias is bias conveyed through sentences or clauses that provide tangential, speculative or background information that can sway readers' opinions towards entities. By nature, informational bias is context-dependent, but…

Interaction information is one of the multivariate generalizations of mutual information, which expresses the amount information shared among a set of variables, beyond the information, which is shared in any proper subset of those…

The work demonstrates that brain might reflect the external world causal relationships in the form of a logically consistent and prognostic model of reality, which shows up as consciousness. The paper analyses and solves the problem of…

This paper introduces several fundamental concepts in information theory from the perspective of their origins in engineering. Understanding such concepts is important in neuroscience for two reasons. Simply applying formulae from…

We consider a hypothesis testing problem where a part of data cannot be observed. Our helper observes the missed data and can send us a limited amount of information about them. What kind of this limited information will allow us to make…

We consider "unphysical", kinematic observables that do not commute with the constraints of a gauge system in the context of an extension of the system. We show that these observables, while not predictable, can nevertheless be said to have…

Working with causal models at different levels of abstraction is an important feature of science. Existing work has already considered the problem of expressing formally the relation of abstraction between causal models. In this paper, we…

The paper demonstrates that falsifiability is fundamental to learning. We prove the following theorem for statistical learning and sequential prediction: If a theory is falsifiable then it is learnable -- i.e. admits a strategy that…

The Maximal Information Coefficient (MIC) of Reshef et al. (Science, 2011) is a statistic for measuring dependence between variable pairs in large datasets. In this note, we prove that MIC is a consistent estimator of the corresponding…

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…

We begin the study of categorical logic for continuous model theory. In particular, we 1. introduce the notions of metric logical categories and functors as categorical equivalents of a metric theory and interpretations, 2. prove a…