Related papers: Diagrammatic Negative Information
Diagram chasing is a customary proof method used in category theory and homological algebra. It involves an element-theoretic approach to show that certain properties hold for a commutative diagram. When dealing with abelian categories for…
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…
In recent years, diagrammatic languages have been shown to be a powerful and expressive tool for reasoning about physical, logical, and semantic processes represented as morphisms in a monoidal category. In particular, categorical quantum…
Observations on the past provide some hints about what will happen in the future, and this can be quantified using information theory. The ``predictive information'' defined in this way has connections to measures of complexity that have…
In designing an intelligent system that must be able to explain its reasoning to a human user, or to provide generalizations that the human user finds reasonable, it may be useful to take into consideration psychological data on what types…
We present an approach to the solution of decision problems formulated as influence diagrams. This approach involves a special triangulation of the underlying graph, the construction of a junction tree with special properties, and a message…
String diagrams are an increasingly popular algebraic language for the analysis of graphical models of computations across different research fields. Whereas string diagrams have been thoroughly studied as semantic structures, much less…
The categorical compositional approach to meaning has been successfully applied in natural language processing, outperforming other models in mainstream empirical language processing tasks. We show how this approach can be generalized to…
The act of telling stories is a fundamental part of what it means to be human. This work introduces the concept of narrative information, which we define to be the overlap in information space between a story and the items that compose the…
The integration of knowledge extracted from different models described by domain experts or from models generated by machine learning algorithms is strongly conditioned by the lack of an appropriated framework to specify and integrate…
In a sequential decision-making problem, the information structure is the description of how events in the system occurring at different points in time affect each other. Classical models of reinforcement learning (e.g., MDPs, POMDPs)…
Diagrammatic, analogical or iconic representations are often contrasted with linguistic or logical representations, in which the shape of the symbols is arbitrary. The aim of this paper is to make a case for the usefulness of diagrams in…
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…
Despite ample evidence that our concepts, our cognitive architecture, and mathematics itself are all deeply compositional, few models take advantage of this structure. We therefore propose a radically compositional approach to computational…
In classification problems, especially those that categorize data into a large number of classes, the classes often naturally follow a hierarchical structure. That is, some classes are likely to share similar structures and features. Those…
Standard methods of using categorical variables as predictors either endow them with an ordinal structure or assume they have no structure at all. However, categorical variables often possess structure that is more complicated than a linear…
In this paper, we develop a qualitative theory of influence diagrams that can be used to model and solve sequential decision making tasks when only qualitative (or imprecise) information is available. Our approach is based on an…
This paper presents a new foundational approach to information theory based on the concept of the information efficiency of a recursive function, which is defined as the difference between the information in the input and the output. The…
Categorification is the process of finding category-theoretic analogs of set-theoretic concepts by replacing sets with categories, functions with functors, and equations between functions by natural isomorphisms between functors, which in…
Information systems experience an ever-growing volume of unstructured data, particularly in the form of textual materials. This represents a rich source of information from which one can create value for people, organizations and…