Related papers: Information geometric methods for complexity
The apparent dichotomy between information-processing and dynamical approaches to complexity science forces researchers to choose between two diverging sets of tools and explanations, creating conflict and often hindering scientific…
Information geometry is the application of differential geometry in statistics, where the Fisher-Rao metric serves as the Riemannian metric on the statistical manifold, providing an intrinsic property for parameter sensitivity. In this…
We propose a unified information-geometric framework that formalizes understanding in learning as a trade-off between informativeness and geometric simplicity. An encoder phi is evaluated by U(phi) = I(phi(X); Y) - beta * C(phi), where…
Graph comparison plays a major role in many network applications. We often need a similarity metric for comparing networks according to their structural properties. Various network features - such as degree distribution and clustering…
The capacity to integrate information is a prominent feature of biological and cognitive systems. Integrated Information Theory (IIT) provides a mathematical approach to quantify the level of integration in a system, yet its computational…
Complex networks can model the structure and dynamics of different types of systems. It has been shown that they are characterized by a set of measures. In this work, we evaluate the variability of complex networks measures face to…
We introduce a class of information measures based on group entropies, allowing us to describe the information-theoretical properties of complex systems. These entropic measures are nonadditive, and are mathematically deduced from a series…
Geometrical methods in quantum information are very promising for both providing technical tools and intuition into difficult control or optimization problems. Moreover, they are of fundamental importance in connecting pure geometrical…
Motivated by the increasing connections between information theory and high-energy physics, particularly in the context of the AdS/CFT correspondence, we explore the information geometry associated to a variety of simple systems. By…
Geometric data analysis and learning has emerged as a distinct and rapidly developing research area, increasingly recognized for its effectiveness across diverse applications. At the heart of this field lies curvature, a powerful and…
Information geometry uses the formal tools of differential geometry to describe the space of probability distributions as a Riemannian manifold with an additional dual structure. The formal equivalence of compositional data with discrete…
Quantum information quantities, such as mutual information and entropies, are essential for characterizing quantum systems and protocols in quantum information science. In this contribution, we identify types of information measures based…
From the Aharonov-Bohm effect to general relativity, geometry plays a central role in modern physics. In quantum mechanics many physical processes depend on the Berry curvature. However, recent advances in quantum information theory have…
We introduce an asymmetric distance in the space of learning tasks, and a framework to compute their complexity. These concepts are foundational for the practice of transfer learning, whereby a parametric model is pre-trained for a task,…
We address the framework of analysing quantum metrology in the information-theoretic picture. Firstly we show how to extract the maximum amount of information in general via suitable state initialization of the probes at the beginning and a…
Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections,…
In physics, two systems that radically differ at short scales can exhibit strikingly similar macroscopic behaviour: they are part of the same long-distance universality class. Here we apply this viewpoint to geometry and initiate a program…
We introduce a new information-geometric structure associated with the dynamics on discrete objects such as graphs and hypergraphs. The presented setup consists of two dually flat structures built on the vertex and edge spaces,…
Studying the geometry of sets appearing in various problems of quantum information helps in understanding different parts of the theory. It is thus worthwhile to approach quantum mechanics from the angle of geometry -- this has already…
We introduce a new information theoretic measure that we call Public Information Complexity (PIC), as a tool for the study of multi-party computation protocols, and of quantities such as their communication complexity, or the amount of…