Related papers: Information Geometry on the $\ell^2$-Simplex via t…
Geometric embedding methods have shown to be useful for multi-hop reasoning on knowledge graphs by mapping entities and logical operations to geometric regions and geometric transformations, respectively. Geometric embeddings provide direct…
We study the geometry of probability distributions with respect to a generalized family of Csisz\'ar $f$-divergences. A member of this family is the relative $\alpha$-entropy which is also a R\'enyi analog of relative entropy in information…
The \emph{index set} of a computable structure $\mathcal{A}$ is the set of indices for computable copies of $\mathcal{A}$. We determine the complexity of the index sets of various mathematically interesting structures, including arbitrary…
We study the relationship between geometry and capacity measures for deep neural networks from an invariance viewpoint. We introduce a new notion of capacity --- the Fisher-Rao norm --- that possesses desirable invariance properties and is…
For a given entanglement entropy of QFT, we investigate how to reconstruct its dual geometry by applying the Ryu-Takayanagi formula and the deep learning method. In the holographic setup, the radial direction of the dual geometry is…
We propose a theory for coupling matter fields with discrete geometry on higher-order networks, i.e. cell complexes. The key idea of the approach is to associate to a higher-order network the quantum entropy of its metric. Specifically we…
We present an information geometric analysis of both entropic speeds and entropy production rates arising from geodesic evolution on manifolds parametrized by pure quantum states. In particular, we employ pure states that emerge as outputs…
Circular and non-flat data distributions are prevalent across diverse domains of data science, yet their specific geometric structures often remain underutilized in machine learning frameworks. A principled approach to accounting for the…
The paper gives a definition of exponential arcs in the manifold of non-degenerate density matrices and uses it as a starting point to develop a parameter-free version of non-commutative Information Geometry in the finite-dimensional case.…
We characterize the complexity of geodesic paths on a curved statistical manifold M_{s} through the asymptotic computation of the information geometric complexity V_{M_{s}} and the Jacobi vector field intensity J_{M_{s}}. The manifold M_{s}…
This paper investigates a family of dynamical systems arising from an evolutionary re-interpretation of certain optimal control and optimization problems. We focus particularly on the application in image registration of the theory of…
Simple time-reversible systems can generate {\it irreversible} flows satisfying the Second Law of Thermodynamics. Maps, and equivalent random walks, can also do this. We study a pair of time-reversible Baker Maps, $N2$ and $N3$, which…
A novel information-geometrodynamical approach to chaotic dynamics (IGAC) on curved statistical manifolds based on Entropic Dynamics (ED) is presented and a new definition of information geometrodynamical entropy (IGE) as a measure of…
We show a relationship between the entropy production in stochastic thermodynamics and the stochastic interaction in the information integrated theory. To clarify this relationship, we newly introduce an information geometric interpretation…
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…
In the recent years, information theory of quantum-mechanical systems have aroused the interest of many Theoretical Physicist. This due to the fact that it provides a deeper insight into the internal structure of the systems. Also, It is…
Arguments inspired by algorithmic information theory predict an inverse relation between the probability and complexity of output patterns in a wide range of input-output maps. This phenomenon is known as \emph{simplicity bias}. By viewing…
A unified framework for the characterization of continuous electromagnetic (EM) manifolds for arbitrary multipleinput multiple-output (MIMO) system geometries is presented. The EM manifold refers to the set of all physically realizable…
Normalizing flows have shown great success as general-purpose density estimators. However, many real world applications require the use of domain-specific knowledge, which normalizing flows cannot readily incorporate. We propose…
We construct a geometric framework for cosmological large-scale structure based on optimal transport theory and Wasserstein geometry. In this framework, Ricci curvature on the probability measure space $\mathcal{P}_2(M)$ is characterized by…