Geometric Science of Information

Probability and Statistics on Riemannian Manifolds.- From Bayesian inference to MCMC and convex optimisation in Hadamard manifolds.- Finite Sample Smeariness on Spheres.- Gaussian distributions on Riemannian symmetric spaces in the large N limit.- Smeariness Begets Finite Sample Smeariness.- Online learning of Riemannian hidden Markov models in homogeneous Hadamard spaces.- Quinten Tupker, Salem Said and Cyrus Mostajeran Sub-Riemannian Geometry and Neuromathematics.- Submanifolds of fixed degree in graded manifolds for perceptual completion.- An auditory cortex model for sound processing.- Conformal model of hypercolumns in V1 cortex and the Moebius group. Application to the visual stability problem.- Extremal controls for Duits car.- Multi-Shape Registration with Constrained Deformations.- Shapes Spaces.- Geodesics of the Quotient-Affine Metrics on Full-Rank Correlation Matrices.- Parallel Transport on Kendall Shape Spaces.- Diffusion Means and Heat Kernel on Manifolds.- A reduced parallel transport equation on Lie Groups with a left-invariant metric.- Currents and K-functions for Fiber Point Processes.- Geometry of Quantum States.- Q-Information Geometry of Systems.- Group actions and Monotone Metric Tensors: The qubit case.- Quantum Jensen-Shannon divergences between infinite-dimensional positive definite operators.- Towards a geometrization of quantum complexity and chaos.- Hunt's colorimetric effect from a quantum measurement viewpoint.- Geometric and Structure Preserving Discretizations.- The Herglotz principle and vakonomic dynamics.- Structure-preserving discretization of a coupled heat-wave system, as interconnected port-Hamiltonian systems.- Examples of symbolic and numerical computation in Poisson geometry.-New directions for contact integrators.- Information Geometry in Physics.- Space-time thermo-mechanics for a material continuum.- Entropic dynamics yields reciprocal relations.- Lie Group Machine Learning.- Gibbs states on symplectic manifolds with symmetries.- Gaussian Distributions on the Space of Symmetric Positive Definite Matrices from Souriau's Gibbs State for Siegel Domains by Coadjoint Orbit and Moment Map.- On Gaussian Group Convex Models.- Exponential-wrapped probability densities on SL(2,C).- Information Geometry and Hamiltonian Systems on Lie Groups.- Geometric and Symplectic Methods for Hydrodynamical Models.- Multisymplectic variational integrators for fluid models with constraints.- Metriplectic Integrators for Dissipative Fluids.- From quantum hydrodynamics to Koopman wavefunctions I.- From quantum hydrodynamics to Koopman wavefunctions II.- Harmonic Analysis on Lie Groups.- The Fisher information of curved exponential families and the elegant Kagan inequality.- Continuous Wavelet transforms for vector-valued functions.- Entropy under disintegrations.- Koszul Information Geometry, Liouville-Mineur Integrable Systems and Moser Isospectral Deformation Method for Hermitian Positive-Definite Matrices.- Flapping Wing Coupled Dynamics in Lie Group Setting.- Statistical Manifold and Hessian Information Geometry.- Canonical foliations of statistical manifolds with hyperbolic compact leaves.- Open problems in global analysis. Structured foliations and the information Geometry.- Curvature inequalities and Simons' type formulas in statistical geometry.- Harmonicity of Conformally-Projectively Equivalent Statistical Manifolds and Conformal Statistical Submersions.- Algorithms for approximating means of semi-infinite quasi-Toeplitz matrices.- Geometric Mechanics.- Archetypal Model of Entropy by Poisson Cohomology as Invariant Casimir Function in Coadjoint Representation and Geometric Fourier Heat Equation.- Bridge Simulation and Metric Estimation on Lie Groups.- Constructing the Hamiltonian from the behaviour of a dynamical system by proper symplectic decomposition.- Non-relativistic Limits of General Relativity.- Deformed Entropy,Cross-entropy, and Relative Entropy.- A Primer on Alpha-Information Theory with Application to Leakage in Secrecy Systems.- Schrödinger encounters Fisher and Rao: a survey.- Projections with logarithmic divergences.- Chernoff, Bhattacharyya, Rényi andSharma-Mittal divergence analysis for Gaussian stationary ARMA processes.- Transport Information Geometry.- Wasserstein statistics in one-dimensional location-scale models.- Traditional and accelerated gradient descent for neural architecture search.- Recent developments on the MTW tensor.- Wasserstein Proximal of GANs.- Statistics, Information and Topology.- Information cohomology of classical vector-valued observables.- On Marginal Estimation Algorithms - Belief Propagation as Diffusion.- Towards a functorial description of quantum relative entropy.- Frobenius Statistical manifolds & geometric invariants.- Geometric Deep Learning.- SU(1, 1) Equivariant Neural Networks and Application to Robust Toeplitz HermitianPositive Definite Matrix Classification.- Iterative SE(3)-Transformers.- End-to-End Similarity Learning and Hierarchical clustering for unfixed size datasets.- Information theory and the embedding problem for Riemannian manifolds.- cCorrGAN: Conditional CorrGAN for Learning Empirical Conditional Distributions in the Correlation Elliptope.- Topological and Geometrical Structures in Neurosciences.- Topological Model of Neural Information Networks.- On Information Links.- Betti Curves of Rank One Symmetric Matrices.- Algebraic Homotopy Interleaving Distance.- A Python hands-on tutorial on network and topological neuroscience.- Computational Information Geometry.- Computing statistical divergences with sigma points.- Remarks to Laplacian of graphical models in various graphs.- Classification in the Siegel space for vectorial autoregressive data.- Information Metrics for Phylogenetic Trees via Distributions of Discrete and Continuous Characters.- Wald Space for Phylogenetic Trees.- Necessary Condition for Semiparametric Efficiency of Experimental Designs.- Parametrisation Independence of the Natural Gradient in Overparametrised Systems.- Properties of nonlinear diffusion equations on networks and their geometric aspects.- Rényi Relative Entropy from Homogeneous Kullback-Leibler Divergence Lagrangian.- Statistical bundle of the transport model.- Manifolds and Optimization.- Endpoint Quasi-geodesics on the Stiefel Manifold.- Optimization of a shape metric based on information theory applied to segmentation fusion and evaluation in multimodal MRI for DIPG tumor analysis.- Metamorphic image registration using a semi-Lagrangian scheme.- Geometry of the symplectic Stiefel manifold endowed with the Euclidean metric.- Divergence Statistics.- On f-divergences between Cauchy distributions.- Transport information Hessian distances.- Minimization with respect to divergences and applications.- Optimal transport with some directed distances.- Robust Empirical Likelihood.- Optimal Transport and Learning.- Mind2Mind : Transfer Learning for GANs.- Fast and asymptotic steering to a steady state for networks flows.- Geometry of Outdoor Virus Avoidance in Cities.- A Particle-Evolving method for approximating the Optimal Transport plan.- Geometric Structures in Thermodynamics and Statistical Physics.- Schrödinger problem for lattice gases: a heuristic point of view.- A variational perspective on the thermodynamics of non-isothermal reacting open systems.- On the Thermodynamic Interpretation of Deep Learning Systems.- Dirac structures in thermodynamics of non-simple systems.