Related papers: An Information-geometric Approach to Sensor Manage…

Wasserstein geometry and information geometry are two important structures introduced in a manifold of probability distributions. The former is defined by using the transportation cost between two distributions, so it reflects the metric…

Imaging systems are represented as linear operators, and their singular value spectra describe the structure recoverable at the operator level. Building on an operator-based information-theoretic framework, this paper introduces a minimal…

In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man…

For robots to work alongside humans and perform in unstructured environments, they must learn new motion skills and adapt them to unseen situations on the fly. This demands learning models that capture relevant motion patterns, while…

This paper develops information geometric representations for nonlinear filters in continuous time. The posterior distribution associated with an abstract nonlinear filtering problem is shown to satisfy a stochastic differential equation on…

Manifolds occur naturally as configuration spaces of robotic systems. They provide global descriptions of local coordinate systems that are common tools in expressing positions of robots. The purpose of this survey is threefold. Firstly, we…

We introduce a novel geometric approach to the image labeling problem. Abstracting from specific labeling applications, a general objective function is defined on a manifold of stochastic matrices, whose elements assign prior data that are…

Understanding intelligence is a central pursuit in neuroscience, cognitive science, and artificial intelligence. Intelligence encompasses learning, problem-solving, creativity, and even consciousness. Recent advancements in geometric…

Steering a language model - intervening on its internal activations to change downstream behaviour - has recently expanded beyond linear interpolation to nonlinear methods such as angular and kernelized steering, which define intervention…

Graph diffusion models have made significant progress in learning structured graph data and have demonstrated strong potential for predictive tasks. Existing approaches typically embed node, edge, and graph-level features into a unified…

We define a local Riemannian metric tensor in the manifold of Gaussian channels and the distance that it induces. We adopt an information-geometric approach and define a metric derived from the Bures-Fisher metric for quantum states. The…

This report concerns the problem of dimensionality reduction through information geometric methods on statistical manifolds. While there has been considerable work recently presented regarding dimensionality reduction for the purposes of…

In order to compare and interpolate signals, we investigate a Riemannian geometry on the space of signals. The metric allows discontinuous signals and measures both horizontal (thus providing many benefits of the Wasserstein metric) and…

Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…

The present paper shows that warped Riemannian metrics, a class of Riemannian metrics which play a prominent role in Riemannian geometry, are also of fundamental importance in information geometry. Precisely, the paper features a new…

Information geometry is a study of statistical manifolds, that is, spaces of probability distributions from a geometric perspective. Its classical information-theoretic applications relate to statistical concepts such as Fisher information,…

We introduce the information geometry module of the Python package Geomstats. The module first implements Fisher-Rao Riemannian manifolds of widely used parametric families of probability distributions, such as normal, gamma, beta,…

Using the square-root map p-->\sqrt{p} a probability density function p can be represented as a point of the unit sphere S in the Hilbert space of square-integrable functions. If the density function depends smoothly on a set of parameters,…

Computing geodesics for Riemannian manifolds is a difficult task that often relies on numerical approximations. However, these approximations tend to be either numerically unstable, have slow convergence, or scale poorly with manifold…

The Riemannian metric on the manifold of positive definite matrices is defined by a kernel function $\phi$ in the form $K_D^\phi(H,K)=\sum_{i,j}\phi(\lambda_i,\lambda_j)^{-1} Tr P_iHP_jK$ when $\sum_i\lambda_iP_i$ is the spectral…