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A central question in cognitive science is whether conceptual representations converge onto a shared manifold to support generalization, or diverge into orthogonal subspaces to minimize task interference. While prior work has discovered…
In the last ten years, the technology of differential geometry, ubiquitous in gravitational physics, has found its place in the field of optics. It has been successfully used in the design of optical metamaterials, through a technique now…
Given an affine transformation $T$, we define its Fisher distortion $Dist_F(T)$. We show that the Fisher distortion has Riemannian metric structure and provide an algorithm for finding mean distorting transformation -- namely -- for a given…
Hypersurfaces embedded in conformal manifolds appear frequently as boundary data in boundary-value problems in cosmology and string theory. Viewed as the non-null conformal infinity of a spacetime, we consider hypersurfaces embedded in a…
Motivated by applications for simulating quantum many body functions, we propose a new universal ansatz for approximating anti-symmetric functions. The main advantage of this ansatz over previous alternatives is that it is bi-Lipschitz with…
Let (M,g) be a compact, connected and oriented Riemannian manifold. We denote D the space of smooth probability density functions on M. In this paper, we show that the Frechet manifold D is equipped with a Riemannian metric g^{D} and an…
Data-driven approaches coupled with physical knowledge are powerful techniques to model systems. The goal of such models is to efficiently solve for the underlying field by combining measurements with known physical laws. As many systems…
This paper is the the third part of a series of paper whose aim is to use of the framework of \emph{twisted spectral triples} to study conformal geometry from a noncommutive geometric viewpoint. In this paper we reformulate the inequality…
The likelihood function plays a crucial role in statistical inference and experimental design. However, it is computationally intractable for several important classes of statistical models, including energy-based models and simulator-based…
An approach is proposed for recovering affine correspondences (ACs) from orientation- and scale-invariant, e.g. SIFT, features. The method calculates the affine parameters consistent with a pre-estimated epipolar geometry from the point…
Information geometry is a mathematical framework that elucidates the manifold structure of the probability distribution space (p-space), providing a systematic approach to transforming probability distributions (PDs). In this study, we…
Information geometry applies concepts in differential geometry to probability and statistics and is especially useful for parameter estimation in exponential families where parameters are known to lie on a Riemannian manifold. Connections…
Diffraction tomography aims to recover an object's scattering potential from measured wave fields. In the classical setting, the object is illuminated by plane waves from many directions, and the Fourier diffraction theorem provides a…
A physical system exposes to us in a real space, while its description often refers to its reciprocal momentum space. A connection between them can be established by exploring patterns of quasiparticles interference (QPI), which is…
The biases exhibited by Text-to-Image (TTI) models are often treated as if they are independent, but in reality, they may be deeply interrelated. Addressing bias along one dimension, such as ethnicity or age, can inadvertently influence…
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,…
In this paper, we introduce complex functional maps, which extend the functional map framework to conformal maps between tangent vector fields on surfaces. A key property of these maps is their orientation awareness. More specifically, we…
Self-supervised learning converts raw perceptual data such as images to a compact space where simple Euclidean distances measure meaningful variations in data. In this paper, we extend this formulation by adding additional geometric…
In many image analysis problems, the contours of objects carry important statistical information about shape. Such contours are typically affected by deformation variables including scaling, translation, rotation, and reparametrization.…
Recently, a method to dynamically define a divergence function $D$ for a given statistical manifold $(\mathcal{M}\,,g\,,T)$ by means of the Hamilton-Jacobi theory associated with a suitable Lagrangian function $\mathfrak{L}$ on…