A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study on convergence of transformed metric spaces as dimensions grow.
Study on conformal transformations of Cahen-Wallach spaces, focusing on fixed points and discontinuous groups.
Transforms Aronszajn to Sikorski subcartesian spaces.
Backlund transformations of admissible curves in the Galilean 3-space and pseudo-Galilean 3-space and also spatial Backlund transformations of space curves in Galilean 4-space preserve the torsions under certain assumptions.
A real valued function of one variable is called a metric transform if for every metric space the composition is also a metric on . We give a complete characterization of the class of approximately nondecreasing, unbounded metric transforms such that the trans…
Transformers adapted to spherical geometry using space-filling curves.
Geometric transformations on null curves in AdS induce KdV solutions.
The conformal geometry of spacelike surfaces in 4-dimensional Lorentzian space forms has been studied by the authors in a previous paper, where the so-called polar transform was introduced. Here it is shown that this transform preserves spacelike conformal isothermic surfaces. We relate this new transform with the know…
New proof of injectivity for broken non-abelian X-ray transform in Minkowski space.
In this paper we study a symmetry group of vector space. Basis manifold is a homogeneous space of a symmetry group. This concept leads us to the definition of active and passive transformations on basis manifold. Active transformation can be expressed as a transformation of vector space. Passive transformation gives ab…
Calculates affine transformations for specific homogeneous spaces.
We study several problems concerning conformal transformation on metric measure spaces, including the Sobolev space, the differential structure and the curvature-dimension condition under conformal transformations. This is the first result about preservation of lower curvature bounds under perturbation, which is new ev…
Study finds formulas for minimal submanifolds using Möbius transformations.
Deep generative networks have been widely used for learning mappings from a low-dimensional latent space to a high-dimensional data space. In many cases, data transformations are defined by linear paths in this latent space. However, the Euclidean structure of the latent space may be a poor match for the underlying lat…
In this paper we prove a new inversion theorem and a refinement of an old support theorem for two Radon transforms on a symmetric space. Included are some new identities for the Abel transform and some results about the Fourier transform from a joint work with Rawat, Sengupta and Sitaram.
The paper studies the Poisson transform of differential forms on hyperbolic spaces.
Paper proves injectivity of non-abelian X-ray transform on certain spaces.
Paper shows X-ray transform invertible on certain curved spaces.
Study fundamental groups of geometric transformation groups using loop spaces.
We consider the generalized Segal-Bargmann transform, defined in terms of the heat operator, for a noncompact symmetric space of the complex type. For radial functions, we show that the Segal-Bargmann transform is a unitary map onto a certain L^2 space of meromorphic functions. For general functions, we give an inversi…
Study on Bayesian transformers finds issues with weight-space inference and prior specification.
We develop some theory of double fibration transforms where the cycle space is a smooth manifold and apply it to complex projective space.
Geometrically transforms word embeddings into a common space for better comparison.
Continuum transformers learn operators in context via gradient descent.
Transformers are explained as infinite-dimensional kernel machines.
This paper analyzes kNN convergence over feature transformations.
This work is dedicated to the study of the Moebius invariant class of constrained Willmore surfaces and its symmetries. We define a spectral deformation by the action of a loop of flat metric connections; Baecklund transformations, by applying a dressing action; and, in 4-space, Darboux transformations, based on the so…
Classification of Finslerian spaces with nontrivial concircular transformations.
Canonical transformation plays a fundamental role in simplifying and solving classical Hamiltonian systems. We construct flexible and powerful canonical transformations as generative models using symplectic neural networks. The model transforms physical variables towards a latent representation with an independent harm…
Various complexes of differential operators are constructed on complex projective space via the Penrose transform, which also computes their cohomology.
Proves conditions for Fourier transforms in rank 1 symmetric spaces.
We describe the range of a restricted spherical mean transform, which sends a function supported inside a closed ball in a hyperbolic space to its mean values on the geodesics spheres centered at the boundary of the ball. The description resembles that of the same transform on the Euclidean spaces obtained by Mark Agra…
Unified proof of end-point estimates for Radon transform on curved spaces.
The basic theory on the conformal geometry of timelike surfaces in pseudo-Riemannian space forms is introduced, which is parallel to the classical framework of Burstall etc. for spacelike surfaces. Then we provide a discussion on the transforms of timelike isothermic surfaces (or real isothermic, complex isothe…
Transforms classical connections using pushforwards and gauge transformations.
State spaces of multifactor approximations of nonnegative Volterra processes are linear transformations of the nonnegative orthant.
Researchers found a Calabi-Yau structure and constructed a Bargmann type transformation on the Cayley projective plane.
Efficient algorithms find optimal monotone transforms for calibration under strictly convex losses.
The paper provides convergence guarantees for ODE-based generative models using transformers.
In this paper, we study the long existence problem of non Berwaldian Landsberg spaces using the conformal transformation point of view. Under conformal transformation, the Berwald and Landesberg tensors are calculated in terms of the T-tensor. By giving examples, we show that under conformal transformation, there are L…
Paper shows invertibility of tensor X-ray transform on certain manifolds.
Study light ray transform in pseudo-Euclidean space, derive inversion formula, and prove stability.
Noting the importance of the latent variables in inference and learning, we propose a novel framework for autoencoders based on the homeomorphic transformation of latent variables, which could reduce the distance between vectors in the transformed space, while preserving the topological properties of the original space…
New minimal hypersurfaces found via transformations.
Unified method for deriving ridgelet transforms for various neural network architectures.
We interpret the setting for a Radon transform as a submanifold of the space of generalized functions, and compute its extrinsic curvature: it is the Hessian composed with the Radon transform.
Using a quaternionic calculus, the Christoffel, Darboux, Goursat, and spectral transformations for discrete isothermic nets are described, with their interrelations. The Darboux and spectral transformations are used to define discrete analogs for cmc-1 surfaces in hyperbolic space and to obtain a discrete version of Br…
This article gives a study of the higher-dimensional Penrose transform between conformally invariant massless fields on space-time and cohomology classes on twistor space, where twistor space is defined to be the space of projective pure spinors of the conformal group. We focus on the 6-dimensional case in which twisto…