arXiv research

The study examines lower and upper bounds of Wasserstein distances for affine transformations of random vectors.

Training only BatchNorm parameters achieves surprisingly high performance in deep networks.

Formula found for probability of random triangles on flat tori being homotopically trivial.

GOAD improves anomaly detection across various data types.

Calculates affine transformations for specific homogeneous spaces.

Algorithm finds optimal affine transformation to minimize overall distortion.

In this paper, we show that a compact affine manifold endowed with an Affine Anosov transformation is finitely covered by a complete affine nilmanifold.

We state and prove a simple Theorem that allows one to generate invariant quantities in Metric-Affine Geometry, under a given transformation of the affine connection. We start by a general functional of the metric and the connection and consider transformations of the affine connection possessing a certain symmetry. We…

New method detects symmetries beyond affine transformations.

We give a characterization of flat affine connections on manifolds by means of a natural affine representation of the universal covering of the Lie group of diffeomorphisms preserving the connection. From the infinitesimal point of view, this representation is determined by the 1-connection form and the fundamental for…

This research studies affine invariance in continuous-domain convolutional neural networks.

Improves MCMC performance with adaptive affine transformations.

Change detection in heterogeneous multitemporal satellite images is an emerging and challenging topic in remote sensing. In particular, one of the main challenges is to tackle the problem in an unsupervised manner. In this paper we propose an unsupervised framework for bitemporal heterogeneous change detection based on…

In this paper we exhibit a family of flat left invariant affine structures on the double Lie group of the oscillator Lie group of dimension 4, associated to each solution of classical Yang-Baxter equation given by Boucetta and Medina. On the other hand, using Koszul's method, we prove the existence of an immersion of L…

Proves nonemptyness of domains for specific group actions.

Transforms classical connections using pushforwards and gauge transformations.

Extend classical theory of affine processes to path-dependent setting

In this paper we propose a novel augmentation technique that improves not only the performance of deep neural networks on clean test data, but also significantly increases their robustness to random transformations, both affine and projective. Inspired by ManiFool, the augmentation is performed by a line-search manifol…

FineMorphs models smooth transformations for multivariate regression.

We show that conformal transformations on the generalized Minkowski space $\mathbb{R}^{p,q}$ map hyperboloids and affine hyperplanes into hyperboloids and affine hyperplanes. We also show that this action on hyperboloids and affine hyperplanes is transitive when $p$ or $q$ is $0$, and that this action has exactly three…

This paper classifies reversible and strongly reversible elements in affine groups.

Automorphisms of Kodaira surfaces are shown to be affine transformations.

New findings on how certain functionals behave in random variable spaces.

This paper deals essentially with affine or projective transformations of Lie groups endowed with a flat left invariant affine or projective structure. These groups are called flat affine or flat projective Lie groups. Our main results determine Lie groups admitting flat bi-invariant affine or projective structures. Th…

Normalizing flows attempt to model an arbitrary probability distribution through a set of invertible mappings. These transformations are required to achieve a tractable Jacobian determinant that can be used in high-dimensional scenarios. The first normalizing flow designs used coupling layer mappings built upon affine …

An (flat) affine $3$-manifold is a $3$-manifold with an atlas of charts to an affine space ${\mathbf R}^3$ with transition maps in the affine transformation group $Aff({\mathbf R}^3)$. Equivalently an affine $3$-manifold is a $3$-manifold with a flat torsion-free affine connection. We show that a closed affine $3$-mani…

Random features enhance control of complex systems.

Classification of cubics (that is, third order planar curves in the $R^2$ up to certain transformations is interested since Newton, and treated by several authors. We classify cubics up to affine transformations, in seven class, and give a complete set of representatives of the these classes. This result is complete an…

Fine-tuning normalization layers can reconstruct smaller networks.

We give characterizations of affine transformations and affine vector fields in terms of the spray. By utilizing the Jacobi type equation that characterizes affine vector fields, we prove some rigidity theorems of affine vector fields on compact or forward complete non-compact Finsler manifolds with non-positive total …

The goal of this survey article is to explain and elucidate the affine structure of recent models appearing in the rough volatility literature, and show how it leads to exponential-affine transform formulas.

Weil algebra morphism induce natural transformations between Weil bundles. In some well known cases, a natural transformation is endowed with a canonical structure of affine bundle. We show that this structure arises only when the Weil algebra morphism is surjective and its kernel has null square. Moreover, in some cas…

Algorithm learns affine transformations robustly from corrupted samples.

This project improves model robustness to affine transformations.

Geodesically complete affine manifolds are quotients of the Euclidean space through a properly discontinuous action of a subgroup of affine Euclidean transformations. An equivalent definition is that the tangent bundle of such a manifold admits a flat, symmetric and complete connection. If the completeness assumption i…

In this paper, we consider affine self-similar solutions for the affine curve shortening flow in the Euclidean plane. We obtain the equations of all affine self-similar solutions up to affine transformations and solve the equations or give descriptions of the solutions for the degenerate case. Some new special solution…

Defines CAMC discrete nets and their properties.

Randomizes AD models for better option pricing.

Clarifies relation for solving control-affine Schrödinger bridge problems.

The paper studies third-order PDEs invariant under affine transformations and connects them to the Fubini-Pick invariant.

Yau's Affine Normal Descent optimizes smooth unconstrained problems with geometrically adapted directions.

Affine manifolds are called integral if there is an atlas such that all transition maps are affine transformations with integer matrices of linear parts. In this paper we describe all complete integral affine structures on compact three-dimensional manifolds up to a finite-sheeted covering. Also a complete list of inte…

New method calculates geometric Brownian motion with affine drift and its integral.

To any connected and simply connected nilpotent Lie group N, one can associate its group of affine transformations Aff(N). In this paper, we study simply transitive actions of a given nilpotent Lie group G on another nilpotent Lie group N, via such affine transformations. We succeed in translating the existence questio…

This work studies formal utility and privacy guarantees for a simple multiplicative database transformation, where the data are compressed by a random linear or affine transformation, reducing the number of data records substantially, while preserving the number of original input variables. We provide an analysis frame…

Affine 3-manifolds with centralizing holonomy are complete.

Gromov showed that for fixed, arbitrarily large C, any uniformly C-Lipschitz affine action of a random group in his graph model on a Hilbert space has a fixed point. We announce a theorem stating that more general affine actions of the same random group on a Hilbert space have a fixed point. We discuss some aspects of …

There are exactly two different types of bi-dimensional improper affine spheres: the non-convex ones can be modeled by the center-chord transform of a pair of planar curves while the convex ones can be modeled by a holomorphic map. In this paper, we show that both constructions can be generalized to arbitrary even dime…