arXiv research

Algorithm finds optimal affine transformation to minimize overall distortion.

Improves MCMC performance with adaptive affine transformations.

Automorphisms of Kodaira surfaces are shown to be affine transformations.

Calculates affine transformations for specific homogeneous spaces.

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…

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…

New method detects symmetries beyond affine transformations.

Construct geometric interpretation of Heston model using group quantization.

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.

This paper uses linear rational splines for invertible modeling, offering a simpler inverse and similar costs.

Algorithm learns affine transformations robustly from corrupted samples.

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

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…

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

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…

This project improves model robustness to affine transformations.

Study of symmetries in deformed q-map spaces reveals a complex group structure.

Study of affine transformations on topological manifolds, focusing on local freeness and solvability.

We show that $\mathfrak{aff}(n)$, the Lie algebra of affine transformations of ${\mathbb R}^n,$ is formally and analytically nondegenerate in the sense of A. Weinstein. This means that every analytic (resp., formal) Poisson structure vanishing at a point with a linear part corresponding to $\mathfrak{aff}(n)$ is locall…

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…

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

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

Study finds optimal loops in hyperbolic space with Finsler structure.

The paper reinterprets knot group invariants using affine transformations.

We shall study the equivalence problem for ordinary differential equations with respect to the affine transformations group.

New framework for equivariant neural networks using Lie group decompositions.

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

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…

GOAD improves anomaly detection across various data types.

FineMorphs models smooth transformations for multivariate regression.

Study shows Kähler gradient Ricci solitons have limited symmetry groups.

Proves nonemptyness of domains for specific group actions.

Recurrent neural networks (RNNs) have been drawing much attention with great success in many applications like speech recognition and neural machine translation. Long short-term memory (LSTM) is one of the most popular RNN units in deep learning applications. LSTM transforms the input and the previous hidden states to …

A very important class of homogeneous Riemannian manifolds are the so-called normal homogeneous spaces, which have associated a canonical connection. In this work we obtain geometrically the (connected component of the) group of affine transformations with respect to the canonical connection for a normal homogeneous sp…

Equivariant CNNs improve RL performance in symmetric environments.

The paper is grown from the lecture course "Metric projective geometry" which I hold at the summer school "Finsler geometry with applications" at Karlovassi, Samos, in 2014, and at the workshop before the 8th seminar on Geometry and Topology of the Iranian Mathematical society at the Amirkabir University of Technology …

In statistical analysis, measuring a score of predictive performance is an important task. In many scientific fields, appropriate scores were tailored to tackle the problems at hand. A proper score is a popular tool to obtain statistically consistent forecasts. Furthermore, a mathematical characterization of the proper…

SPTN uses invertible transformations to improve sum-product networks.

We solve two classical conjectures by showing that if an action of a connected Lie group on a complete Riemannian manifold preserves the geodesics (considered as unparameterized curves), then the metric has constant positive sectional curvature, or the group acts by affine transformations.

Constructs special Kähler structures on Lie groups.

We show that for a closed Riemannian manifold the quotient of the group of projective transformations by the group of isometries contains at most two elements unless the metric has constant positive sectional curvature or every projective transformation is an affine transformation.

New framework discovers non-affine continuous symmetries in neural networks.

New shape representation for airfoils improves design and manufacturing.

This paper studies actions of solvable Lie groups on nilpotent Lie groups.

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 …

Classification of curves up to affine transformation in a finite dimensional space was studied by some different methods. In this paper, we achieve the exact formulas of affine invariants via the equivalence problem and in the view of Cartan's lemma and then, state a necessary and sufficient condition for classificatio…

We describe the compact Lorentzian $3$-manifolds admitting a parallel lightlike vector field. The classification of compact Lorentzian $3$-manifolds admitting non-isometric affine diffeomorphisms follows, together with the complete description of these morphisms. Such a Lorentzian manifold is in some sense an equivaria…

Few-shot domain adaptation improves autoencoder performance in changing wireless channels.