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Concept

Prime manifold

Related publications (14)

A graph convolutional autoencoder approach to model order reduction for parametrized PDEs

Jan Sickmann Hesthaven, Federico Pichi

The present work proposes a framework for nonlinear model order reduction based on a Graph Convolutional Autoencoder (GCA-ROM). In the reduced order modeling (ROM) context, one is interested in obtaining real -time and many-query evaluations of parametric ...

Academic Press Inc Elsevier Science2024

OSLO: On-the-Sphere Learning for Omnidirectional Images and Its Application to 360-Degree Image Compression

Pascal Frossard, Thomas Maugey, Roberto Gerson De Albuquerque Azevedo

State-of-the-art 2D image compression schemes rely on the power of convolutional neural networks (CNNs). Although CNNs offer promising perspectives for 2D image compression, extending such models to omnidirectional images is not straightforward. First, omn ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022

How Lagrangian States Evolve Into Random Waves

Alejandro Rivera

In this paper, we consider a compact connected manifold (X, g) of negative curvature, and a family of semi-classical Lagrangian states f(h)(x) = a(x)e(i phi(x)/h) on X. For a wide family of phases phi, we show that f(h), when evolved by the semi-classical ...

ECOLE POLYTECHNIQUE2022

Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances

Wulfram Gerstner, Clément Hongler, Johanni Michael Brea, Francesco Spadaro, Berfin Simsek

We study how permutation symmetries in overparameterized multi-layer neural networks generate `symmetry-induced' critical points. Assuming a network with

L

layers of minimal widths

r_1^*, \ldots, r_{L-1}^*

reaches a zero-loss minimum at $ r_1^*! \c ...

2021

Shrinking Scale Equidistribution for Monochromatic Random Waves on Compact Manifolds

Matthew De Courcy-Ireland

We prove equidistribution at shrinking scales for the monochromatic ensemble on a compact Riemannian manifold of any dimension. This ensemble on an arbitrary manifold takes a slowly growing spectral window in order to synthesize a random function. With hig ...

OXFORD UNIV PRESS2021

Dynamical Reduced Basis Methods for Hamiltonian Systems

Cecilia Pagliantini

We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main factors: the ric ...

Springer2021

The connectivity at infinity of a manifold and Sobolev inequalities

Marc Troyanov

The purpose of this paper is to give a self-contained proof that a complete manifold with more than one end never supports an L-q,L-p-Sobolev inequality (2

Elsevier2014

Learning Smooth Pattern Transformation Manifolds

Pascal Frossard, Elif Vural

Manifold models provide low-dimensional representations that are useful for processing and analyzing data in a transformation-invariant way. In this paper, we study the problem of learning smooth pattern transformation manifolds from image sets that are ob ...

Institute of Electrical and Electronics Engineers2013

Learning Pattern Transformation Manifolds for Classification

Pascal Frossard, Elif Vural

Manifold models provide low-dimensional representations that are useful for analyzing and classifying data in a transformation-invariant way. In this paper we study the problem of jointly building multiple pattern transformation manifolds from a collection ...

2012

Discretization of Parametrizable Signal Manifolds

Pascal Frossard, Elif Vural

Transformation-invariant analysis of signals often requires the computation of the distance from a test pattern to a transformation manifold. In particular, the estimation of the distances between a transformed query signal and several transformation manif ...

Institute of Electrical and Electronics Engineers2011

Geodesic Active Fields : A Geometric Framework for Image Registration

Dominique Zosso

Image registration is the concept of mapping homologous points in a pair of images. In other words, one is looking for an underlying deformation field that matches one image to a target image. The spectrum of applications of image registration is extremely ...

EPFL2011

Optimal image alignment with random projections of manifolds: algorithm and geometric analysis

Pascal Frossard, Daniel Kressner, Effrosyni Kokiopoulou

This paper addresses the problem of image alignment based on random measurements. Image alignment consists of estimating the relative transformation between a query image and a reference image. We consider the specific problem where the query image is prov ...

2011

A NUMERICAL MANIFOLD METHOD FOR PLANE MICROPOLAR ELASTICITY

Hua Zhang, Jian Zhao, Gaofeng Zhao

A numerical manifold method (NMM) for plane micropolar elasticity is proposed in this paper to consider the microstructure influence of materials. First, the basic formulations of plane micropolar elasticity are briefly introduced. Then, the equations of s ...

2010

Wavelet transform on manifolds: old and new approaches

Pierre Vandergheynst

Given a two-dimensional smooth manifold M and a bijective pro jection p from M on a ﬁxed plane (or a subset of that plane), we explore systematically how a wavelet transform (WT) on M may be generated from a plane WT by the inverse projection. Examples whe ...

Elsevier2010

Related publications (14)

L

layers of minimal widths

r_1^*, \ldots, r_{L-1}^*

reaches a zero-loss minimum at $ r_1^*! \c ...

2021

Elsevier2014