Publications related to Gaussians on Riemannian Manifolds for Robot Learning and Adaptive Control

A b-symplectic slice theorem

In this article, motivated by the study of symplectic structures on manifolds with boundary and the systematic study of b-symplectic manifolds started in Guillemin, Miranda, and Pires Adv. Math. 264 (2014), 864-896, we prove a slice theorem for Lie group a ...

WILEY2022

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

Slow-fast Dynamics of Strongly Coupled Adaptive Frequency Oscillators*

Auke Ijspeert, Jonas Buchli, Ludovic Righetti

Oscillators have two main limitations: their synchronization properties are limited (i.e., they have a finite synchronization region) and they have no memory of past interactions (i.e., they return to their intrinsic frequency whenever the entraining signa ...

SIAM PUBLICATIONS2021

On The Singular Set In The Thin Obstacle Problem: Higher-Order Blow-Ups And The Very Thin Obstacle Problem

Xavier Fernandez-Real Girona

We consider the singular set in the thin obstacle problem with weight vertical bar x(n +1)vertical bar(a) for a epsilon (-1, 1), which arises as the local extension of the obstacle problem for the fractional Laplacian (a nonlocal problem). We develop a ref ...

MATHEMATICAL SCIENCE PUBL2021

Robot skills learning with Riemannian manifolds: Leveraging geometry-awareness in robot learning, optimization and control

Noémie Laure Gwendoline Jaquier

Humans exhibit outstanding learning and adaptation capabilities while performing various types of manipulation tasks. When learning new skills, humans are able to extract important information by observing examples of a task and efficiently refine a priori ...

EPFL2020

A Gauss-Bonnet Theorem for Asymptotically Conical Manifolds and Manifolds with Conical Singularities

Adrien Giuliano Marcone

The purpose of this thesis is to provide an intrinsic proof of a Gauss-Bonnet-Chern formula for complete Riemannian manifolds with finitely many conical singularities and asymptotically conical ends. A geometric invariant is associated to the link of both ...

EPFL2019

Bayesian Optimization Meets Riemannian Manifolds in Robot Learning

Sylvain Calinon, Noémie Laure Gwendoline Jaquier

Bayesian optimization (BO) recently became popular in robotics to optimize control parameters and parametric policies in direct reinforcement learning due to its data efficiency and gradient-free approach. However, its performance may be seriously compromi ...

2019

Escaping from saddle points on Riemannian manifolds

Nicolas Henri Bernard Flammarion, Yue Sun

We consider minimizing a nonconvex, smooth function f on a Riemannian manifold M. We show that a perturbed version of Riemannian gradient descent algorithm converges to a second-order stationary point (and hence is able to escape saddle points on the manif ...

2019

Renormalization of quantum field theory on Riemannian manifolds

In this paper, we provide a simple pedagogical proof of the existence of covariant renormalizations in Euclidean perturbative quantum field theory on closed Riemannian manifolds, following the Epstein–Glaser philosophy. We rely on a local method that allow ...

2019

Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexity

Nicolas Henri Bernard Flammarion

We consider minimizing a nonconvex, smooth function

f

on a Riemannian manifold

\mathcal{M}

. We show that a perturbed version of Riemannian gradient descent algorithm converges to a second-order stationary point (and hence is able to escape saddle point ...

2019

Gaussians on Riemannian Manifolds for Robot Learning and Adaptive Control

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A b-symplectic slice theorem

Shrinking Scale Equidistribution for Monochromatic Random Waves on Compact Manifolds

Slow-fast Dynamics of Strongly Coupled Adaptive Frequency Oscillators*

On The Singular Set In The Thin Obstacle Problem: Higher-Order Blow-Ups And The Very Thin Obstacle Problem

Robot skills learning with Riemannian manifolds: Leveraging geometry-awareness in robot learning, optimization and control

A Gauss-Bonnet Theorem for Asymptotically Conical Manifolds and Manifolds with Conical Singularities

Bayesian Optimization Meets Riemannian Manifolds in Robot Learning

Escaping from saddle points on Riemannian manifolds

Renormalization of quantum field theory on Riemannian manifolds

Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexity

Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexity

A b-symplectic slice theorem

Shrinking Scale Equidistribution for Monochromatic Random Waves on Compact Manifolds

A Gauss-Bonnet Theorem for Asymptotically Conical Manifolds and Manifolds with Conical Singularities

Robot skills learning with Riemannian manifolds: Leveraging geometry-awareness in robot learning, optimization and control

Bayesian Optimization Meets Riemannian Manifolds in Robot Learning

Escaping from saddle points on Riemannian manifolds

Slow-fast Dynamics of Strongly Coupled Adaptive Frequency Oscillators*

On The Singular Set In The Thin Obstacle Problem: Higher-Order Blow-Ups And The Very Thin Obstacle Problem

Renormalization of quantum field theory on Riemannian manifolds