Publications related to Smoothness

Ill-posedness of the quasilinear wave equation in the space $H^7/4 (ln H)^-Béta$ in dimension 2+1

We are interested in the well posedness of quasilinear partial differential equations of order two. Motivated by the study of the Einstein equation in relativity theory, there are a number of works dedicated to the local well-posedness issue for the quasil ...

EPFL2021

On Linear Interpolation in the Latent Space of Deep Generative Models

Quentin Christian Becker, Mike Yan Michelis

The underlying geometrical structure of the latent space in deep generative models is in most cases not Euclidean, which may lead to biases when comparing interpolation capabilities of two models. Smoothness and plausibility of linear interpolations in lat ...

2021

On the asymptotic optimality of spectral coarse spaces

Tommaso Vanzan

This paper is concerned with the asymptotic optimality of spectral coarse spaces for two-level iterative methods. Spectral coarse spaces, namely coarse spaces obtained as the span of the slowest modes of the used one-level smoother, are known to be very ef ...

Springer-Verlag2021

Regret Minimization in Stochastic Non-Convex Learning via a Proximal-Gradient Approach

Volkan Cevher, Shaul Nadav Hallak

This paper develops a methodology for regret minimization with stochastic first-order oracle feedback in online, constrained, non-smooth, non-convex problems. In this setting, the minimization of external regret is beyond reach for first-order methods, and ...

JMLR-JOURNAL MACHINE LEARNING RESEARCH2021

Fast Projection Onto Convex Smooth Constraints

Maryam Kamgarpour, Andreas Krause, Ilnura Usmanova

The Euclidean projection onto a convex set is an important problem that arises in numerous constrained optimization tasks. Unfortunately, in many cases, computing projections is computationally demanding. In this work, we focus on projection problems where ...

PMLR2021

A critically degenerate elliptic Dirichlet problem, spectral theory and bifurcation

Charles Stuart

In an open, bounded subset Omega of R-N such that 0 is an element of Omega we consider the nonlinear eigenvalue problem -Sigma(N)(i,j,=1) partial derivative(i){A(ij)(x)partial derivative(j)u} + V(x)u + n(x,del u)+ g(x, u) = lambda u in Omega integral(Omega ...

2020

On the asymptotic behavior of the solutions to parabolic variational inequalities

Maria Colombo

We consider various versions of the obstacle and thin-obstacle problems, we interpret them as variational inequalities, with non-smooth constraint, and prove that they satisfy a new constrained Lojasiewicz inequality. The difficulty lies in the fact that, ...

2020

A stability theory beyond the co-rotational setting for critical wave maps blow up

Joachim Krieger, Shuang Miao

We exhibit non-equivariant perturbations of the blowup solutions constructed in [18] for energy critical wave maps into

\mathbb{S}^2

. Our admissible class of perturbations is an open set in some sufficiently smooth topology and vanishes near the light co ...

2020

Adaptive Gradient Descent without Descent

Konstantin Mishchenko

We present a strikingly simple proof that two rules are sufficient to automate gradient descent: 1) don’t increase the stepsize too fast and 2) don’t overstep the local curvature. No need for functional values, no line search, no information about the func ...

2020

Forward-Backward Splitting for Optimal Transport Based Problems

Pascal Frossard, Guillermo Ortiz Jimenez, Mireille El Gheche, Hermina Petric Maretic, Effrosyni Simou

Optimal transport aims to estimate a transportation plan that minimizes a displacement cost. This is realized by optimizing the scalar product between the sought plan and the given cost, over the space of doubly stochastic matrices. When the entropy regula ...

2020

Smoothness

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Ill-posedness of the quasilinear wave equation in the space $H^7/4 (ln H)^-Béta$ in dimension 2+1

On Linear Interpolation in the Latent Space of Deep Generative Models

On the asymptotic optimality of spectral coarse spaces

Regret Minimization in Stochastic Non-Convex Learning via a Proximal-Gradient Approach

Fast Projection Onto Convex Smooth Constraints

A critically degenerate elliptic Dirichlet problem, spectral theory and bifurcation

On the asymptotic behavior of the solutions to parabolic variational inequalities

A stability theory beyond the co-rotational setting for critical wave maps blow up

Adaptive Gradient Descent without Descent

Forward-Backward Splitting for Optimal Transport Based Problems

On the asymptotic optimality of spectral coarse spaces

Regret Minimization in Stochastic Non-Convex Learning via a Proximal-Gradient Approach

On the asymptotic behavior of the solutions to parabolic variational inequalities

On Linear Interpolation in the Latent Space of Deep Generative Models

Fast Projection Onto Convex Smooth Constraints

Adaptive Gradient Descent without Descent

Ill-posedness of the quasilinear wave equation in the space $H^7/4 (ln H)^-Béta$ in dimension 2+1

Forward-Backward Splitting for Optimal Transport Based Problems

A critically degenerate elliptic Dirichlet problem, spectral theory and bifurcation

A stability theory beyond the co-rotational setting for critical wave maps blow up