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Found 11 papers, 3 papers with code
Algorithms for mean-field variational inference via polyhedral optimization in the Wasserstein space
We develop a theory of finite-dimensional polyhedral subsets over the Wasserstein space and optimization of functionals over them via first-order methods.
Learning Costs for Structured Monge Displacements
Because of such difficulties, existing approaches rarely depart from the default choice of estimating such maps with the simple squared-Euclidean distance as the ground cost, $c(x, y)=\|x-y\|^2_2$.
Multisample Flow Matching: Straightening Flows with Minibatch Couplings
Simulation-free methods for training continuous-time generative models construct probability paths that go between noise distributions and individual data samples.
An Explicit Expansion of the Kullback-Leibler Divergence along its Fisher-Rao Gradient Flow
In this short note, we complement these existing results in the literature by providing an explicit expansion of $\text{KL}(\rho_t^{\text{FR}}\|\pi)$ in terms of $e^{-t}$, where $(\rho_t^{\text{FR}})_{t\geq 0}$ is the FR gradient flow of the KL divergence.
Minimax estimation of discontinuous optimal transport maps: The semi-discrete case
We consider the problem of estimating the optimal transport map between two probability distributions, $P$ and $Q$ in $\mathbb R^d$, on the basis of i. i. d.
Optimal transport map estimation in general function spaces
To ensure identifiability, we assume that $T = \nabla \varphi_0$ is the gradient of a convex function, in which case $T$ is known as an \emph{optimal transport map}.
Entropic estimation of optimal transport maps
We develop a computationally tractable method for estimating the optimal map between two distributions over $\mathbb{R}^d$ with rigorous finite-sample guarantees.
Learning normalizing flows from Entropy-Kantorovich potentials
We approach the problem of learning continuous normalizing flows from a dual perspective motivated by entropy-regularized optimal transport, in which continuous normalizing flows are cast as gradients of scalar potential functions.
Farkas layers: don't shift the data, fix the geometry
Successfully training deep neural networks often requires either batch normalization, appropriate weight initialization, both of which come with their own challenges.
A principled approach for generating adversarial images under non-smooth dissimilarity metrics
This includes, but is not limited to, $\ell_1, \ell_2$, and $\ell_\infty$ perturbations; the $\ell_0$ counting "norm" (i. e. true sparseness); and the total variation seminorm, which is a (non-$\ell_p$) convolutional dissimilarity measuring local pixel changes.
The LogBarrier adversarial attack: making effective use of decision boundary information
Adversarial attacks formally correspond to an optimization problem: find a minimum norm image perturbation, constrained to cause misclassification.
