109 citations · 522 across the 51 of their papers we have counts for
10 papers · 1 filter
No-collision Transportation Maps
Levon Nurbekyan, Alexander Iannantuono, Adam M. Oberman
Transportation maps between probability measures are critical objects in numerous areas of mathematics and applications such as PDE, fluid mechanics, geometry, machine learning, co…
Farkas layers: don't shift the data, fix the geometry
Aram-Alexandre Pooladian, Chris Finlay, Adam M Oberman
Successfully training deep neural networks often requires either batch normalization, appropriate weight initialization, both of which come with their own challenges. We propose an…
Partial differential equation regularization for supervised machine learning
Adam M Oberman
This article is an overview of supervised machine learning problems for regression and classification. Topics include: kernel methods, training by stochastic gradient descent, deep…
Nesterov's method with decreasing learning rate leads to accelerated stochastic gradient descent
Maxime Laborde, Adam M. Oberman
We present a coupled system of ODEs which, when discretized with a constant time step/learning rate, recovers Nesterov's accelerated gradient descent algorithm. The same ODEs, when…
A principled approach for generating adversarial images under non-smooth dissimilarity metrics
Aram-Alexandre Pooladian, Chris Finlay, Tim Hoheisel +1
Deep neural networks perform well on real world data but are prone to adversarial perturbations: small changes in the input easily lead to misclassification. In this work, we propo…
A Partial Differential Equation Obstacle Problem for the Level Set Approach to Visibility
Adam Oberman, Tiago Salvador
In this article we consider the problem of finding the visibility set from a given point when the obstacles are represented as the level set of a given function. Although the visib…
Scaleable input gradient regularization for adversarial robustness
Chris Finlay, Adam M Oberman
In this work we revisit gradient regularization for adversarial robustness with some new ingredients. First, we derive new per-image theoretical robustness bounds based on local gr…
The LogBarrier adversarial attack: making effective use of decision boundary information
Chris Finlay, Aram-Alexandre Pooladian, Adam M. Oberman
Adversarial attacks for image classification are small perturbations to images that are designed to cause misclassification by a model. Adversarial attacks formally correspond to a…
Calibrated Top-1 Uncertainty estimates for classification by score based models
Adam M. Oberman, Chris Finlay, Alexander Iannantuono +1
While the accuracy of modern deep learning models has significantly improved in recent years, the ability of these models to generate uncertainty estimates has not progressed to th…
Stochastic Gradient Descent with Polyak's Learning Rate
Adam M. Oberman, Mariana Prazeres
Stochastic gradient descent (SGD) for strongly convex functions converges at the rate $\bO(1/k)$. However, achieving good results in practice requires tuning the parameters (for ex…