Publications by Fabian Ricardo Latorre Gomez

Improving SAM Requires Rethinking its Optimization Formulation

Volkan Cevher, Fabian Ricardo Latorre Gomez, Thomas Michaelsen Pethick, Kimon Antonakopoulos, Wanyun Xie

This paper rethinks Sharpness-Aware Minimization (SAM), which is originally formulated as a zero-sum game where the weights of a network and a bounded perturbation try to minimize/maximize, respectively, the same differentiable loss. We argue that SAM shou ...

2024

Finding Actual Descent Directions For Adversarial Training

Volkan Cevher, Igor Krawczuk, Fabian Ricardo Latorre Gomez, Thomas Michaelsen Pethick, Leello Tadesse Dadi

Adversarial Training using a strong first-order adversary (PGD) is the gold standard for training Deep Neural Networks that are robust to adversarial examples. We show that, contrary to the general understanding of the method, the gradient at an optimal ad ...

2023

Robust Training and Verification of Deep Neural Networks

Fabian Ricardo Latorre Gomez

According to the proposed Artificial Intelligence Act by the European Comission (expected to pass at the end of 2023), the class of High-Risk AI Systems (Title III) comprises several important applications of Deep Learning like autonomous driving vehicles ...

EPFL2023

Adversarial Training Should Be Cast As a Non-Zero-Sum Game

Seyed Hamed Hassani, Volkan Cevher, Fabian Ricardo Latorre Gomez

One prominent approach toward resolving the adversarial vulnerability of deep neural networks is the two-player zero-sum paradigm of adversarial training, in which predictors are trained against adversarially-chosen perturbations of data. Despite the promi ...

2023

Controlling the Complexity and Lipschitz Constant improves Polynomial Nets

Volkan Cevher, Fabian Ricardo Latorre Gomez, Zhenyu Zhu, Grigorios Chrysos

While the class of Polynomial Nets demonstrates comparable performance to neural networks (NN), it currently has neither theoretical generalization characterization nor robustness guarantees. To this end, we derive new complexity bounds for the set of Coup ...

2022

The Effect of the Intrinsic Dimension on the Generalization of Quadratic Classifiers

Paul Thierry Yves Rolland, Fabian Ricardo Latorre Gomez, Leello Tadesse Dadi

It has been recently observed that neural networks, unlike kernel methods, enjoy a reduced sample complexity when the distribution is isotropic (i.e., when the covariance matrix is the identity). We find that this sensitivity to the data distribution is no ...

2021

A Plug-and-Play Deep Image Prior

Volkan Cevher, Thomas Sanchez, Fabian Ricardo Latorre Gomez, Zhaodong Sun

Deep image priors (DIP) offer a novel approach for the regularization that leverages the inductive bias of a deep convolutional architecture in inverse problems. However, the quality of DIP approaches often degrades when the number of iterations exceeds a ...

IEEE2021

Efficient Proximal Mapping of the 1-path-norm of Shallow Networks

Volkan Cevher, Paul Thierry Yves Rolland, Fabian Ricardo Latorre Gomez, Shaul Nadav Hallak

We demonstrate two new important properties of the 1-path-norm of shallow neural networks. First, despite its non-smoothness and non-convexity it allows a closed form proximal operator which can be efficiently computed, allowing the use of stochastic proxi ...

JMLR-JOURNAL MACHINE LEARNING RESEARCH2020

Lipschitz constant estimation for Neural Networks via sparse polynomial optimization

Volkan Cevher, Paul Thierry Yves Rolland, Fabian Ricardo Latorre Gomez

We introduce LiPopt, a polynomial optimization framework for computing increasingly tighter upper bounds on the Lipschitz constant of neural networks. The underlying optimization problems boil down to either linear (LP) or semidefinite (SDP) programming. W ...

2020

An Inexact Augmented Lagrangian Framework for Nonconvex Optimization with Nonlinear Constraints

Armin Eftekhari, Volkan Cevher, Ahmet Alacaoglu, Mehmet Fatih Sahin, Fabian Ricardo Latorre Gomez

We propose a practical inexact augmented Lagrangian method (iALM) for nonconvex problems with nonlinear constraints. We characterize the total computational complexity of our method subject to a verifiable geometric condition, which is closely related to t ...

2019

Fast and Provable ADMM for Learning with Generative Priors

Armin Eftekhari, Volkan Cevher, Fabian Ricardo Latorre Gomez

In this work, we propose a (linearized) Alternating Direction Method-of-Multipliers (ADMM) algorithm for minimizing a convex function subject to a nonconvex constraint. We focus on the special case where such constraint arises from the specification that a ...

2019