On Lipschitz Regularization of Convolutional Layers using Toeplitz Matrix Theory

This paper tackles the problem of Lipschitz regularization of Convolutional Neural Networks. Lipschitz regularity is now established as a key property of modern deep learning with implications in training stability, generalization, robustness against adversarial examples, etc. However, computing the exact value of the Lipschitz constant of a neural network is known to be NP-hard. Recent attempts from the literature introduce upper bounds to approximate this constant that are either efficient but loose or accurate but computationally expensive. In this work, by leveraging the theory of Toeplitz matrices, we introduce a new upper bound for convolutional layers that is both tight and easy to compute. Based on this result we devise an algorithm to train Lipschitz regularized Convolutional Neural Networks

Robust Neural Networks using Randomized Adversarial Training

Since the discovery of adversarial examples in machine learning, researchers have designed several techniques to train neural networks that are robust against different types of attacks (most notably ∞ and 2 based attacks). However , it has been observed that the defense mechanisms designed to protect against one type of attack often offer poor performance against the other. In this paper, we introduce Randomized Adversarial Training (RAT), a technique that is efficient both against 2 and ∞ attacks. To obtain this result, we build upon adversarial training, a technique that is efficient against ∞ attacks, and demonstrate that adding random noise at training and inference time further improves performance against 2 attacks. We then show that RAT is as efficient as adversarial training against ∞ attacks while being robust against strong 2 attacks. Our final comparative experiments demonstrate that RAT outperforms all state-of-the-art approaches against 2 and ∞ attacks

Precision-Recall Divergence Optimization for Generative Modeling with GANs and Normalizing Flows

Achieving a balance between image quality (precision) and diversity (recall) is a significant challenge in the domain of generative models. Current state-of-the-art models primarily rely on optimizing heuristics, such as the Fr\'echet Inception Distance. While recent developments have introduced principled methods for evaluating precision and recall, they have yet to be successfully integrated into the training of generative models. Our main contribution is a novel training method for generative models, such as Generative Adversarial Networks and Normalizing Flows, which explicitly optimizes a user-defined trade-off between precision and recall. More precisely, we show that achieving a specified precision-recall trade-off corresponds to minimizing a unique $f$-divergence from a family we call the \mbox{\em PR-divergences}. Conversely, any $f$-divergence can be written as a linear combination of PR-divergences and corresponds to a weighted precision-recall trade-off. Through comprehensive evaluations, we show that our approach improves the performance of existing state-of-the-art models like BigGAN in terms of either precision or recall when tested on datasets such as ImageNet

Randomization for adversarial robustness: the Good, the Bad and the Ugly

Deep neural networks are known to be vulnerable to adversarial attacks: A small perturbation that is imperceptible to a human can easily make a well-trained deep neural network misclassify. To defend against adversarial attacks, randomized classifiers have been proposed as a robust alternative to deterministic ones. In this work we show that in the binary classification setting, for any randomized classifier, there is always a deterministic classifier with better adversarial risk. In other words, randomization is not necessary for robustness. In many common randomization schemes, the deterministic classifiers with better risk are explicitly described: For example, we show that ensembles of classifiers are more robust than mixtures of classifiers, and randomized smoothing is more robust than input noise injection. Finally, experiments confirm our theoretical results with the two families of randomized classifiers we analyze.Comment: 8 pages + bibliography and appendix, 3 figures. Submitted to ICML 202

Un algorithme de fouille de données générique et parallèle pour architecture multi-coeurs

In the pattern mining field, there exist a large number of algorithms that can solve a large variety of distinct but similar pattern mining problems. This variety prevent broad adoption of data analysis with pattern mining algorithms. In this thesis we propose a formal framework that is able to capture a broad range of pattern mining problems. We illustrate the generality of our framework by formalizing three different pattern mining problems: the problem of closed frequent itemset mining, the problem of closed relational graph mining and the problem of closed gradual itemset mining. Building on this framework, we have designed ParaMiner, a generic and parallel algorithm for pattern mining. ParaMiner is able to solve any pattern mining problem that can be formalized within our framework. In order to achieve practical efficiency we have generalized important optimizations from state of the art algorithms and we have made ParaMiner able to exploit parallel computing platforms. We have conducted thorough experiments that demonstrate that despite being a generic algorithm, ParaMiner can compete with the fastest ad-hoc algorithms.Dans le domaine de l'extraction de motifs, il existe un grand nombre d'algorithmes pour résoudre une large variété de sous problèmes sensiblement identiques. Cette variété d'algorithmes freine l'adoption des techniques d'extraction de motifs pour l'analyse de données. Dans cette thèse, nous proposons un formalisme qui permet de capturer une large gamme de problèmes d'extraction de motifs. Pour démontrer la généralité de ce formalisme, nous l'utilisons pour décrire trois problèmes d'extraction de motifs : le problème d'extraction d'itemsets fréquents fermés, le problème d'extraction de graphes relationnels fermés ou le problème d'extraction d'itemsets graduels fermés. Ce formalisme nous permet de construire ParaMiner qui est un algorithme générique et parallèle pour les problèmes d'extraction de motifs. ParaMiner est capable de résoudre tous les problèmes d'extraction de motifs qui peuvent ˆtre décrit dans notre formalisme. Pour obtenir de bonne performances, nous avons généralisé plusieurs optimisations proposées par la communauté dans le cadre de problèmes spécifique d'extraction de motifs. Nous avons également exploité la puissance de calcul parallèle disponible dans les archi- tectures parallèles. Nos expériences démontrent qu'en dépit de la généricité de ParaMiner ses performances sont comparables avec celles obtenues par les algorithmes les plus rapides de l'état de l'art. Ces algorithmes bénéficient pourtant d'un avantage important, puisqu'ils incorporent de nombreuses optimisations spécifiques au sous problème d'extraction de motifs qu'ils résolvent

A generic and parallel pattern mining algorithm for multi-core architectures.

Dans le domaine de l'extraction de motifs, il existe un grand nombre d'algorithmes pour résoudre une large variété de sous problèmes sensiblement identiques. Cette variété d'algorithmes freine l'adoption des techniques d'extraction de motifs pour l'analyse de données. Dans cette thèse, nous proposons un formalisme qui permet de capturer une large gamme de problèmes d'extraction de motifs. Pour démontrer la généralité de ce formalisme, nous l'utilisons pour décrire trois problèmes d'extraction de motifs : le problème d'extraction d'itemsets fréquents fermés, le problème d'extraction de graphes relationnels fermés ou le problème d'extraction d'itemsets graduels fermés. Ce formalisme nous permet de construire ParaMiner qui est un algorithme générique et parallèle pour les problèmes d'extraction de motifs. ParaMiner est capable de résoudre tous les problèmes d'extraction de motifs qui peuvent ˆtre décrit dans notre formalisme. Pour obtenir de bonne performances, nous avons généralisé plusieurs optimisations proposées par la communauté dans le cadre de problèmes spécifique d'extraction de motifs. Nous avons également exploité la puissance de calcul parallèle disponible dans les archi- tectures parallèles. Nos expériences démontrent qu'en dépit de la généricité de ParaMiner ses performances sont comparables avec celles obtenues par les algorithmes les plus rapides de l'état de l'art. Ces algorithmes bénéficient pourtant d'un avantage important, puisqu'ils incorporent de nombreuses optimisations spécifiques au sous problème d'extraction de motifs qu'ils résolvent.In the pattern mining field, there exist a large number of algorithms that can solve a large variety of distinct but similar pattern mining problems. This variety prevent broad adoption of data analysis with pattern mining algorithms. In this thesis we propose a formal framework that is able to capture a broad range of pattern mining problems. We illustrate the generality of our framework by formalizing three different pattern mining problems: the problem of closed frequent itemset mining, the problem of closed relational graph mining and the problem of closed gradual itemset mining. Building on this framework, we have designed ParaMiner, a generic and parallel algorithm for pattern mining. ParaMiner is able to solve any pattern mining problem that can be formalized within our framework. In order to achieve practical efficiency we have generalized important optimizations from state of the art algorithms and we have made ParaMiner able to exploit parallel computing platforms. We have conducted thorough experiments that demonstrate that despite being a generic algorithm, ParaMiner can compete with the fastest ad-hoc algorithms

Constraint-based sequence mining using constraint programming

The goal of constraint-based sequence mining is to find sequences of symbols that are included in a large number of input sequences and that satisfy some constraints specified by the user. Many constraints have been proposed in the literature, but a general framework is still missing. We investigate the use of constraint programming as general framework for this task. We first identify four categories of constraints that are applicable to sequence mining. We then propose two constraint programming formulations. The first formulation introduces a new global constraint called exists-embedding. This formulation is the most efficient but does not support one type of constraint. To support such constraints, we develop a second formulation that is more general but incurs more overhead. Both formulations can use the projected database technique used in specialised algorithms. Experiments demonstrate the flexibility towards constraint-based settings and compare the approach to existing methods.In Integration of AI and OR Techniques in Constraint Programming (CPAIOR), 2015status: publishe