Graph-based methods coupled with specific distributional distances for adversarial attack detection

Artificial neural networks are prone to being fooled by carefully perturbed inputs which cause an egregious misclassification. These \textit{adversarial} attacks have been the focus of extensive research. Likewise, there has been an abundance of research in ways to detect and defend against them. We introduce a novel approach of detection and interpretation of adversarial attacks from a graph perspective. For an image, benign or adversarial, we study how a neural network's architecture can induce an associated graph. We study this graph and introduce specific measures used to predict and interpret adversarial attacks. We show that graphs-based approaches help to investigate the inner workings of adversarial attacks

Graphes pour l’exploration des réseaux de neurones artificiels et de la connectivité cérébrale humaine

The main objective of this thesis is to explore brain and artificial neural network connectivity from agraph-based perspective. While structural and functional connectivity analysis has been extensivelystudied in the context of the human brain, there is a lack of a similar analysis framework in artificialsystems.To address this gap, this research focuses on two main axes.In the first axis, the main objective is to determine a healthy signature characterization of the humanbrain resting state functional connectivity. To achieve this objective, a novel framework is proposed,integrating traditional graph statistics and network reduction tools, to determine healthy connectivitypatterns. Hence, we build a graph pair-wise comparison and a classifier to identify pathological statesand rank associated perturbed brain regions. Additionally, the generalization and robustness of theproposed framework were investigated across multiple datasets and variations in data quality.The second research axis explores the benefits of brain-inspired connectivity exploration of artificialneural networks (ANNs) in the future perspective of more robust artificial systems development. Amajor robustness issue in ANN models is represented by catastrophic forgetting when the networkdramatically forgets previously learned tasks when adapting to new ones. Our work demonstrates thatgraph modeling offers a simple and elegant framework for investigating ANNs, comparing differentlearning strategies, and detecting deleterious behaviors such as catastrophic forgetting.Moreover, we explore the potential of leveraging graph-based insights to effectively mitigatecatastrophic forgetting, laying a foundation for future research and explorations in this area.L'objectif principal de cette thèse est d'explorer la connectivité cérébrale et celle des réseaux de neurones artificiels d'un point de vue de leur connectivité. Un modèle par graphes pour l'analyse de la connectivité structurelle et fonctionnelle a été largement étudié dans le contexte du cerveau humain mais, un tel cadre d'analyse manque encore pour l'analyse des systèmes artificiels. Avec l'objectif d'intégrer l'analyse de la connectivité dans les système artificiels, cette recherche se concentre sur deux axes principaux. Dans le premier axe, l'objectif principal est de déterminer une caractérisation de la signature saine de la connectivité fonctionnelle de repos du cerveau humain. Pour atteindre cet objectif, une nouvelle méthode est proposée, intégrant des statistiques de graphe traditionnelles et des outils de réduction de réseau, pour déterminer des modèles de connectivité sains. Ainsi, nous construisons une comparaison en paires de graphes et un classifieur pour identifier les états pathologiques et identifier les régions cérébrales perturbées par une pathologie. De plus, la généralisation et la robustesse de la méthode proposée ont été étudiées sur plusieurs bases de données et variations de la qualité des données. Le deuxième axe de recherche explore les avantages de l'intégration des études de la connectivité inspirée du cerveau aux réseaux de neurones artificiels (ANNs) dans la perspective du développement de systèmes artificiels plus robustes. Un problème majeur de robustesse dans les modèles d'ANN est représenté par l'oubli catastrophique qui apparaît lorsque le réseau oublie dramatiquement les tâches précédemment apprises lors de l'adaptation à de nouvelles tâches. Notre travail démontre que la modélisation par graphes offre un cadre simple et élégant pour étudier les ANNs, comparer différentes stratégies d'apprentissage et détecter des comportements nuisibles tels que l'oubli catastrophique. De plus, nous soulignons le potentiel d'une adaptation à de nouvelles tâches en contrôlant les graphes afin d'atténuer efficacement l'oubli catastrophique et jetant ainsi les bases de futures recherches et explorations dans ce domaine

Superfici minime tra matematica e architettura

Il problema di Plateau richiede di trovare tra tutte le superfici con un assegnato contorno quella di area minima. Le superfici soluzione di tale problema godono di una proprietà geometrica particolare: ogni punto della superficie ha curvature principali opposte. Le superfici che soddisfano quest’ultima proprietà si dicono superfici minime. Anche l’architettura ha fatto ampio uso di tali superfici, sia per la proprietà di assicurare un equilibrio stabile, sia perché permettono di contenere i costi in termini di minor materiale utilizzato, ma anche per la loro eleganza. In questo studio si riprendono alcuni dei concetti e dei principali risultati della geometria differenziale necessari per dare, nel secondo capitolo, una definizione rigorosa di superficie minima e di studiarne le principali proprietà. Successivamente, si studiano alcuni esempi di superfici minime, quali la superficie di Catalan, l’elicoide, unica superficie rigata non banale, e la catenoide, unica superficie minima di rotazione. Nel terzo capitolo vengono analizzati alcuni esempi di applicazione delle superfici minime in architettura

Nodal statistics-based structural pattern detection for graph collections characterization

International audienceo Human consciousness states can be differentiated by nodal organization inbrain functional connectivity networks▶ structural pattern definition▶ extend node role discovery to graph collections▶ graph collections comparison based on structural patter

Nodal statistics-based structural pattern detection for graph collections characterization

International audienceo Human consciousness states can be differentiated by nodal organization inbrain functional connectivity networks▶ structural pattern definition▶ extend node role discovery to graph collections▶ graph collections comparison based on structural patter

Network embedding for brain connectivity

International audienceIn Neurosciences, networks are currently used for representing the brain connections system with the purpose of determining the specific characteristics of the brain itself. However, discriminating between a healthy human brain network and a pathological one using common network descriptors could be misleading. For this reason, we explored network embedding techniques with the purpose of brain connectivity networks comparison. We proposed first the definition of representative graph for healthy brain connectivity. Then, two classification procedures through embedding are introduced, achieving good accuracy results in different datasets. Moreover, the intriguing power of this technique is given by the possibility of visualizing networks in a low-dimensional space, facilitating the interpretation of the differences between networks under diverse conditions e.g. normal or pathological

Network embedding for brain connectivity

International audienceIn Neurosciences, networks are currently used for representing the brain connections system with the purpose of determining the specific characteristics of the brain itself. However, discriminating between a healthy human brain network and a pathological one using common network descriptors could be misleading. For this reason, we explored network embedding techniques with the purpose of brain connectivity networks comparison. We proposed first the definition of representative graph for healthy brain connectivity. Then, two classification procedures through embedding are introduced, achieving good accuracy results in different datasets. Moreover, the intriguing power of this technique is given by the possibility of visualizing networks in a low-dimensional space, facilitating the interpretation of the differences between networks under diverse conditions e.g. normal or pathological

Network embedding for brain connectivity

International audienceIn Neurosciences, networks are currently used for representing the brain connections system with the purpose of determining the specific characteristics of the brain itself. However, discriminating between a healthy human brain network and a pathological one using common network descriptors could be misleading. For this reason, we explored network embedding techniques with the purpose of brain connectivity networks comparison. We proposed first the definition of representative graph for healthy brain connectivity. Then, two classification procedures through embedding are introduced, achieving good accuracy results in different datasets. Moreover, the intriguing power of this technique is given by the possibility of visualizing networks in a low-dimensional space, facilitating the interpretation of the differences between networks under diverse conditions e.g. normal or pathological

Nodal statistics-based equivalence relation for graph collections

Node role explainability in complex networks is very difficult, yet is crucial in different application domains such as social science, neurosciences or computer science. Many efforts have been made on the quantification of hubs revealing particular nodes in a network using a given structural property. Yet, in several applications, when multiple instances of networks are available and several structural properties appear to be relevant, the identification of node roles remains largely unexplored. Inspired by the node automorphically equivalence relation, we define an equivalence relation on graph nodes associated with any collection of nodal statistics (i.e. any functions on the node-set). This allows us to define new graph global measures: the power coefficient, and the orthogonality score to evaluate the parsimony and heterogeneity of a given nodal statistics collection. In addition, we introduce a new method based on structural patterns to compare graphs that have the same vertices set. This method assigns a value to a node to determine its role distinctiveness in a graph family. Extensive numerical results of our method are conducted on both generative graph models and real data concerning human brain functional connectivity. The differences in nodal statistics are shown to be dependent on the underlying graph structure. Comparisons between generative models and real networks combining two different nodal statistics reveal the complexity of human brain functional connectivity with differences at both global and nodal levels. Using a group of 200 healthy controls connectivity networks, our method computes high correspondence scores among the whole population, to detect homotopy, and finally quantify differences between comatose patients and healthy controls

Nodal statistics-based equivalence relation for graph collections

Node role explainability in complex networks is very difficult, yet is crucial in different application domains such as social science, neurosciences or computer science. Many efforts have been made on the quantification of hubs revealing particular nodes in a network using a given structural property. Yet, in several applications, when multiple instances of networks are available and several structural properties appear to be relevant, the identification of node roles remains largely unexplored. Inspired by the node automorphically equivalence relation, we define an equivalence relation on graph nodes associated with any collection of nodal statistics (i.e. any functions on the node-set). This allows us to define new graph global measures: the power coefficient, and the orthogonality score to evaluate the parsimony and heterogeneity of a given nodal statistics collection. In addition, we introduce a new method based on structural patterns to compare graphs that have the same vertices set. This method assigns a value to a node to determine its role distinctiveness in a graph family. Extensive numerical results of our method are conducted on both generative graph models and real data concerning human brain functional connectivity. The differences in nodal statistics are shown to be dependent on the underlying graph structure. Comparisons between generative models and real networks combining two different nodal statistics reveal the complexity of human brain functional connectivity with differences at both global and nodal levels. Using a group of 200 healthy controls connectivity networks, our method computes high correspondence scores among the whole population, to detect homotopy, and finally quantify differences between comatose patients and healthy controls