An Efficient Algorithm for Mining Frequent Sequence with Constraint Programming

The main advantage of Constraint Programming (CP) approaches for sequential pattern mining (SPM) is their modularity, which includes the ability to add new constraints (regular expressions, length restrictions, etc). The current best CP approach for SPM uses a global constraint (module) that computes the projected database and enforces the minimum frequency; it does this with a filtering algorithm similar to the PrefixSpan method. However, the resulting system is not as scalable as some of the most advanced mining systems like Zaki's cSPADE. We show how, using techniques from both data mining and CP, one can use a generic constraint solver and yet outperform existing specialized systems. This is mainly due to two improvements in the module that computes the projected frequencies: first, computing the projected database can be sped up by pre-computing the positions at which an symbol can become unsupported by a sequence, thereby avoiding to scan the full sequence each time; and second by taking inspiration from the trailing used in CP solvers to devise a backtracking-aware data structure that allows fast incremental storing and restoring of the projected database. Detailed experiments show how this approach outperforms existing CP as well as specialized systems for SPM, and that the gain in efficiency translates directly into increased efficiency for other settings such as mining with regular expressions.Comment: frequent sequence mining, constraint programmin

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

Characterization of complex quantum dynamics with a scalable NMR information processor

We present experimental results on the measurement of fidelity decay under contrasting system dynamics using a nuclear magnetic resonance quantum information processor. The measurements were performed by implementing a scalable circuit in the model of deterministic quantum computation with only one quantum bit. The results show measurable differences between regular and complex behaviour and for complex dynamics are faithful to the expected theoretical decay rate. Moreover, we illustrate how the experimental method can be seen as an efficient way for either extracting coarse-grained information about the dynamics of a large system, or measuring the decoherence rate from engineered environments.Comment: 4pages, 3 figures, revtex4, updated with version closer to that publishe

Contrôle quantique grâce aux méthodes de RMN. Application à la simulation de systèmes quantiques

Manipuler l'information selon les lois de la physique quantique permet d'améliorer l'efficacité avec laquelle on traite certains problèmes. Les méthodes de Résonance Magnétique Nucléaire en solution permettent d'initialiser, de manipuler et d'observer l'état d'un système de spins 1/2 couplés. Ces méthodes ont été utilisées pour réaliser expérimentalement un petit processeur d'information quantique (QIP pour "Quantum Information Processor") pouvant exécuter une centaine d'opérations élémentaires. Un des thèmes principaux de ce travail a été de concevoir, d'optimiser et de valider des séquences d'impulsions nécessaires pour "programmer" ce QIP. Ces techniques ont été utilisées pour exécuter un algorithme quantique de simulation des systèmes anyoniques. Des résultats expérimentaux pour la détermination des énergies propres et de fonctions de corrélation d'un système illustratif de fermions sur réseaux ont été obtenus permettant de valider l'algorithme de simulation dans son principe et son exécution expérimentale.Manipulating information according to quantum laws allows improvements in the efficency of the way we treat certain problems. Liquid state Nuclear Magnetic Resonance methods allow us to initialize, manipulate and read the quantum state of a system of coupled spins. These methods have been used to realize an experimental small Quantum Information Processor (QIP) able to pocess information through around hundred elementary operations. One of the main themes of this work was to design, optimize and validate realiable RF-pulse sequences used to "program" the QIP. Such techniques have been used to run a quantum simulation algorithm for anyonic systems. Some experimental results have been obtained on the determination of eigenenergies and correlation function for a toy problem consisting of fermions on a lattice, showing an experimental proof of principle for such quantum simulations

Prefix-Projection Global Constraint for Sequential Pattern Mining

Sequential pattern mining under constraints is a challenging data mining task. Many efficient ad hoc methods have been developed for mining sequential patterns, but they are all suffering from a lack of genericity. Recent works have investigated Constraint Programming (CP) methods, but they are not still effective because of their encoding. In this paper, we propose a global constraint based on the projected databases principle which remedies to this drawback. Experiments show that our approach clearly outperforms CP approaches and competes well with ad hoc methods on large datasets