Learning a local symmetry with neural networks

We explore the capacity of neural networks to detect a symmetry with complex local and non-local patterns: the gauge symmetry Z2. This symmetry is present in physical problems from topological transitions to quantum chromodynamics, and controls the computational hardness of instances of spin-glasses. Here, we show how to design a neural network, and a dataset, able to learn this symmetry and to find compressed latent representations of the gauge orbits. Our method pays special attention to system-wrapping loops, the so-called Polyakov loops, known to be particularly relevant for computational complexity

Exact Training of Restricted Boltzmann Machines on Intrinsically Low Dimensional Data

International audienc

Manufacturing knowledge sharing in PLM: a progression towards the use of heavy weight ontologies

The drive to maximize the potential benefits of decision support systems continues to increase as industry is continually driven by the competitive needs of operating in dynamic global environments. The more extensive information support tools which are becoming available in the PLM world appear to have great potential but require a substantial overhead in their configuration. However, sharing information and knowledge in cross-disciplinary teams and across system and company boundaries is not straightforward and there is a clear need for more effective frameworks for information and knowledge sharing if new product development processes are to have effective ICT support. This paper presents a view of the current status of manufacturing information sharing using light-weight ontologies and goes on to discuss the potential for heavyweight ontological engineering approaches such as the Process Specification Language (PSL). It explains why such languages are needed and how they provide an important step towards process knowledge sharing. Machining examples are used to illustrate how PSL provides a rigorous basis for process knowledge sharing and subsequently to illustrate the value of linking foundation and domain ontologies to provide a basis for multi-context knowledge sharing

Finite-size scaling analysis of the distributions of pseudo-critical temperatures in spin glasses

Using the results of large scale numerical simulations we study the probability distribution of the pseudo critical temperature for the three-dimensional Edwards-Anderson Ising spin glass and for the fully connected Sherrington-Kirkpatrick model. We find that the behavior of our data is nicely described by straightforward finite-size scaling relations.Comment: 23 pages, 9 figures. Version accepted for publication in J. Stat. Mec

Cycle-based Cluster Variational Method for Direct and Inverse Inference

We elaborate on the idea that loop corrections to belief propagation could be dealt with in a systematic way on pairwise Markov random fields, by using the elements of a cycle basis to define region in a generalized belief propagation setting. The region graph is specified in such a way as to avoid dual loops as much as possible, by discarding redundant Lagrange multipliers, in order to facilitate the convergence, while avoiding instabilities associated to minimal factor graph construction. We end up with a two-level algorithm, where a belief propagation algorithm is run alternatively at the level of each cycle and at the inter-region level. The inverse problem of finding the couplings of a Markov random field from empirical covariances can be addressed region wise. It turns out that this can be done efficiently in particular in the Ising context, where fixed point equations can be derived along with a one-parameter log likelihood function to minimize. Numerical experiments confirm the effectiveness of these considerations both for the direct and inverse MRF inference.Comment: 47 pages, 16 figure

Real space Renormalization Group analysis of a non-mean field spin-glass

A real space Renormalization Group approach is presented for a non-mean field spin-glass. This approach has been conceived in the effort to develop an alternative method to the Renormalization Group approaches based on the replica method. Indeed, non-perturbative effects in the latter are quite generally out of control, in such a way that these approaches are non-predictive. On the contrary, we show that the real space method developed in this work yields precise predictions for the critical behavior and exponents of the model

Spatial correlations in attribute communities

Community detection is an important tool for exploring and classifying the properties of large complex networks and should be of great help for spatial networks. Indeed, in addition to their location, nodes in spatial networks can have attributes such as the language for individuals, or any other socio-economical feature that we would like to identify in communities. We discuss in this paper a crucial aspect which was not considered in previous studies which is the possible existence of correlations between space and attributes. Introducing a simple toy model in which both space and node attributes are considered, we discuss the effect of space-attribute correlations on the results of various community detection methods proposed for spatial networks in this paper and in previous studies. When space is irrelevant, our model is equivalent to the stochastic block model which has been shown to display a detectability-non detectability transition. In the regime where space dominates the link formation process, most methods can fail to recover the communities, an effect which is particularly marked when space-attributes correlations are strong. In this latter case, community detection methods which remove the spatial component of the network can miss a large part of the community structure and can lead to incorrect results.Comment: 10 pages and 7 figure

Towards the ontology-based consolidation of production-centric standards

Production-­centric international standards are intended to serve as an important route towards information sharing across manufacturing decision support systems. As a consequence of textual-­based definitions of concepts acknowledged within these standards, their inability to fully interoperate becomes an issue especially since a multitude of standards are required to cover the needs of extensive domains such as manufacturing industries. To help reinforce the current understanding to support the consolidation of production-­centric standards for improved information sharing, this article explores the specification of well-defined core concepts which can be used as a basis for capturing tailored semantic definitions. The potentials of two heavyweight ontological approaches, notably Common Logic (CL) and the Web Ontology Language (OWL) as candidates for the task, are also exposed. An important finding regarding these two methods is that while an OWL-­based approach shows capabilities towards applications which may require flexible hierarchies of concepts, a CL-­based method represents a favoured contender for scoped and facts-­driven manufacturing applications

Extending product lifecycle management for manufacturing knowledge sharing

Product lifecycle management provides a framework for information sharing that promotes various types of decisionmaking procedures. For product lifecycle management to advance towards knowledge-driven decision support, then this demands more than simply exchanging information. There is, therefore, a need to formally capture best practice through-life engineering knowledge that can be fed back across the product lifecycle. This article investigates the interoperable manufacturing knowledge systems concept. Interoperable manufacturing knowledge systems use an expressive ontological approach that drives the improved configuration of product lifecycle management systems for manufacturing knowledge sharing. An ontology of relevant core product lifecycle concepts is identified from which viewpoint-specific domains, such as design and manufacture, can be formalised. Essential ontology-based mechanisms are accommodated to support the verification and sharing of manufacturing knowledge across domains. The work has been experimentally assessed using an aerospace compressor disc design and manufacture example. While it has been demonstrated that the approach supports the representation of disparate design and manufacture perspectives as well as manufacturing knowledge feedback in a timely manner, areas for improvement have also been identified for future work

Router-level community structure of the Internet Autonomous Systems

The Internet is composed of routing devices connected between them and organized into independent administrative entities: the Autonomous Systems. The existence of different types of Autonomous Systems (like large connectivity providers, Internet Service Providers or universities) together with geographical and economical constraints, turns the Internet into a complex modular and hierarchical network. This organization is reflected in many properties of the Internet topology, like its high degree of clustering and its robustness. In this work, we study the modular structure of the Internet router-level graph in order to assess to what extent the Autonomous Systems satisfy some of the known notions of community structure. We show that the modular structure of the Internet is much richer than what can be captured by the current community detection methods, which are severely affected by resolution limits and by the heterogeneity of the Autonomous Systems. Here we overcome this issue by using a multiresolution detection algorithm combined with a small sample of nodes. We also discuss recent work on community structure in the light of our results