Uniform Random Sampling Product Configurations of Feature Models That Have Numerical Features

Analyses of Software Product Lines (SPLs) rely on automated solvers to navigate complex dependencies among features and find legal configurations. Often these analyses do not support numerical features with constraints because propositional formulas use only Boolean variables. Some automated solvers can represent numerical features natively, but are limited in their ability to count and Uniform Random Sample (URS) conigurations, which are key operations to derive unbiased statistics on configuration spaces. Bit-blasting is a technique to encode numerical constraints as propositional formulas. We use bit-blasting to encode Boolean and numerical constraints so that we can exploit existing #SAT solvers to count and URS conigurations. Compared to state-of-art Satisfiability Modulo Theory and Constraint Programming solvers, our approach has two advantages: 1) faster and more scalable coniguration counting and 2) reliable URS of SPL configurations. We also show that our work can be used to extend prior SAT-based SPL analyses to support numerical features and constraints.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Practical recommendations for gradient-based training of deep architectures

Learning algorithms related to artificial neural networks and in particular for Deep Learning may seem to involve many bells and whistles, called hyper-parameters. This chapter is meant as a practical guide with recommendations for some of the most commonly used hyper-parameters, in particular in the context of learning algorithms based on back-propagated gradient and gradient-based optimization. It also discusses how to deal with the fact that more interesting results can be obtained when allowing one to adjust many hyper-parameters. Overall, it describes elements of the practice used to successfully and efficiently train and debug large-scale and often deep multi-layer neural networks. It closes with open questions about the training difficulties observed with deeper architectures

A statistical method for revealing form-function relations in biological networks

Over the past decade, a number of researchers in systems biology have sought to relate the function of biological systems to their network-level descriptions -- lists of the most important players and the pairwise interactions between them. Both for large networks (in which statistical analysis is often framed in terms of the abundance of repeated small subgraphs) and for small networks which can be analyzed in greater detail (or even synthesized in vivo and subjected to experiment), revealing the relationship between the topology of small subgraphs and their biological function has been a central goal. We here seek to pose this revelation as a statistical task, illustrated using a particular setup which has been constructed experimentally and for which parameterized models of transcriptional regulation have been studied extensively. The question "how does function follow form" is here mathematized by identifying which topological attributes correlate with the diverse possible information-processing tasks which a transcriptional regulatory network can realize. The resulting method reveals one form-function relationship which had earlier been predicted based on analytic results, and reveals a second for which we can provide an analytic interpretation. Resulting source code is distributed via http://formfunction.sourceforge.net.Comment: To appear in Proc. Natl. Acad. Sci. USA. 17 pages, 9 figures, 2 table

Numerical evidences of universal trap-like aging dynamics

Trap models have been initially proposed as toy models for dynamical relaxation in extremely simplified rough potential energy landscapes. Their importance has considerably grown recently thanks to the discovery that the trap like aging mechanism is directly controlling the out-of-equilibrium relaxation processes of more sophisticated spin models, that are considered as the solvable counterpart of real disordered systems. Establishing on a firmer ground the connection between these spin model out-of-equilibrium behavior and the trap like aging mechanism would shed new light on the properties, still largely mysterious, of the activated out-of-equilibrium dynamics of disordered systems. In this work we discuss numerical evidences of emergent trap-like aging behavior in a variety of disordered models. Our numerical results are backed by analytic derivations and heuristic discussions. Such exploration reveals some of the tricks needed to analyze the trap behavior in spite of the occurrence of secondary processes, of the existence of dynamical correlations and of finite system's size effects.Comment: 25 pages, 15 figure

Edge and Line Feature Extraction Based on Covariance Models

age segmentation based on contour extraction usually involves three stages of image operations: feature extraction, edge detection and edge linking. This paper is devoted to the first stage: a method to design feature extractors used to detect edges from noisy and/or blurred images. The method relies on a model that describes the existence of image discontinuities (e.g. edges) in terms of covariance functions. The feature extractor transforms the input image into a “log-likelihood ratio” image. Such an image is a good starting point of the edge detection stage since it represents a balanced trade-off between signal-to-noise ratio and the ability to resolve detailed structures. For 1-D signals, the performance of the edge detector based on this feature extractor is quantitatively assessed by the so called “average risk measure”. The results are compared with the performances of 1-D edge detectors known from literature. Generalizations to 2-D operators are given. Applications on real world images are presented showing the capability of the covariance model to build edge and line feature extractors. Finally it is shown that the covariance model can be coupled to a MRF-model of edge configurations so as to arrive at a maximum a posteriori estimate of the edges or lines in the image

Coverage, Continuity and Visual Cortical Architecture

The primary visual cortex of many mammals contains a continuous representation of visual space, with a roughly repetitive aperiodic map of orientation preferences superimposed. It was recently found that orientation preference maps (OPMs) obey statistical laws which are apparently invariant among species widely separated in eutherian evolution. Here, we examine whether one of the most prominent models for the optimization of cortical maps, the elastic net (EN) model, can reproduce this common design. The EN model generates representations which optimally trade of stimulus space coverage and map continuity. While this model has been used in numerous studies, no analytical results about the precise layout of the predicted OPMs have been obtained so far. We present a mathematical approach to analytically calculate the cortical representations predicted by the EN model for the joint mapping of stimulus position and orientation. We find that in all previously studied regimes, predicted OPM layouts are perfectly periodic. An unbiased search through the EN parameter space identifies a novel regime of aperiodic OPMs with pinwheel densities lower than found in experiments. In an extreme limit, aperiodic OPMs quantitatively resembling experimental observations emerge. Stabilization of these layouts results from strong nonlocal interactions rather than from a coverage-continuity-compromise. Our results demonstrate that optimization models for stimulus representations dominated by nonlocal suppressive interactions are in principle capable of correctly predicting the common OPM design. They question that visual cortical feature representations can be explained by a coverage-continuity-compromise.Comment: 100 pages, including an Appendix, 21 + 7 figure