A Unified View of Piecewise Linear Neural Network Verification

The success of Deep Learning and its potential use in many safety-critical applications has motivated research on formal verification of Neural Network (NN) models. Despite the reputation of learned NN models to behave as black boxes and the theoretical hardness of proving their properties, researchers have been successful in verifying some classes of models by exploiting their piecewise linear structure and taking insights from formal methods such as Satisifiability Modulo Theory. These methods are however still far from scaling to realistic neural networks. To facilitate progress on this crucial area, we make two key contributions. First, we present a unified framework that encompasses previous methods. This analysis results in the identification of new methods that combine the strengths of multiple existing approaches, accomplishing a speedup of two orders of magnitude compared to the previous state of the art. Second, we propose a new data set of benchmarks which includes a collection of previously released testcases. We use the benchmark to provide the first experimental comparison of existing algorithms and identify the factors impacting the hardness of verification problems.Comment: Updated version of "Piecewise Linear Neural Network verification: A comparative study

Branch and Bound for Piecewise Linear Neural Network Verification

The success of Deep Learning and its potential use in many safety-critical applications has motivated research on formal verification of Neural Network (NN) models. In this context, verification involves proving or disproving that an NN model satisfies certain input-output properties. Despite the reputation of learned NN models as black boxes, and the theoretical hardness of proving useful properties about them, researchers have been successful in verifying some classes of models by exploiting their piecewise linear structure and taking insights from formal methods such as Satisifiability Modulo Theory. However, these methods are still far from scaling to realistic neural networks. To facilitate progress on this crucial area, we exploit the Mixed Integer Linear Programming (MIP) formulation of verification to propose a family of algorithms based on Branch-and-Bound (BaB). We show that our family contains previous verification methods as special cases. With the help of the BaB framework, we make three key contributions. Firstly, we identify new methods that combine the strengths of multiple existing approaches, accomplishing significant performance improvements over previous state of the art. Secondly, we introduce an effective branching strategy on ReLU non-linearities. This branching strategy allows us to efficiently and successfully deal with high input dimensional problems with convolutional network architecture, on which previous methods fail frequently. Finally, we propose comprehensive test data sets and benchmarks which includes a collection of previously released testcases. We use the data sets to conduct a thorough experimental comparison of existing and new algorithms and to provide an inclusive analysis of the factors impacting the hardness of verification problems

Fracture strengths of chair‑side‑generated veneers cemented with glass fibers

Introduction: CAD/CAM (computer‑aided design and computer‑aided manufacturing) systems have refreshed the idea of chair‑side production of restorations, but the fracture of ceramic veneers remains a problem. Cementation with glass fibers may improve the fracture strengths and affect the failure modes of CAD/CAM‑generated ceramic veneers. Therefore, this study compared the fracture strengths of ceramic veneers produced at chair side and cemented with or without glass fibers with those of composite veneers. Methodology: Thirty intact mandibular incisors were randomly divided into three groups (n = 10) and treated with CAD/CAM‑fabricated veneers cemented with dual‑cure composite resin luting cement (CRLC; Group 1), CAD/CAM‑fabricated veneers cemented with a glass fiber network (GFN) and dual‑cure CRLC (Group 2), and a direct particulate filler composite veneer constructed utilizing fiber and a restorative composite resin (Group 3). The specimens were tested with a universal testing machine after thermal cycling treatment. Result: The loads at the start of fracture were the lowest for traditionally fabricated composite veneers and higher for CAD/CAM‑generated. Veneers cemented either without or with the GFN. The failure initiation loads (N) for the veneers were 798.92 for Group 1, 836.27 for Group 2, and 585.93 for Group 3. The predominant failure mode is adhesive failure between the laminates and teeth for Group 1, cohesive failure in the luting layer for Group 2, and cohesive laminate failure for Group 3, which showed chipping and small fractures. Conclusion: Ceramic material is a reliable alternative for veneer construction at chair side. Fibers at the cementation interface may improve the clinical longevity and provide higher fracture strength values.Key words: Computer-aided design and computer-aided manufacturing, cementation, fracture strength, glass fiber, laminate venee

Influences of elastic foundations and material gradient on the dynamic response of polymer cylindrical pipes patterned by carbon nanotube subjected to moving pressures

Composite materials are frequently used in the construction of rail, tunnels, and pipelines as well as in the construction of aircraft, ships, and chemical pipelines. When such structural elements are formed from new-generation composites, such as CNT-reinforced composites, and their interaction with the ground, there is a need to renew the dynamic response calculations under moving pressures and to create new mathematical solution methods during their design. The aim of this study was to analyze the influences of elastic foundations (EFs) and material gradient on the dynamic response of infinitely long carbon nanotube (CNT)-based polymer pipes under combined static and moving pressures. The CNT-based polymer pipes resting on the EFs were exposed to the axial and moving pressures. The uniform and heterogeneous reinforcement distributions of CNTs, which varied linearly throughout the thickness of polymer pipes, were considered. After setting the problem, the fundamental equations derived to find new analytical expressions for dynamic coefficients and critical velocity, which are dynamic characteristics of cylindrical pipes reinforced by the uniform and linear distributions of CNTs, were solved in the framework of the vibration theory. Finally, numerical computations were performed to examine the effects of EFs on the critical parameters depending on the characteristics of the pipes, the speed of moving pressures, the shape of the distribution of CNTs, and the change in volume fractions