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

Embedded Commissioning for Building Design

Building Commissioning has a broad scope that extends to all phases of building delivery. We view commissioning as a building delivery embedded process that persistently verifies and validates design intent throughout the building lifecycle process. In the building lifecycle approach, buildings are considered to have cradle-to-grave life spans. They are modeled through a variety of different developmental phases. In this research project, we intend to build the necessary theory and tools to support the embedded commissioning process as a co-function of building lifecycle

Histopathological and biochemical findings of congenital copper deficiency: are these similar to those of caprine arthritis-encephalitis?

This study was done after identifying animals with a twisted carpal joint in goat herd. These included a kid goat walking on its articulus carpii and a newborn goat with a stiff leg. Necropsies of the diseased goats revealed swollen carpal joints that were twisted backwards. Arthritis was observed during microscopic examination of the carpal joints. Very low levels of eosinophil, leucocyte, and lymphocyte cell infiltration were found in the central nervous system and meninges. Serum copper levels were significantly decreased in most of the animals. All of these results led us to diagnose the animals with swayback disease