Related papers: Verification of Neural Networks (Lecture Notes)

These lecture notes provide an overview of Neural Network architectures from a mathematical point of view. Especially, Machine Learning with Neural Networks is seen as an optimization problem. Covered are an introduction to Neural Networks…

Deep learning has transformed the way we think of software and what it can do. But deep neural networks are fragile and their behaviors are often surprising. In many settings, we need to provide formal guarantees on the safety, security,…

Deep neural networks are widely used for nonlinear function approximation with applications ranging from computer vision to control. Although these networks involve the composition of simple arithmetic operations, it can be very challenging…

Neural networks are one of the most investigated and widely used techniques in Machine Learning. In spite of their success, they still find limited application in safety- and security-related contexts, wherein assurance about networks'…

Deep neural networks are revolutionizing the way complex systems are developed. However, these automatically-generated networks are opaque to humans, making it difficult to reason about them and guarantee their correctness. Here, we propose…

Learning-based methods could provide solutions to many of the long-standing challenges in control. However, the neural networks (NNs) commonly used in modern learning approaches present substantial challenges for analyzing the resulting…

Verification of deep neural networks has witnessed a recent surge of interest, fueled by success stories in diverse domains and by abreast concerns about safety and security in envisaged applications. Complexity and sheer size of such…

Neural network verification is a new and rapidly developing field of research. So far, the main priority has been establishing efficient verification algorithms and tools, while proper support from the programming language perspective has…

The rising popularity of neural networks (NNs) in recent years and their increasing prevalence in real-world applications have drawn attention to the importance of their verification. While verification is known to be computationally…

On the one hand, there has been considerable progress on neural network verification in recent years, which makes certifying neural networks a possibility. On the other hand, neural networks in practice are often re-trained over time to…

We investigate the computational complexity of neural network verification in quantised settings. We distinguish three classes of Feedforward Neural Networks (FNNs): rational FNNs with exact rational weights, quantised FNNs whose weights…

This note presents in a technical though hopefully pedagogical way the three most common forms of neural network architectures: Feedforward, Convolutional and Recurrent. For each network, their fundamental building blocks are detailed. The…

Neural networks are increasingly applied to support decision making in safety-critical applications (like autonomous cars, unmanned aerial vehicles and face recognition based authentication). While many impressive static verification…

This paper proposes a new algorithmic framework, predictor-verifier training, to train neural networks that are verifiable, i.e., networks that provably satisfy some desired input-output properties. The key idea is to simultaneously train…

Artificial neural networks are algorithms which have been developed to tackle a range of computational problems. These range from modelling brain function to making predictions of time-dependent phenomena to solving hard (NP-complete)…

Recurrent neural networks (RNNs) are capable of learning features and long term dependencies from sequential and time-series data. The RNNs have a stack of non-linear units where at least one connection between units forms a directed cycle.…

Extensive research on formal verification of machine learning systems indicates that learning from data alone often fails to capture underlying background knowledge, such as specifications implicitly available in the data. Various neural…

Formal verification provides critical security assurances for neural networks, yet its practical application suffers from the long verification time. This work introduces a novel method for training verification-friendly neural networks,…

State-of-the-art solutions in the areas of "Language Modelling & Generating Text", "Speech Recognition", "Generating Image Descriptions" or "Video Tagging" have been using Recurrent Neural Networks as the foundation for their approaches.…

A wide range of verification methods have been proposed to verify the safety properties of deep neural networks ensuring that the networks function correctly in critical applications. However, many well-known verification tools still…