Related papers: Bounding the Complexity of Formally Verifying Neur…

We study regularized deep neural networks (DNNs) and introduce a convex analytic framework to characterize the structure of the hidden layers. We show that a set of optimal hidden layer weights for a norm regularized DNN training problem…

In this paper, we consider the problem of automatically designing a Rectified Linear Unit (ReLU) Neural Network (NN) architecture (number of layers and number of neurons per layer) with the guarantee that it is sufficiently parametrized to…

Universal approximation theory offers a foundational framework to verify neural network expressiveness, enabling principled utilization in real-world applications. However, most existing theoretical constructions are established by…

Branch-and-bound (BaB) is among the most effective techniques for neural network (NN) verification. However, existing works on BaB for NN verification have mostly focused on NNs with piecewise linear activations, especially ReLU networks.…

Neural networks with the Rectified Linear Unit (ReLU) nonlinearity are described by a vector of parameters $\theta$, and realized as a piecewise linear continuous function $R_{\theta}: x \in \mathbb R^{d} \mapsto R_{\theta}(x) \in \mathbb…

Analog neural networks are gaining attention due to their efficiency in terms of power consumption and processing speed. However, since analog neural networks are implemented as physical circuits, they are highly sensitive to manufacturing…

We develop a method for the efficient verification of neural networks against convolutional perturbations such as blurring or sharpening. To define input perturbations we use well-known camera shake, box blur and sharpen kernels. We…

We consider the classic problem of Network Reliability. A network is given together with a source vertex, one or more target vertices, and probabilities assigned to each of the edges. Each edge appears in the network with its associated…

Neural networks have proved an effective means of learning control policies for autonomous systems, but these learned policies are difficult to understand due to the black-box nature of neural networks. This lack of interpretability makes…

Many approaches for verifying input-output properties of neural networks have been proposed recently. However, existing algorithms do not scale well to large networks. Recent work in the field of model compression studied binarized neural…

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…

Rectified Linear Unit (ReLU) networks are piecewise-linear (PWL), so universal linear safety properties can be reduced to reasoning about linear constraints. Modern verifiers rely on SMT(LRA) procedures or MILP encodings, but a safety claim…

Understanding the fundamental mechanism behind the success of deep neural networks is one of the key challenges in the modern machine learning literature. Despite numerous attempts, a solid theoretical analysis is yet to be developed. In…

Convolutional neural networks (CNNs), one of the key architectures of deep learning models, have achieved superior performance on many machine learning tasks such as image classification, video recognition, and power systems. Despite their…

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…

Understanding the fundamental principles behind the success of deep neural networks is one of the most important open questions in the current literature. To this end, we study the training problem of deep neural networks and introduce an…

We develop the first (to the best of our knowledge) provably correct neural networks for a precise computational task, with the proof of correctness generated by an automated verification algorithm without any human input. Prior work on…

Deep neural networks (DNNs) are widely used in real-world applications, yet they remain vulnerable to errors and adversarial attacks. Formal verification offers a systematic approach to identify and mitigate these vulnerabilities, enhancing…

In this paper, we consider the problem of formally verifying a Neural Network (NN) based autonomous landing system. In such a system, a NN controller processes images from a camera to guide the aircraft while approaching the runway. A…

We study robustness verification of neural networks via metric algebraic geometry. For polynomial neural networks, certifying a robustness radius amounts to computing the distance to the algebraic decision boundary. We use the Euclidean…