Related papers: Reachability In Simple Neural Networks

Neural network verification tools currently support only a narrow class of specifications, typically expressed as low-level constraints over raw inputs and outputs. This limitation significantly hinders their adoption and practical…

The success of neural networks across most machine learning tasks and the persistence of adversarial examples have made the verification of such models an important quest. Several techniques have been successfully developed to verify…

A supervised learning algorithm has access to a distribution of labeled examples, and needs to return a function (hypothesis) that correctly labels the examples. The hypothesis of the learner is taken from some fixed class of functions…

Neural network width and depth are fundamental aspects of network topology. Universal approximation theorems provide that with increasing width or depth, there exists a neural network that approximates a function arbitrarily well. These…

In this work, we assess the theoretical limitations of determining guaranteed stability and accuracy of neural networks in classification tasks. We consider classical distribution-agnostic framework and algorithms minimising empirical risks…

The unprecedented success of deep learning (DL) makes it unchallenged when it comes to classification problems. However, it is well established that the current DL methodology produces universally unstable neural networks (NNs). The…

This paper studies the approximation capacity of neural networks with an arbitrary activation function and with norm constraint on the weights. Upper and lower bounds on the approximation error of these networks are computed for smooth…

One hypothesis for the success of deep neural networks (DNNs) is that they are highly expressive, which enables them to be applied to many problems, and they have a strong inductive bias towards solutions that are simple, known as…

It is shown that for deep neural networks, a single wide layer of width $N+1$ ($N$ being the number of training samples) suffices to prove the connectivity of sublevel sets of the training loss function. In the two-layer setting, the same…

Deep Neural Networks (DNNs) have grown in popularity over the past decade and are now being used in safety-critical domains such as aircraft collision avoidance. This has motivated a large number of techniques for finding unsafe behavior in…

There has been an increasing interest in using neural networks in closed-loop control systems to improve performance and reduce computational costs for on-line implementation. However, providing safety and stability guarantees for these…

Vector Addition Systems with States (VASS), equivalent to Petri nets, are a well-established model of concurrency. The central algorithmic challenge in VASS is the reachability problem: is there a run from a given starting state and counter…

Machine learning techniques often lack formal correctness guarantees, evidenced by the widespread adversarial examples that plague most deep-learning applications. This lack of formal guarantees resulted in several research efforts that aim…

Deep Neural Networks (DNNs) achieve state-of-the-art performance on numerous applications. However, it is difficult to tell beforehand if a DNN receiving an input will deliver the correct output since their decision criteria are usually…

Building on the results published in arxiv:2004.12849 we present a general framework for demonstrating the NP-hardness of satisfying many genres of loop and path puzzles using a 'T-metacell' gadget. We then use this to prove the…

While known algorithms for sensitivity analysis and parameter tuning in probabilistic networks have a running time that is exponential in the size of the network, the exact computational complexity of these problems has not been established…

We show that under some widely believed assumptions, there are no higher-order algorithms for basic tasks in computational mathematics such as: Computing integrals with neural network integrands, computing solutions of a Poisson equation…

Quantifying the robustness of neural networks or verifying their safety properties against input uncertainties or adversarial attacks have become an important research area in learning-enabled systems. Most results concentrate around the…

Probabilistic verification problems of neural networks are concerned with formally analysing the output distribution of a neural network under a probability distribution of the inputs. Examples of probabilistic verification problems include…

We examine the necessary and sufficient complexity of neural networks to approximate functions from different smoothness spaces under the restriction of encodable network weights. Based on an entropy argument, we start by proving lower…