Related papers: Open- and Closed-Loop Neural Network Verification …
The success of deep convolutional neural network (CNN) in computer vision especially image classification problems requests a new information theory for function of image, instead of image itself. In this article, after establishing a deep…
Implicit neural networks are a general class of learning models that replace the layers in traditional feedforward models with implicit algebraic equations. Compared to traditional learning models, implicit networks offer competitive…
Neural Networks (NNs) have increasingly apparent safety implications commensurate with their proliferation in real-world applications: both unanticipated as well as adversarial misclassifications can result in fatal outcomes. As a…
Neural networks are known to be vulnerable to adversarial attacks, which are small, imperceptible perturbations that can significantly alter the network's output. Conversely, there may exist large, meaningful perturbations that do not…
In this article we present new results on neural networks with linear threshold activation functions. We precisely characterize the class of functions that are representable by such neural networks and show that 2 hidden layers are…
This paper proposes a theoretical and computational framework for training and robustness verification of implicit neural networks based upon non-Euclidean contraction theory. The basic idea is to cast the robustness analysis of a neural…
This paper introduces zonoLAB, a MATLAB-based toolbox for set-based control system analysis using the hybrid zonotope set representation. Hybrid zonotopes have proven to be an expressive set representation that can exactly represent the…
Polynomial Networks (PNs) have demonstrated promising performance on face and image recognition recently. However, robustness of PNs is unclear and thus obtaining certificates becomes imperative for enabling their adoption in real-world…
Zonotopes are widely used for over-approximating forward reachable sets of uncertain linear systems for verification purposes. In this paper, we use zonotopes to achieve more scalable algorithms that under-approximate backward reachable…
A central challenge in sensory neuroscience is describing how the activity of populations of neurons can represent useful features of the external environment. However, while neurophysiologists have long been able to record the responses of…
In this paper we investigate formal verification of extracted rules for Neural Networks under a complexity theoretic point of view. A rule is a global property or a pattern concerning a large portion of the input space of a network. These…
Deep learning methods can be used to produce control policies, but certifying their safety is challenging. The resulting networks are nonlinear and often very large. In response to this challenge, we present OVERT: a sound algorithm for…
We investigate properties of neural networks that use both ReLU and $x^2$ as activation functions and build upon previous results to show that both analytic functions and functions in Sobolev spaces can be approximated by such networks of…
We analyze the problem of high-order polynomial approximation from a many-body physics perspective, and demonstrate the descriptive power of entanglement entropy in capturing model capacity and task complexity. Instantiated with 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…
Outsourcing deep neural networks (DNNs) inference tasks to an untrusted cloud raises data privacy and integrity concerns. While there are many techniques to ensure privacy and integrity for polynomial-based computations, DNNs involve…
Deep neural networks are known to be fragile to small adversarial perturbations. This issue becomes more critical when a neural network is interconnected with a physical system in a closed loop. In this paper, we show how to combine recent…
We consider neural network approximation spaces that classify functions according to the rate at which they can be approximated (with error measured in $L^p$) by ReLU neural networks with an increasing number of coefficients, subject to…
The robustness of deep neural networks has received significant interest recently, especially when being deployed in safety-critical systems, as it is important to analyze how sensitive the model output is under input perturbations. While…
We develop a novel theoretical framework for analyzing ReLU neural networks through the lens of a combinatorial object we term the ReLU Transition Graph (RTG). In this graph, each node corresponds to a linear region induced by the network's…