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We propose a methodology to address two analysis problems concerning complex systems, namely bounding state functionals of stochastic differential equations (SDEs) and verifying set avoidance of systems described by partial differential…

We consider the design of fast and reliable neural network (NN)-based approximations of traditional stabilizing controllers for linear systems with polytopic uncertainty, including control laws with variable structure and those based on a…

Deep neural network with rectified linear units (ReLU) is getting more and more popular recently. However, the derivatives of the function represented by a ReLU network are not continuous, which limit the usage of ReLU network to situations…

Recently, barrier certificates have been introduced to prove the safety of continuous or hybrid dynamical systems. A barrier certificate needs to exhibit some barrier function, which partitions the state space in two subsets: the safe…

Model inversion is a fundamental technique in feedforward control. Unstable inverse models present a challenge in that useful feedforward control trajectories cannot be generated by directly propagating them. Stable inversion is a process…

Privacy-Preserving Neural Networks (PPNN) are advanced to perform inference without breaching user privacy, which can serve as an essential tool for medical diagnosis to simultaneously achieve big data utility and privacy protection. As one…

This paper introduces a class of mixed-integer formulations for trained ReLU neural networks. The approach balances model size and tightness by partitioning node inputs into a number of groups and forming the convex hull over the partitions…

Accurately modeling and verifying the correct operation of systems interacting in dynamic environments is challenging. By leveraging parametric uncertainty within the model description, one can relax the requirement to describe exactly the…

Verifying set invariance has classical solutions stemming from the seminal work by Nagumo, and defining sets via a smooth barrier function constraint inequality results in computable flow conditions for guaranteeing set invariance. While a…

It is known that the Frank-Wolfe (FW) algorithm, which is affine-covariant, enjoys accelerated convergence rates when the constraint set is strongly convex. However, these results rely on norm-dependent assumptions, usually incurring…

State-of-the-art methods for computer vision rely heavily on the translation equivariance and spatial sharing properties of convolutional layers without explicitly taking into consideration the input content. Modern techniques employ deep…

It is well-known that deep neural networks are vulnerable to adversarial attacks. Recent studies show that well-designed classification parts can lead to better robustness. However, there is still much space for improvement along this line.…

The concept of positively invariant (PI) sets has proven effective in the formal verification of stability and safety properties for autonomous systems. However, the characterization of such sets is challenging for nonlinear systems in…

It has been widely assumed that a neural network cannot be recovered from its outputs, as the network depends on its parameters in a highly nonlinear way. Here, we prove that in fact it is often possible to identify the architecture,…

Neural networks are powerful tools for data-driven modeling of complex dynamical systems, enhancing predictive capability for control applications. However, their inherent nonlinearity and black-box nature challenge control designs that…

Activation function is a pivotal component of deep learning, facilitating the extraction of intricate data patterns. While classical activation functions like ReLU and its variants are extensively utilized, their static nature and…

In this paper, we propose a simple but effective semantic part-based weighting aggregation (PWA) for image retrieval. The proposed PWA utilizes the discriminative filters of deep convolutional layers as part detectors. Moreover, we propose…

Verifying the input-output relationships of a neural network so as to achieve some desired performance specification is a difficult, yet important, problem due to the growing ubiquity of neural nets in many engineering applications. We use…

We consider the inverse problem of reconstructing an unknown function $u$ from a finite set of measurements, under the assumption that $u$ is the trajectory of a transport-dominated problem with unknown input parameters. We propose an…

Relu Fully Connected Networks are ubiquitous but uninterpretable because they fit piecewise linear functions emerging from multi-layered structures and complex interactions of model weights. This paper takes a novel approach to piecewise…