Related papers: Reachability Analysis for Feed-Forward Neural Netw…

This paper provides a theoretical framework on the solution of feedforward ReLU networks for interpolations, in terms of what is called an interpolation matrix, which is the summary, extension and generalization of our three preceding…

This paper investigates one-step backward reachability for uncertain max-plus linear systems with additive disturbances. Given a target set, the problem is to compute the set of states from which there exists an admissible control input…

In the past five years we have observed the rise of incredibly well performing feed-forward neural networks trained supervisedly for vision related tasks. These models have achieved super-human performance on object recognition,…

One of the most important steps toward interpretability and explainability of neural network models is feature selection, which aims to identify the subset of relevant features. Theoretical results in the field have mostly focused on the…

"Deep Learning"/"Deep Neural Nets" is a technological marvel that is now increasingly deployed at the cutting-edge of artificial intelligence tasks. This dramatic success of deep learning in the last few years has been hinged on an enormous…

We study the approximation of the median of $d$ inputs using ReLU neural networks. We present depth-width tradeoffs under several settings, culminating in a constant-depth, linear-width construction that achieves exponentially small…

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…

One main obstacle for the wide use of deep learning in medical and engineering sciences is its interpretability. While neural network models are strong tools for making predictions, they often provide little information about which features…

With edge-AI finding an increasing number of real-world applications, especially in industry, the question of functionally safe applications using AI has begun to be asked. In this body of work, we explore the issue of achieving dependable…

Approximating the set of reachable states of a dynamical system is an algorithmic yet mathematically rigorous way to reason about its safety. Although progress has been made in the development of efficient algorithms for affine dynamical…

Neural networks are now extensively used in perception, prediction and control of autonomous systems. Their deployment in safety-critical systems brings forth the need for verification techniques for such networks. As an alternative to…

Neural networks are increasingly deployed in real-world safety-critical domains such as autonomous driving, aircraft collision avoidance, and malware detection. However, these networks have been shown to often mispredict on inputs with…

We develop a geometric approximation theory for deep feed-forward neural networks with ReLU activations. Given a $d$-dimensional hypersurface in $\mathbb{R}^{d+1}$ represented as the graph of a $C^2$-function $\phi$, we show that a deep…

The great performance of machine learning algorithms and deep neural networks in several perception and control tasks is pushing the industry to adopt such technologies in safety-critical applications, as autonomous robots and self-driving…

Neural networks (NNs) playing the role of controllers have demonstrated impressive empirical performances on challenging control problems. However, the potential adoption of NN controllers in real-life applications also gives rise to a…

In multirotor systems, guaranteeing safety while considering unknown disturbances is essential for robust trajectory planning. The Forward reachable set (FRS), the set of feasible states subject to bounded disturbances, can be utilized to…

Multi-face alignment aims to identify geometry structures of multiple faces in an image, and its performance is essential for the many practical tasks, such as face recognition, face tracking, and face animation. In this work, we present a…

Beyond the traditional neural network training methods based on gradient descent and its variants, state estimation techniques have been proposed to determine a set of ideal weights from a control-theoretic perspective. Hence, the concept…

We establish, for the first time, connections between feedforward neural networks with ReLU activation and tropical geometry --- we show that the family of such neural networks is equivalent to the family of tropical rational maps. Among…

Face presentation attack detection (PAD) has become a thorny problem for biometric systems and numerous countermeasures have been proposed to address it. However, majority of them directly extract feature descriptors and distinguish fake…