Related papers: Open- and Closed-Loop Neural Network Verification …
Verifying that input-output relationships of a neural network conform to prescribed operational specifications is a key enabler towards deploying these networks in safety-critical applications. Semidefinite programming (SDP)-based…
The reliable deployment of neural networks in control systems requires rigorous robustness guarantees. In this paper, we obtain tight robustness certificates over convex attack sets for min-max representations of ReLU neural networks by…
Neural networks have revolutionized the field of data science, yielding remarkable solutions in a data-driven manner. For instance, in the field of mathematical imaging, they have surpassed traditional methods based on convex…
A ReLU neural network leads to a finite polyhedral decomposition of input space and a corresponding finite dual graph. We show that while this dual graph is a coarse quantization of input space, it is sufficiently robust that it can be…
Deep neural networks (DNNs) are increasingly being deployed to perform safety-critical tasks. The opacity of DNNs, which prevents humans from reasoning about them, presents new safety and security challenges. To address these challenges,…
Neural network controllers have shown potential in achieving superior performance in feedback control systems. Although a neural network can be trained efficiently using deep and reinforcement learning methods, providing formal guarantees…
A ReLU neural network determines/is a continuous piecewise linear map from an input space to an output space. The weights in the neural network determine a decomposition of the input space into convex polytopes and on each of these…
The prevalence of neural networks in society is expanding at an increasing rate. It is becoming clear that providing robust guarantees on systems that use neural networks is very important, especially in safety-critical applications. A…
Optical neural networks promise ultrafast, low-energy information processing by performing computation directly with photons. Current implementations, however, are largely restricted to steady-state operation and rely on high-latency…
Visual loop closure detection, which can be considered as an image retrieval task, is an important problem in SLAM (Simultaneous Localization and Mapping) systems. The frequently used bag-of-words (BoW) models can achieve high precision and…
This paper introduces a novel neural network for efficiently solving Structured Inverse Eigenvalue Problems (SIEPs). The main contributions lie in two aspects: firstly, a unified framework is proposed that can handle various SIEPs…
Deep learning has been widely used in many fields, but the model training process usually consumes massive computational resources and time. Therefore, designing an efficient neural network training method with a provable convergence…
We study deep neural networks with polynomial activations, particularly their expressive power. For a fixed architecture and activation degree, a polynomial neural network defines an algebraic map from weights to polynomials. The image of…
Neural networks and rational functions efficiently approximate each other. In more detail, it is shown here that for any ReLU network, there exists a rational function of degree $O(\text{polylog}(1/\epsilon))$ which is $\epsilon$-close, and…
We study the representation capacity of deep hyperbolic neural networks (HNNs) with a ReLU activation function. We establish the first proof that HNNs can $\varepsilon$-isometrically embed any finite weighted tree into a hyperbolic space of…
Understanding the inner working mechanism of deep neural networks (DNNs) is essential and important for researchers to design and improve the performance of DNNs. In this work, the entropy analysis is leveraged to study the neurons…
Training neural networks is a challenging non-convex optimization problem, and backpropagation or gradient descent can get stuck in spurious local optima. We propose a novel algorithm based on tensor decomposition for guaranteed training of…
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 present an approach to identify concise equations from data using a shallow neural network approach. In contrast to ordinary black-box regression, this approach allows understanding functional relations and generalizing them from…
We derive bounds on the error, in high-order Sobolev norms, incurred in the approximation of Sobolev-regular as well as analytic functions by neural networks with the hyperbolic tangent activation function. These bounds provide explicit…