We survey the adversarial robustness of neural networks from the perspective of Lipschitz
calculus in a unifying fashion by expressing models, attacks and safety guarantees, that is, a …

Abstract Deep Neural Networks (DNNs) have obtained impressive performance across
tasks, however they still remain as black boxes, eg, hard to theoretically analyze. At the …

Neural tangent kernel (NTK) is a powerful tool to analyze training dynamics of neural
networks and their generalization bounds. The study on NTK has been devoted to typical …

Lipschitz constrained networks have gathered considerable attention in the deep learning
community, with usages ranging from Wasserstein distance estimation to the training of …

Abstract Polynomial Networks (PNs) have demonstrated promising performance on face and
image recognition recently. However, robustness of PNs is unclear and thus obtaining …

In this article, we propose the concept of random polynomial neural networks (RPNNs)
realized based on the architecture of polynomial neural networks (PNNs) with random …

Tensors are multidimensional arrays that can naturally represent data and mappings of
multiple dimensions, playing a central role in modern deep learning. Indeed, the basic …

Historically, we are taught to use task-dependent architecture design and objectives to
tackle data science tasks. Counter intuitively, this dogma has been proven (partly) wrong by …

As a general type of machine learning approach, artificial neural networks have established
state-of-art benchmarks in many pattern recognition and data analysis tasks. Among various …

The theory of Signatures [,] is a fast growing field which has demonstrated wide applicability
to a large range of fields, from finance to health monitoring [,,]. Computing signatures often …