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Pseudospectral analysis is fundamental for quantifying the sensitivity and transient behavior of nonnormal matrices, yet its computational cost scales cubically with dimension, rendering it prohibitive for large-scale systems. While…

Pseudospectra and structured pseudospectra are important tools for the analysis of matrices. Their computation, however, can be very demanding for all but small matrices. A new approach to compute approximations of pseudospectra and…

In many applications it is important to understand the sensitivity of eigenvalues of a matrix polynomial to perturbations of the polynomial. The sensitivity commonly is described by condition numbers or pseudospectra. However, the…

The robustness and anomaly detection capability of neural networks are crucial topics for their safe adoption in the real-world. Moreover, the over-parameterization of recent networks comes with high computational costs and raises questions…

In this paper, we focus on fraud detection on a signed graph with only a small set of labeled training data. We propose a novel framework that combines deep neural networks and spectral graph analysis. In particular, we use the node…

Motivated by a need to characterize transient behaviors in large network systems in terms of relevant signal norms and worst-case input scenarios, we propose a novel approach based on existing theory for matrix pseudospectra. We extend…

Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…

Deep neural networks have become widely used, obtaining remarkable results in domains such as computer vision, speech recognition, natural language processing, audio recognition, social network filtering, machine translation, and…

Neural networks are trained primarily based on their inputs and outputs, without regard for their internal mechanisms. These neglected mechanisms determine properties that are critical for safety, like (i) transparency; (ii) the absence of…

A fundamental bottleneck in utilising complex machine learning systems for critical applications has been not knowing why they do and what they do, thus preventing the development of any crucial safety protocols. To date, no method exist…

Incorporating computational fluid dynamics in the design process of jets, spacecraft, or gas turbine engines is often challenged by the required computational resources and simulation time, which depend on the chosen physics-based…

Many complex systems can be reduced to their key components through spectrally decomposing matrices that capture their dynamics. These matrices can in turn be constructed from data, often by least-squares fitting: examples of algorithms to…

Reliably characterised pulses are the starting point of any application of ultrafast techniques. Unfortunately, experimental constraints do not always allow optimising the characterisation conditions. This dictates the need for refined…

The pseudospectrum of a linear time-invariant system is the set in the complex plane consisting of all the roots of the characteristic equation when the system matrices are subjected to all possible perturbations with a given upper bound.…

Neural Bayes estimators are neural networks that approximate Bayes estimators in a fast and likelihood-free manner. Although they are appealing to use with spatial models, where estimation is often a computational bottleneck, neural Bayes…

Neural network models are widely used in solving many challenging problems, such as computer vision, personalized recommendation, and natural language processing. Those models are very computationally intensive and reach the hardware limit…

Saliency maps are widely used in the computer vision community for interpreting neural network classifiers. However, due to the randomness of training samples and optimization algorithms, the resulting saliency maps suffer from a…

We propose a spurious region guided refinement approach for robustness verification of deep neural networks. Our method starts with applying the DeepPoly abstract domain to analyze the network. If the robustness property cannot be verified,…

Uncertain data streams have been widely generated in many Web applications. The uncertainty in data streams makes anomaly detection from sensor data streams far more challenging. In this paper, we present a novel framework that supports…

Novel computing hardwares are necessary to keep up with today's increasing demand for data storage and processing power. In this research project, we turn to the brain for inspiration to develop novel computing substrates that are…