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Real-world networks in technology, engineering and biology often exhibit dynamics that cannot be adequately reproduced using network models given by smooth dynamical systems and a fixed network topology. Asynchronous networks give a…

Imitation learning presents an effective approach to alleviate the resource-intensive and time-consuming nature of policy learning from scratch in the solution space. Even though the resulting policy can mimic expert demonstrations…

We say that an algorithm is stable if small changes in the input result in small changes in the output. This kind of algorithm stability is particularly relevant when analyzing and visualizing time-varying data. Stability in general plays…

In this discussion paper, we survey recent research surrounding robustness of machine learning models. As learning algorithms become increasingly more popular in data-driven control systems, their robustness to data uncertainty must be…

Despite the success of convolutional neural networks (CNNs) in many academic benchmarks for computer vision tasks, their application in the real-world is still facing fundamental challenges. One of these open problems is the inherent lack…

Surrogate Neural Networks are nowadays routinely used in industry as substitutes for computationally demanding engineering simulations (e.g., in structural analysis). They allow to generate faster predictions and thus analyses in industrial…

Robust control theory studies the effect of noise, disturbances, and other uncertainty on system performance. Despite growing recognition across science and engineering that robustness and efficiency tradeoffs dominate the evolution and…

This work primarily focuses on an operator inference methodology aimed at constructing low-dimensional dynamical models based on a priori hypotheses about their structure, often informed by established physics or expert insights. Stability…

Neural networks, being susceptible to adversarial attacks, should face a strict level of scrutiny before being deployed in critical or adversarial applications. This paper uses ideas from Chaos Theory to explain, analyze, and quantify the…

The residual neural network (ResNet) is a popular deep network architecture which has the ability to obtain high-accuracy results on several image processing problems. In order to analyze the behavior and structure of ResNet, recent work…

We study a generic family of nonlinear dynamics on undirected networks generalising linear consensus. We find a compact expression for its equilibrium points in terms of the topology of the network and classify their stability using the…

Deep Neural Network-based systems are now the state-of-the-art in many robotics tasks, but their application in safety-critical domains remains dangerous without formal guarantees on network robustness. Small perturbations to sensor inputs…

The objective of this paper is to enhance the optimization process for neural networks by developing a dynamic learning rate algorithm that effectively integrates exponential decay and advanced anti-overfitting strategies. Our primary…

Determining a stability domain, i.e. a set of equilibria for which a dynamical system remains stable, is a core problem in control. When dealing with controlled systems, the problem is generally transformed into a robustness analysis…

Networks are useful descriptions of the structure of many complex systems. Unsurprisingly, it is thus important to analyze the robustness of networks in many scientific disciplines. In applications in communication, logistics, finance,…

In complex systems, information propagation can be defined as diffused or delocalized, weakly localized, and strongly localized. This study investigates the application of graph neural network models to learn the behavior of a linear…

For a given stable recurrent neural network (RNN) that is trained to perform a classification task using sequential inputs, we quantify explicit robustness bounds as a function of trainable weight matrices. The sequential inputs can be…

This paper uses the notion of algorithmic stability to derive novel generalization bounds for several families of transductive regression algorithms, both by using convexity and closed-form solutions. Our analysis helps compare the…

We believe three ingredients are needed for further progress in persistence and its use: invariants not relying on decomposition theorems to go beyond 1-dimension, outcomes suitable for statistical analysis and a setup adopted for…

Given the widespread use of deep learning models in safety-critical applications, ensuring that the decisions of such models are robust against adversarial exploitation is of fundamental importance. In this thesis, we discuss recent…