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Many statistical estimators are defined as the fixed point of a data-dependent operator, with estimators based on minimizing a cost function being an important special case. The limiting performance of such estimators depends on the…
Quantifying the complexity of feed-forward neural networks (FFNNs) remains challenging due to their nonlinear, hierarchical structure and numerous parameters. We apply generalized degrees of freedom (GDF) to measure model complexity in…
This article proposes a Graph Neural Network (GNN) approach to estimate nonstabilizerness in quantum circuits, measured by the stabilizer R\'enyi entropy (SRE). Nonstabilizerness is a fundamental resource for quantum advantage, and…
Now that Bayesian Networks (BNs) have become widely used, an appreciation is developing of just how critical an awareness of the sensitivity and robustness of certain target variables are to changes in the model. When time resources are…
Bayesian networks are one of the most widely used classes of probabilistic models for risk management and decision support because of their interpretability and flexibility in including heterogeneous pieces of information. In any applied…
This paper presents a formal definition of stability for node centrality measures in weighted graphs. It is shown that the commonly used measures of degree, closeness and eigenvector centrality are stable whereas betweenness centrality is…
We study the out-of-sample properties of robust empirical optimization problems with smooth $\phi$-divergence penalties and smooth concave objective functions, and develop a theory for data-driven calibration of the non-negative "robustness…
Neural networks (NNs) are increasingly applied in safety-critical systems such as autonomous vehicles. However, they are fragile and are often ill-behaved. Consequently, their behaviors should undergo rigorous guarantees before deployment…
This paper provides a normalized field product approach for topology optimization to achieve close-to-binary optimal designs. The method employs a parameter-free density measure that implicitly enforces a minimum length scale on the solid…
Deployment of deep neural networks (DNNs) in safety- or security-critical systems requires provable guarantees on their correct behaviour. A common requirement is robustness to adversarial perturbations in a neighbourhood around an input.…
We introduce Harmonic Robustness, a powerful and intuitive method to test the robustness of any machine-learning model either during training or in black-box real-time inference monitoring without ground-truth labels. It is based on…
Deep neural networks (DNNs) are increasingly used in real-world applications (e.g. facial recognition). This has resulted in concerns about the fairness of decisions made by these models. Various notions and measures of fairness have been…
We present a computational framework for analyzing and quantifying system flexibility. Our framework incorporates new features that include: general uncertainty characterizations that are constructed using composition of sets, procedures…
We consider endomorphisms of a compact manifold which are expanding except for a finite number of points and prove the existence and uniqueness of a physical measure and its stochastical stability. We also characterize the zero-noise limit…
In this paper, we obtain complete characterization for nested canalyzing functions (NCFs) by obtaining its unique algebraic normal form (polynomial form). We introduce a new concept, LAYER NUMBER for NCF. Based on this, we obtain explicit…
Understanding simplicity biases in deep learning offers a promising path toward developing reliable AI. A common metric for this, inspired by Boolean function analysis, is average sensitivity, which captures a model's robustness to…
Probabilistic models of data sets often exhibit salient geometric structure. Such a phenomenon is summed up in the manifold distribution hypothesis, and can be exploited in probabilistic learning. Here we present normal-bundle bootstrap…
Adversarial attack perturbs an image with an imperceptible noise, leading to incorrect model prediction. Recently, a few works showed inherent bias associated with such attack (robustness bias), where certain subgroups in a dataset (e.g.…
This paper presents a new neural network (NN) paradigm for scalable and generalizable stability analysis of power systems. The paradigm consists of two parts: the neural stability descriptor and the sample-augmented iterative training…
Control barrier function (CBF)-QP safety filters enforce safety by minimally modifying a nominal controller. While prior work has mainly addressed robustness of safety under uncertainty, robustness of the resulting closed-loop…