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Table 9 compares these abstracts to the corresponding examples from Tables I.25-27 in section I of [46]. The abstracts are decoded using greedy algorithm with temperature T = 0.5.

In this section, we present some preliminary results that will be useful in proving Theorem 3.2, Theorem 3.3 and Proposition 3.4. We draw upon existing theory on properties of random kernel matrices and extend these properties to cluster-correlated data. Specifically, we show the convergence of eigenvalues and eigenvectors of an empirical kernel matrix based on clustered data. Let (X,F,P) be a probability space and H be a Hilbert space over (X,F,P) with a symmetric kernel function k: X X R. Let H be a compact operator on H, defined by Hg(x) = Z Equivalently, Hn can be viewed as an n nreal matrix whose (i,j)-th entry is {Hn}i,j = 1 n k(Xi,Xj). This is the empirical kernel matrix scaled by a factor of 1/n. Here we restrict our discussion to a reproducing kernel Hilbert space (RKHS) H, where the kernel function k is positive semi-definite. We also assume that the operator H is Hilbert-Schmidt, with E[k2(X,X0)] < . Let λ(T) denote the spectrum of a compact, symmetric operator T. Then λ(H) and λ(Hn) are the sets of eigenvalues for H and Hn, respectively.

The Hilbert-Schmidt Independence Criterion (HSIC) is a powerful kernel-based statistic for assessing the generalized dependence between two multivariate variables. However, independence testing based on the HSIC is not directly possible for cluster-correlated data. Such a correlation pattern among the observations arises in many practical situations, e.g., family-based and longitudinal data, and requires proper accommodation. Therefore, we propose a novel HSIC-based independence test to evaluate the dependence between two multivariate variables based on clustercorrelated data. Using the previously proposed empirical HSIC as our test statistic, we derive its asymptotic distribution under the null hypothesis of independence between the two variables but in the presence of sample correlation. Based on both simulation studies and real data analysis, we show that, with clustered data, our approach effectively controls type I error and has a higher statistical power than competing methods.

Adversarial examples for neural network image classifiers are known to be transferable: examples optimized to be misclassified by a source classifier are often misclassified as well by classifiers with different architectures. However, targeted adversarial examples--optimized to be classified as a chosen target class--tend to be less transferable between architectures. While prior research on constructing transferable targeted attacks has focused on improving the optimization procedure, in this work we examine the role of the source classifier. Here, we show that training the source classifier to be "slightly robust"--that is, robust to small-magnitude adversarial examples--substantially improves the transferability of class-targeted and representation-targeted adversarial attacks, even between architectures as different as convolutional neural networks and transformers. The results we present provide insight into the nature of adversarial examples as well as the mechanisms underlying so-called "robust" classifiers.

Active learning sequentially selects the best instance for labeling by optimizing an acquisition function to enhance data/label efficiency. The selection can be either from a discrete instance set (pool-based scenario) or a continuous instance space (query synthesis scenario). In this work, we study both active learning scenarios for Gaussian Process Classification (GPC). The existing active learning strategies that maximize the Estimated Error Reduction (EER) aim at reducing the classification error after training with the new acquired instance in a onestep-look-ahead manner. The computation of EER-based acquisition functions is typically prohibitive as it requires retraining the GPC with every new query.