Boosting Transferability of Targeted Adversarial Examples via Hierarchical Generative Networks

Transfer-based adversarial attacks can effectively evaluate model robustness in the black-box setting. Though several methods have demonstrated impressive transferability of untargeted adversarial examples, targeted adversarial transferability is still challenging. The existing methods either have low targeted transferability or sacrifice computational efficiency. In this paper, we develop a simple yet practical framework to efficiently craft targeted transfer-based adversarial examples. Specifically, we propose a conditional generative attacking model, which can generate the adversarial examples targeted at different classes by simply altering the class embedding and share a single backbone. Extensive experiments demonstrate that our method improves the success rates of targeted black-box attacks by a significant margin over the existing methods -- it reaches an average success rate of 29.6\% against six diverse models based only on one substitute white-box model in the standard testing of NeurIPS 2017 competition, which outperforms the state-of-the-art gradient-based attack methods (with an average success rate of $<$2\%) by a large margin. Moreover, the proposed method is also more efficient beyond an order of magnitude than gradient-based methods

Unified description of structure and reactions: implementing the Nuclear Field Theory program

The modern theory of the atomic nucleus results from the merging of the liquid drop (Niels Bohr and Fritz Kalckar) and of the shell model (Marie Goeppert Meyer and Axel Jensen), which contributed the concepts of collective excitations and of independent-particle motion respectively. The unification of these apparently contradictory views in terms of the particle-vibration (rotation) coupling (Aage Bohr and Ben Mottelson) has allowed for an ever increasingly complete, accurate and detailed description of the nuclear structure, Nuclear Field Theory (NFT, developed by the Copenhagen-Buenos Aires collaboration) providing a powerful quantal embodiment. In keeping with the fact that reactions are not only at the basis of quantum mechanics (statistical interpretation, Max Born) , but also the specific tools to probe the atomic nucleus, NFT is being extended to deal with processes which involve the continuum in an intrinsic fashion, so as to be able to treat them on an equal footing with those associated with discrete states (nuclear structure). As a result, spectroscopic studies of transfer to continuum states could eventually use at profit the NFT rules, extended to take care of recoil effects. In the present contribution we review the implementation of the NFT program of structure and reactions, setting special emphasis on open problems and outstanding predictions.Comment: submitted to Physica Scripta to the Focus Issue on Nuclear Structure: Celebrating the 1975 Nobel Priz

Singular Value Computation and Subspace Clustering

In this dissertation we discuss two problems. In the first part, we consider the problem of computing a few extreme eigenvalues of a symmetric definite generalized eigenvalue problem or a few extreme singular values of a large and sparse matrix. The standard method of choice of computing a few extreme eigenvalues of a large symmetric matrix is the Lanczos or the implicitly restarted Lanczos method. These methods usually employ a shift-and-invert transformation to accelerate the speed of convergence, which is not practical for truly large problems. With this in mind, Golub and Ye proposes an inverse-free preconditioned Krylov subspace method, which uses preconditioning instead of shift-and-invert to accelerate the convergence. To compute several eigenvalues, Wielandt is used in a straightforward manner. However, the Wielandt deflation alters the structure of the problem and may cause some difficulties in certain applications such as the singular value computations. So we first propose to consider a deflation by restriction method for the inverse-free Krylov subspace method. We generalize the original convergence theory for the inverse-free preconditioned Krylov subspace method to justify this deflation scheme. We next extend the inverse-free Krylov subspace method with deflation by restriction to the singular value problem. We consider preconditioning based on robust incomplete factorization to accelerate the convergence. Numerical examples are provided to demonstrate efficiency and robustness of the new algorithm. In the second part of this thesis, we consider the so-called subspace clustering problem, which aims for extracting a multi-subspace structure from a collection of points lying in a high-dimensional space. Recently, methods based on self expressiveness property (SEP) such as Sparse Subspace Clustering and Low Rank Representations have been shown to enjoy superior performances than other methods. However, methods with SEP may result in representations that are not amenable to clustering through graph partitioning. We propose a method where the points are expressed in terms of an orthonormal basis. The orthonormal basis is optimally chosen in the sense that the representation of all points is sparsest. Numerical results are given to illustrate the effectiveness and efficiency of this method

Discriminant analysis based feature extraction for pattern recognition

Fisher's linear discriminant analysis (FLDA) has been widely used in pattern recognition applications. However, this method cannot be applied for solving the pattern recognition problems if the within-class scatter matrix is singular, a condition that occurs when the number of the samples is small relative to the dimension of the samples. This problem is commonly known as the small sample size (SSS) problem and many of the FLDA variants proposed in the past to deal with this problem suffer from excessive computational load because of the high dimensionality of patterns or lose some useful discriminant information. This study is concerned with developing efficient techniques for discriminant analysis of patterns while at the same time overcoming the small sample size problem. With this objective in mind, the work of this research is divided into two parts. In part 1, a technique by solving the problem of generalized singular value decomposition (GSVD) through eigen-decomposition is developed for linear discriminant analysis (LDA). The resulting algorithm referred to as modified GSVD-LDA (MGSVD-LDA) algorithm is thus devoid of the singularity problem of the scatter matrices of the traditional LDA methods. A theorem enunciating certain properties of the discriminant subspace derived by the proposed GSVD-based algorithms is established. It is shown that if the samples of a dataset are linearly independent, then the samples belonging to different classes are linearly separable in the derived discriminant subspace; and thus, the proposed MGSVD-LDA algorithm effectively captures the class structure of datasets with linearly independent samples. Inspired by the results of this theorem that essentially establishes a class separability of linearly independent samples in a specific discriminant subspace, in part 2, a new systematic framework for the pattern recognition of linearly independent samples is developed. Within this framework, a discriminant model, in which the samples of the individual classes of the dataset lie on parallel hyperplanes and project to single distinct points of a discriminant subspace of the underlying input space, is shown to exist. Based on this model, a number of algorithms that are devoid of the SSS problem are developed to obtain this discriminant subspace for datasets with linearly independent samples. For the discriminant analysis of datasets for which the samples are not linearly independent, some of the linear algorithms developed in this thesis are also kernelized. Extensive experiments are conducted throughout this investigation in order to demonstrate the validity and effectiveness of the ideas developed in this study. It is shown through simulation results that the linear and nonlinear algorithms for discriminant analysis developed in this thesis provide superior performance in terms of the recognition accuracy and computational complexit

Data driven regularization by projection

Abstract: We study linear inverse problems under the premise that the forward operator is not at hand but given indirectly through some input-output training pairs. We demonstrate that regularization by projection and variational regularization can be formulated by using the training data only and without making use of the forward operator. We study convergence and stability of the regularized solutions in view of Seidman (1980 J. Optim. Theory Appl. 30 535), who showed that regularization by projection is not convergent in general, by giving some insight on the generality of Seidman’s nonconvergence example. Moreover, we show, analytically and numerically, that regularization by projection is indeed capable of learning linear operators, such as the Radon transform