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While deep neural networks have excellent results in many fields, they are susceptible to interference from attacking samples resulting in erroneous judgments. Feature-level attacks are one of the effective attack types, which targets the learnt features in the hidden layers to improve its transferability across different models. Yet it is observed that the transferability has been largely impacted by the neuron importance estimation results. In this paper, a double adversarial neuron attribution attack method, termed `DANAA', is proposed to obtain more accurate feature importance estimation. In our method, the model outputs are attributed to the middle layer based on an adversarial non-linear path. The goal is to measure the weight of individual neurons and retain the features that are more important towards transferability. We have conducted extensive experiments on the benchmark datasets to demonstrate the state-of-the-art performance of our method. Our code is available at: //github.com/Davidjinzb/DANAA

SUMMARY A widespread practice to implement a flexible array is to consider the storage area into two parts: the used area, which is already available for read/write operations, and the supply area, which is used in case of enlargement of the array. The main purpose of the supply area is to avoid as much as possible the reallocation of the whole storage area in case of enlargement. As the supply area is not used by the application, the main idea of the paper is to convey the information to the garbage collector, making it possible to avoid completely the marking of the supply area. We also present a simple method to analyze the types of objects, which are stored in an array as well as the possible presence of NULL values within the array. This allows us to better specialize the work of the garbage collector when marking the used area, and also, by transitivity, to improve overall results for type analysis of all expressions of the source code. After introducing several abstract data types, which represent the main arrays concerned by our technique (i.e., zero or variable indexing, circular arrays and hash maps), we measure its impact during the bootstrap of two compilers whose libraries are equipped with these abstract data types. We then measure, on various software products we have not written, the frequency of certain habits of manipulation of arrays, to assess the validity of our approach. Copyright {\copyright} 2014 John Wiley \& Sons, Ltd.

We consider a new splitting based on the Sherman-Morrison-Woodbury formula, which is particularly effective with iterative methods for the numerical solution of large linear systems. These systems involve matrices that are perturbations of circulant or block circulant matrices, which commonly arise in the discretization of differential equations using finite element or finite difference methods. We prove the convergence of the new iteration without making any assumptions regarding the symmetry or diagonal-dominance of the matrix. To illustrate the efficacy of the new iteration we present various applications. These include extensions of the new iteration to block matrices that arise in certain saddle point problems as well as two-dimensional finite difference discretizations. The new method exhibits fast convergence in all of the test cases we used. It has minimal storage requirements, straightforward implementation and compatibility with nearly circulant matrices via the Fast Fourier Transform. For this reasons it can be a valuable tool for the solution of various finite element and finite difference discretizations of differential equations.

Deep Learning models like Convolutional Neural Networks (CNN) are powerful image classifiers, but what factors determine whether they attend to similar image areas as humans do? While previous studies have focused on technological factors, little is known about the role of factors that affect human attention. In the present study, we investigated how the tasks used to elicit human attention maps interact with image characteristics in modulating the similarity between humans and CNN. We varied the intentionality of human tasks, ranging from spontaneous gaze during categorization over intentional gaze-pointing up to manual area selection. Moreover, we varied the type of image to be categorized, using either singular, salient objects, indoor scenes consisting of object arrangements, or landscapes without distinct objects defining the category. The human attention maps generated in this way were compared to the CNN attention maps revealed by explainable artificial intelligence (Grad-CAM). The influence of human tasks strongly depended on image type: For objects, human manual selection produced maps that were most similar to CNN, while the specific eye movement task has little impact. For indoor scenes, spontaneous gaze produced the least similarity, while for landscapes, similarity was equally low across all human tasks. To better understand these results, we also compared the different human attention maps to each other. Our results highlight the importance of taking human factors into account when comparing the attention of humans and CNN.

Identifying replicable signals across different studies provides stronger scientific evidence and more powerful inference. Existing literature on high dimensional applicability analysis either imposes strong modeling assumptions or has low power. We develop a powerful and robust empirical Bayes approach for high dimensional replicability analysis. Our method effectively borrows information from different features and studies while accounting for heterogeneity. We show that the proposed method has better power than competing methods while controlling the false discovery rate, both empirically and theoretically. Analyzing datasets from the genome-wide association studies reveals new biological insights that otherwise cannot be obtained by using existing methods.

Gaussian boson sampling, a computational model that is widely believed to admit quantum supremacy, has already been experimentally demonstrated and is claimed to surpass the classical simulation capabilities of even the most powerful supercomputers today. However, whether the current approach limited by photon loss and noise in such experiments prescribes a scalable path to quantum advantage is an open question. To understand the effect of photon loss on the scalability of Gaussian boson sampling, we analytically derive the asymptotic operator entanglement entropy scaling, which relates to the simulation complexity. As a result, we observe that efficient tensor network simulations are likely possible under the $N_\text{out}\propto\sqrt{N}$ scaling of the number of surviving photons orange$N_\text{out}$ in the number of input photons $N$. We numerically verify this result using a tensor network algorithm with $U(1)$ symmetry, and overcome previous challenges due to the large local Hilbert space dimensions in Gaussian boson sampling with hardware acceleration. Additionally, we observe that increasing the photon number through larger squeezing does not increase the entanglement entropy significantly. Finally, we numerically find the bond dimension necessary for fixed accuracy simulations, providing more direct evidence for the complexity of tensor networks.

Complexity is a fundamental concept underlying statistical learning theory that aims to inform generalization performance. Parameter count, while successful in low-dimensional settings, is not well-justified for overparameterized settings when the number of parameters is more than the number of training samples. We revisit complexity measures based on Rissanen's principle of minimum description length (MDL) and define a novel MDL-based complexity (MDL-COMP) that remains valid for overparameterized models. MDL-COMP is defined via an optimality criterion over the encodings induced by a good Ridge estimator class. We provide an extensive theoretical characterization of MDL-COMP for linear models and kernel methods and show that it is not just a function of parameter count, but rather a function of the singular values of the design or the kernel matrix and the signal-to-noise ratio. For a linear model with $n$ observations, $d$ parameters, and i.i.d. Gaussian predictors, MDL-COMP scales linearly with $d$ when $d<n$, but the scaling is exponentially smaller -- $\log d$ for $d>n$. For kernel methods, we show that MDL-COMP informs minimax in-sample error, and can decrease as the dimensionality of the input increases. We also prove that MDL-COMP upper bounds the in-sample mean squared error (MSE). Via an array of simulations and real-data experiments, we show that a data-driven Prac-MDL-COMP informs hyper-parameter tuning for optimizing test MSE with ridge regression in limited data settings, sometimes improving upon cross-validation and (always) saving computational costs. Finally, our findings also suggest that the recently observed double decent phenomenons in overparameterized models might be a consequence of the choice of non-ideal estimators.

A key challenge when trying to understand innovation is that it is a dynamic, ongoing process, which can be highly contingent on ephemeral factors such as culture, economics, or luck. This means that any analysis of the real-world process must necessarily be historical - and thus probably too late to be most useful - but also cannot be sure what the properties of the web of connections between innovations is or was. Here I try to address this by designing and generating a set of synthetic innovation web "dictionaries" that can be used to host sampled innovation timelines, probe the overall statistics and behaviours of these processes, and determine the degree of their reliance on the structure or generating algorithm. Thus, inspired by the work of Fink, Reeves, Palma and Farr (2017) on innovation in language, gastronomy, and technology, I study how new symbol discovery manifests itself in terms of additional "word" vocabulary being available from dictionaries generated from a finite number of symbols. Several distinct dictionary generation models are investigated using numerical simulation, with emphasis on the scaling of knowledge as dictionary generators and parameters are varied, and the role of which order the symbols are discovered in.

Evaluating the predictive performance of a statistical model is commonly done using cross-validation. Although the leave-one-out method is frequently employed, its application is justified primarily for independent and identically distributed observations. However, this method tends to mimic interpolation rather than prediction when dealing with dependent observations. This paper proposes a modified cross-validation for dependent observations. This is achieved by excluding an automatically determined set of observations from the training set to mimic a more reasonable prediction scenario. Also, within the framework of latent Gaussian models, we illustrate a method to adjust the joint posterior for this modified cross-validation to avoid model refitting. This new approach is accessible in the R-INLA package (www.r-inla.org).