Small Noise Research Articles

Dual-Targeted Textfooler Attack on Text Classification Systems

Deep neural networks provide good performance on classification tasks such as those for image, audio, and text classification. However, such neural networks are vulnerable to adversarial examples. An adversarial example is a sample created by adding a small adversarial noise to an original data sample in such a way that it will be correctly classified by a human but misclassified by a deep neural network. Studies on adversarial examples have focused mainly on the image field, but research is expanding into the text field as well. Adversarial examples in the text field that are designed with two targets in mind can be useful in certain situations. In a military scenario, for example, if enemy models A and B use a text recognition model, it may be desirable to cause enemy model A tanks to go to the right and enemy model B self-propelled guns to go to the left by using strategically designed adversarial messages. Such a dual-targeted adversarial example could accomplish this by causing different misclassifications in different models, in contrast to single-target adversarial examples produced by existing methods. In this paper, I propose a method for creating a dual-targeted textual adversarial example for attacking a text classification system. Unlike the existing adversarial methods, which are designed for images, the proposed method creates dual-targeted adversarial examples that will be misclassified as a different class by each of two models while maintaining the meaning and grammar of the original sentence, by substituting words of importance. Experiments were conducted using the SNLI dataset and the TensorFlow library. The results demonstrate that the proposed method can generate a dual-targeted adversarial example with an average attack success rate of 82.2% on the two models.

A Quantitative Notion of Persistency of Excitation and the Robust Fundamental Lemma

The fundamental lemma by Willems and coauthors enables a parameterization of all trajectories of a linear time-invariant system in terms of a single, measured one. This result plays a key role in data-driven simulation and control. The fundamental lemma relies on a persistently exciting input to the system to ensure that the Hankel matrix of resulting input/output data has the “right” rank, meaning that its columns span the entire subspace of trajectories. However, such binary rank conditions are known to be fragile in the sense that a small additive noise could already cause the Hankel matrix to have full rank. In this letter we present a robust version of the fundamental lemma. The idea behind the approach is to guarantee certain lower bounds on the singular values of the data Hankel matrix, rather than qualitative rank conditions. This is achieved by designing the inputs of the experiment such that the minimum singular value of an input Hankel matrix is sufficiently large, inspiring a quantitative notion of persistency of excitation. We highlight the relevance of the result in a data-driven control case study by comparing the predictive control performance for varying degrees of persistently exciting data.

Exploring the Effect of Randomness on Transferability of Adversarial Samples Against Deep Neural Networks

We investigate the transferability of adversarial attacks against deep neural networks (DNNs)—the contagion effect of adversarial attacks that, once deceiving one DNN model, can easily deceive other DNN models built on similar data. We demonstrate that introducing randomness to DNN models can break the curse of the transferability of adversarial attacks, given that the adversary does not have an unlimited attack budget. Two randomization schemes are explored: 1.) a random selection—single or ensemble—from a set of DNNs is surprisingly more robust against the strongest form of complete-knowledge attacks (a.k.a, white box attacks); 2.) after a small Gaussian random noise is added to its learned weights, a DNN model can potentially increase its resilience to adversarial attacks by as much as 74.2%. We compare the two randomization techniques to the Ensemble Adversarial Training technique and show that our randomization techniques are superior under different attack budget constraints. Furthermore, we explore the relationship between attack severity and decision boundary robustness in the version space. Finally, we connect the dots between the effectiveness of randomization to prevent attack transferability and the variability of DNN models through analyzing the differential entropy of sample hypotheses in the hypothesis space.

Multistatic Localization by Differential Time Delays and Time Differences of Arrival in the Absence of Transmitter Position

We can only extract the differential time delay (DTD) measurements between the direct and reflected paths in multistatic localization when there is no synchronization in time between the transmitter and receiver and among the receivers. This paper first addresses the problem of multistatic localization of a fixed object when the transmitter position is not available by using the DTD measurements. We propose a two-step optimization method for jointly estimating the object and transmitter positions. In the first step, we formulate a non-convex constrained weighted least squares (CWLS) problem by transforming the DTD measurement model and introducing nuisance variables. Such a non-convex CWLS problem is then relaxed to a tractable convex semidefinite programming (SDP) problem by applying semidefinite relaxation. In the second step, the error coming from relaxation and approximation in the SDP solution is reduced iteratively through solving a generalized trust region subproblem (GTRS) in each iteration. If the receivers are synchronized such that the time difference of arrival (TDOA) measurements can be acquired in addition to DTD, we formulate a different CWLS problem by utilizing both DTD and TDOA measurements, which is solved by convex relaxation as well. The relaxed SDP problem can achieve the optimal solution of the CWLS problem, and further refinement is no longer needed. We conduct the mean square error (MSE) analysis to validate that both proposed methods are able to achieve the Cramer-Rao Lower Bound (CRLB) performance under small Gaussian noise, which is also validated by simulations.

Approximation of linear controlled dynamical systems with small random noise and fast periodic sampling

<p style='text-indent:20px;'>In this paper, we study the dynamics of a linear control system with given state feedback control law in the presence of fast periodic sampling at temporal frequency <inline-formula><tex-math id="M1">\begin{document}$ 1/\delta $\end{document}</tex-math></inline-formula> (<inline-formula><tex-math id="M2">\begin{document}$ 0 < \delta \ll 1 $\end{document}</tex-math></inline-formula>), together with small white noise perturbations of size <inline-formula><tex-math id="M3">\begin{document}$ \varepsilon $\end{document}</tex-math></inline-formula> (<inline-formula><tex-math id="M4">\begin{document}$ 0< \varepsilon \ll 1 $\end{document}</tex-math></inline-formula>) in the state dynamics. For the ensuing continuous-time stochastic process indexed by two small parameters <inline-formula><tex-math id="M5">\begin{document}$ \varepsilon,\delta $\end{document}</tex-math></inline-formula>, we obtain effective ordinary and stochastic differential equations describing the mean behavior and the typical fluctuations about the mean in the limit as <inline-formula><tex-math id="M6">\begin{document}$ \varepsilon,\delta \searrow 0 $\end{document}</tex-math></inline-formula>. The effective fluctuation process is found to vary, depending on whether <inline-formula><tex-math id="M7">\begin{document}$ \delta \searrow 0 $\end{document}</tex-math></inline-formula> faster than/at the same rate as/slower than <inline-formula><tex-math id="M8">\begin{document}$ \varepsilon \searrow 0 $\end{document}</tex-math></inline-formula>. The most interesting case is found to be the one where <inline-formula><tex-math id="M9">\begin{document}$ \delta, \varepsilon $\end{document}</tex-math></inline-formula> are comparable in size; here, the limiting stochastic differential equation for the fluctuations has both a diffusive term due to the small noise and an effective drift term which captures the cumulative effect of the fast sampling. In this regime, our results yield a time-inhomogeneous Markov process which provides a strong (pathwise) approximation of the original non-Markovian process, together with estimates on the ensuing error. A simple example involving an infinite time horizon linear quadratic regulation problem illustrates the results.</p>

Stochastic differential equations driven by small general Gaussian noise: Non parametric estimation

Stochastic differential equations driven by small general Gaussian noise: Non parametric estimation

Analysis of thermal noise characteristics in 10 nm metal oxide semiconductor field effect transistor

<sec>Small size metal-oxide-semiconductor field effect transistor (MOSFET), owing to their high theoretical efficiency and low production cost, have received much attention and are at the frontier of transistors. At present, their development is bottlenecked by physical limits due to equal scaling down of devices, which requires further improvement in terms of materials choice and device fabrication. As the MOSFET devices scale down to nanometer scale, on the one hand, the resulting short channel effect affects severely the thermal noise property; on the other hand, it makes the ratio of thermal noise in the gate, source, drain and substrate regions become higher and higher. However, the traditional thermal noise model mainly considers thermal noise of large-size devices, and its model does not consider the channel saturation region. In view of this, it is necessary to establish a small size MOSFET thermal noise model and analyze its characteristics.</sec><sec>At present, there are some researches on MOSFET thermal noise, but they mainly focus on the thermal noise in channel region of large size nanoscale MOSFET. In the present work, according to the device structure and inherent thermal noise characteristics, we establish a thermal noise model for MOSFETs of 10 nm feature size. The model includes contributions of substrate region, gate-source-drain region, and channel region. In the channel region is also included the thermal noise related to the device saturation regime. Using such a model, the dependence of channel thermal noise and total thermal noise on the device bias condition and device parameters are investigated, evidencing the existence of thermal noise in the device saturation regime, which are consistent with the experimental results in the literature. The thermal noise increases with the gate voltage and source-drain voltage rising as the device structure shrinks. In a temperature range of 100–400 K, the thermal noise is basically on the order of 10<sup>21</sup>, indicating that the temperature has a great influence on the thermal noise. The thermal noise model established in this work can be applied to analyzing the noise performances of small size MOSFET devices, and the conclusions drawn from the present study are beneficial to improving the efficiency, lifetime, and response speed of MOSFETs on a nanometer scale.</sec>

Stability and decoherence rates of a GKP qubit protected by dissipation⋆

We analyze an experimentally accessible Lindblad master equation for a quantum harmonic oscillator. It approximately stabilizes finite-energy periodic grid states called Gottesman-Kitaev-Preskill (GKP) states, that can be used to encode and protect a logical qubit. We give explicit upper bounds for the energy of the solutions of the Lindblad master equation. Using three periodic observables to define the Bloch sphere coordinates of a logical qubit, we show that their dynamics is governed by a diffusion partial differential equation on a 2D-torus with a Witten Laplacian. We show that the evolution of these logical coordinates is exponentially slow even in presence of small diffusive noise processes along the two quadratures of the phase space. Numerical simulations indicate similar results for other physically relevant noise processes.

Electronic structures and molecular doping of germanane regulated by hydrogen vacancy clusters

Germanane is expected to substitute for existing silicon-based or germanium-based material. Germanane is regarded as an ideal candidate for next-generation semiconductor material due to its suitable band gap, high electron mobility, better environmental stability, small electrical noise and ultrathin geometry. In this work, the effects of different configuration and concentration of hydrogen vacancy cluster on the electronic properties of germanane and its molecular doping are systematically investigated through the first-principles method based on density functional theory and none-quilibrium Green’s function. The results show that the hydrogen vacancy clusters with different configurations can induce magnetism with different characteristics in Germanane<sub>Dehydrogenated-<i>x</i>H</sub> (G<sub>D-<i>x</i>H</sub>) system, and the magnetic moments are consistent with the predictions of Lieb’s theorem. Moreover, the p-type-liked doping effects caused by defective state under G<sub>D-<i>x</i>H</sub> (<i>x</i> = 1, 4, 6) systems can be realized in their spin-down band structures. The corresponding energy values for exciting electron would gradually decrease with the increase of the concentration of hydrogen vacancy clusters under different configurations. After adsorbing tetrathiafulvalene (TTF) molecules, G/TTF and G<sub>D-<i>x</i>H</sub>/TTF (<i>x</i> = 1, 2, 6) systems exhibit molecular doping characteristics induced by the TTF molecules. More importantly, for G<sub>D-<i>x</i>H</sub>/TTF (<i>x</i> = 1, 6) system, the different molecular doping types can be introduced in spin-up and spin-down band structures due to the hybridization composed of molecular orbitals and defective states under spin polarization. Further calculations of their transport properties indicate that germanane-based device with Armchair and Zigzag configurations both exhibit intensive isotropy, and the performance of <i>I-V</i> characteristics can be dramatically enhanced owing to the carrier doping by TTF adsorption.

Approximation of BSDE with hidden forward equation and unknown volatility

The focus is on the approximation of the solution of BSDE in the case where the solution of forward equation is observed in the presence of small Gaussian noise. The volatility of the forward equation is considered to depend on some unknown parameter. This approximation is made in several steps. First a preliminary estimator of the unknown volatility is obtained, then using Kalman-Bucy filtration equations and Fisher-score device one-step MLE-process of this parameter is constructed. The solution of BSDE is approximated by means of the solution of PDE and the One-step MLE-process. The error of approximation is described in different metrics.

An ADS‐B signal poisoning method based on generative adversarial network

Automatic dependent surveillance-broadcast (ADS-B) has been widely used due to its low cost and high precision. The deep learning methods for ADS-B signal classification have achieved a high performance. However, recent studies have shown that deep learning networks are very sensitive and vulnerable to small noise. An ADS-B signal poisoning method based on Generative Adversarial Network is proposed. This method can generate poisoned signals. One of ADS-B signal classification networks is assigned as the attacked network and another one as the protected network. When poisoned signals are fed into these two well-performed classification networks, the poisoned signal will be recognized incorrectly by the attacked network while classified correctly by the protected network. An attack-protect-similar loss function is further proposed to achieve ‘triple-win’ in leading attacked network poor performance, protected network well performance and the poisoned signals similar to unpoisoned signals. Experimental results show that the attacked network classifies poisoned signals with 1.55% classification accuracy, while the protected network classifies rate is still maintained at 99.38%.

Vanishing Opinions in Latané Model of Opinion Formation.

In this paper, the results of computer simulations based on the Nowak-Szamrej-Latané model with multiple (from two to five) opinions available in the system are presented. We introduce the noise discrimination level (which says how small the clusters of agents could be considered negligible) as a quite useful quantity that allows qualitative characterization of the system. We show that depending on the introduced noise discrimination level, the range of actors' interactions (controlled indirectly by an exponent in the distance scaling function, the larger the exponent, the more influential the nearest neighbors are) and the information noise level (modeled as social temperature, which increases results in the increase in randomness in taking the opinion by the agents), the ultimate number of the opinions (measured as the number of clusters of actors sharing the same opinion in clusters greater than the noise discrimination level) may be smaller than the number of opinions available in the system. These are observed in small and large information noise limits but result in either unanimity, or polarization, or randomization of opinions.

Synchronization on star graph with noise

We investigate synchronization in the Kuramoto model with noise on a star graph. By revising the case of a complete graph, we propose a closed form of self-consistency equation for the conventional order parameter and generalize it for a star graph. Using the obtained self-consistency equation, we demonstrate that there is a crossover between the abrupt synchronization at small noise and the continuous phase transition for quite large noise. We probe this crossover numerically and analytically.

AEGuard: Image Feature-Based Independent Adversarial Example Detection Model

With the rapid development of image processing technology, image recognition systems based on massive image data are being developed and deployed. The wrong decision regarding an image recognition system for security-sensitive systems can cause serious problems such as personal accidents and property damage. Furthermore, adversarial attacks, which are security attacks that cause malfunctions in image recognition systems by inserting adversarial noise, have emerged and evolved. Several studies have been conducted to prevent adversarial attacks. However, existing mechanisms have low classification accuracy and low detection accuracy for adversarial examples with small adversarial noise. This paper proposes an adversarial example detection mechanism based on image feature extraction and a deep neural network (DNN) model. The proposed system achieves versatility and independence by detecting adversarial examples based on image features, such as edge noise and discrete cosine transform (DCT) bias, which adversarial examples have in common. The proposed system shows relatively higher detection accuracy than existing mechanisms for various types and amounts of adversarial noise and different sharpness of adversarial examples because the proposed system detects them depending on the characteristics of each type of adversarial example.

Near-Collision Dynamics in a Noisy Car-Following Model

We consider a small stochastic perturbation of an optimal velocity car-following model. We give a detailed analysis of behavior near a collision singularity. We show that collision is impossible in a simplified model without noise, and then show that collision is asymptotically unlikely over large time intervals in the presence of small noise, with the large time interval scaling like the square of the reciprocal of the strength of the noise. Our calculations depend on careful boundary-layer analyses.

Constructive finite-dimensional boundary control of stochastic 1D parabolic PDEs

Recently, a constructive method for the finite-dimensional observer-based control of deterministic parabolic PDEs was suggested by employing a modal decomposition approach. In this paper, for the first time we extend this method to the stochastic 1D heat equation with nonlinear multiplicative noise. We consider the Neumann actuation and study the observer-based as well as the state-feedback controls via the modal decomposition approach. We employ either trigonometric or polynomial dynamic extension. For observer-based control we consider a noisy boundary measurement. First, we show the well-posedness of strong solutions to the closed-loop systems. Then by suggesting a direct Lyapunov method and employing Itô’s formula, we provide mean-square L2 exponential stability analysis of the full-order closed-loop system, leading to linear matrix inequality (LMI) conditions for finding the observer dimension and as large as possible noise intensity bound for the mean-square stabilizability. We prove that the LMIs are always feasible for small enough noise intensity and large enough observer dimension (for observer-based control). We further show that in the case of state-feedback and linear noise, the system is always stabilizable for noise intensities that guarantee the stabilizability of the stochastic finite-dimensional part of the closed-loop system with deterministic measurement. Numerical simulations are carried out to illustrate the efficiency of our method. For both state-feedback and observer-based controls, the trigonometric extension always allows for a larger noise than the polynomial one in the example.

On the conservative character of discretizations to Itô-Hamiltonian systems with small noise

In this paper, we consider stochastic Hamiltonian systems of Itô type driven by a multiplicative small noise. It is well-known, indeed, that stochastic Hamiltonian problems are suitable candidates to reconcile the Hamiltonian classical mechanics with the non-differentiability of the Wiener process, which provides the innovative character of stochastic effects. In particular, in this work, we provide a characterization of the behavior of averaged Hamiltonians arised in such systems, with more emphasis on the separable and quadratic Hamiltonians. Next, we show that, in general, first order approximations to such systems are not able to retain the same behavior discovered for the exact averaged Hamiltonian. Hence, the analysis for the specific case of ϑ-methods is performed. Finally, numerical evidence is depicted in order to confirm theoretical results.

Comparison of Several Methods for Automated Noise Measurements in Computed Tomography

Purpose: To compare the methods of automated noise measurement at the polyester resin (PESR) phantom images and clinical abdominal images. Method: The PESR phantom was scanned with a Siemens SOMATOM Emotion 6 CT scanner for various tube voltages, i.e., 80, 110, and 130 kV. Noises from images of the PESR phantom and 27 clinical abdominal scans were automatically measured. The methods used for automatic measurements were methods proposed by Christianson et al (2015), Malkus et al (2017), and Anam et al (2019), respectively. Results: Three methods of automatic noise measurements can distinguish the noise of the three tube voltages. The measured noises from three methods decrease with increasing tube voltage. It can also be seen that the highest noise in PESR phantom images is Christianson et al (2015) method, and the smallest noise is Malkus et al (2017) method. The highest noise in clinical abdominal images is Malkus et al (2017) method, and the smallest noise is Anam et al (2019) method. Conclusion: The algorithms to automatically measure noises proposed by Christianson et al (2015), Malkus et al (2017), and Anam et al (2019) have been compared. Although the three methods can distinguish noise for different exposure factors, the magnitude of the noise from the three methods can vary. Until now there is no standard for automatic noise determination.

Bound-state soliton gas as a limit of adiabatically growing integrable turbulence

We study numerically the integrable turbulence in the framework of the one-dimensional nonlinear Schrodinger equation (1D-NLSE) of the focusing type using a new approach called the “growing of turbulence”. In this approach, we add a small linear pumping term to the equation and start evolution from statistically homogeneous Gaussian noise. After reaching a certain level of average intensity, we switch off the pumping and examine the resulting integrable turbulence. For sufficiently small initial noise and pumping coefficient, and also for not very wide simulation box (basin length), we observe that the turbulence grows in a universal adiabatic regime, moving successively through the statistically stationary states of the integrable 1D-NLSE, which do not depend on the pumping coefficient, amplitude of the initial noise or basing length. Waiting longer in the growth stage, we transit from weakly nonlinear states to strongly nonlinear ones, characterized by a high frequency of rogue waves. Using the inverse scattering transform (IST) method to monitor the evolution, we observe that the solitonic part of the wavefield becomes dominant even when the (linear) dispersion effects are still leading in the dynamics and with increasing average intensity the wavefield approaches a dense bound-state soliton gas, whose properties are defined by the Fourier spectrum of the initial noise. Regimes deviating from the universal adiabatic growth also lead to solitonic states, but solitons in these states have noticeably different velocities and a significantly wider distribution by amplitude, while the statistics of wavefield indicates a much more frequent appearance of very large waves.

Error Propagation in NISQ Devices for Solving Classical Optimization Problems

We propose a random circuit model to analyze the impact of noise on the performance of variational quantum circuits for classical optimization problems. Our model accounts for the propagation of arbitrary single qubit errors through the circuit. We find that even with a small noise rate, the quality of the obtained classical optima is low on average and a single-qubit error rate of $1 / nD$, where $n$ is the number of qubits and $D$ is the circuit depth, is needed for the possibility of a quantum advantage. We estimate that this translates to an error rate lower than $10^{-6}$ using QAOA for classical optimization problems with 2D circuits.