Random Input Vectors Research Articles

Recurrent neural networks-guided vector-valued synchronized key exchange for secure and privacy-preserving communication in Industrial Internet of Things

This paper presents an innovative approach to the problem of key exchange in the Industrial Internet of Things (IIoT) implementation. Recurrent Neural Networks (RNNs) and vector-valued neural synchronization are the key components of the proposed secure transmission method. Drive-response methods are integrated to improve speed in important applications, meeting the continuous need for effective cryptographic key exchange between IIoT devices. Conventional algorithms face drawn-out assessment procedures that jeopardize neural synchronization concealment. This work examines how random input vector generation and synchronization issues in RNNs with drive-response are affected by proportional and non-proportional delays. Furthermore, it delves into an unexplored domain, investigating the synchronization of response-based RNN systems without delays and drive-response-based RNN systems with various proportional delays. It also suggests a simplified analysis of Artificial Neural Networks (ANNs) synchronization, organizing ANNs for session key switch-over using an RNN system. To achieve polynomial and non-polynomial synchronization in the proposed driver response systems, this method offers several benefits: it introduces a polynomial synchronization theory for RNNs to generate synchronized input vectors for ANN synchronization; it uses inequality assessment techniques and Lyapunov formulas to derive relevant control inputs and time-dependent conditions; it establishes the relationship between polynomial and non-polynomial synchronization; and it provides numerical examples demonstrating its effectiveness. It also builds a neural network for generating session keys throughout the IIoT network by aligning vector-valued ANNs in a reciprocal manner. This strategy outperforms previous approaches in the literature, validated through simulations, balances resilience against attacks with minimal computational load, resulting in more effective and resilient industrial applications.

Meta model-based and cross entropy-based importance sampling algorithms for efficiently solving system failure probability function

The multi-mode system failure probability function (SFPF) can quantify how the distribution parameters of the random input vector affect the system safety and decouple the system reliability-based design optimization model. However, for a problem with a time-consuming implicit performance function and rare failure domain, efficiently solving the SFPF remains significantly challenging. Therefore, in this study, two efficient algorithms are proposed, namely, the meta model-based importance sampling and cross entropy-based importance sampling. The contributions of this study are twofold. The first is constructing a single-loop optimal importance sampling density (SL-OISD) method to decouple the double-loop framework for analyzing the SFPF. The second is establishing two methods to efficiently approximate the SL-OISD and complete the SFPF estimation. The first method is based on the meta model of the system performance function, which is abbreviated as SL-Meta-IS. The second method is based on minimizing the cross entropy between the Gaussian mixture density model and SL-OISD, which is abbreviated as SL-CE-IS. To reduce the number of evaluating the system performance function when approximating the SL-OISD, sampling the SL-OISD, and identifying the state of the samples for completing the SFPF estimation, an adaptive Kriging model of the system performance function is introduced into SL-Meta-IS and SL-CE-IS. Owing to decoupling the double-loop framework into a single-loop framework, replacing the time-consuming system performance function with the economic Kriging model, and employing importance sampling variance reduction techniques to address issues related to the rare failure domain, the proposed SL-Meta-IS and SL-CE-IS methods greatly enhance the efficiency of SFPF estimations. The numerical and practical examples demonstrate that the two proposed methods are superior to the existing algorithms; moreover, the efficiency of SL-CE-IS is higher than that of SL-Meta-IS.

Polynomial-chaos-based conditional statistics for probabilistic learning with heterogeneous data applied to atomic collisions of Helium on graphite substrate

A formulation and an algorithm are presented to construct a truncated polynomial chaos representation of a vector-valued random output. This representation depends on a vector-valued random input with a known probability measure and a vector-valued random latent variable with an unknown probability measure. The construction of this PCE representation relies solely on a training set comprising a small number of independent realizations of the non-Gaussian dependent random output and input vectors. The training set consists of heterogeneous data, which poses challenges in accurately estimating the chaos coefficients. Despite the heterogeneity of the data, the proposed formulation and algorithm allow for the construction of a highly accurate global surrogate model. Additionally, we propose an alternative approach by constructing a surrogate model based on prior separation of the heterogeneous dataset into subsets, each containing “quasi-homogeneous” data. The separation method is designed to account for a partial overlap of the probability measure supports associated with the subsets. The identification of the PCE is performed offline. By utilizing the PCE, a fast online surrogate model is obtained, enabling analysis of large dynamical systems beyond the computational capabilities currently available. An application to atomic collisions of Helium on a graphite substrate is presented, where the training set was generated by Molecular Dynamics simulations done in a previous paper. The obtained results demonstrate accuracy of the proposed approach.

Convergence Rates for Learning Linear Operators from Noisy Data

This paper studies the learning of linear operators between infinite-dimensional Hilbert spaces. The training data comprises pairs of random input vectors in a Hilbert space and their noisy images under an unknown self-adjoint linear operator. Assuming that the operator is diagonalizable in a known basis, this work solves the equivalent inverse problem of estimating the operator's eigenvalues given the data. Adopting a Bayesian approach, the theoretical analysis establishes posterior contraction rates in the infinite data limit with Gaussian priors that are not directly linked to the forward map of the inverse problem. The main results also include learning-theoretic generalization error guarantees for a wide range of distribution shifts. These convergence rates quantify the effects of data smoothness and true eigenvalue decay or growth, for compact or unbounded operators, respectively, on sample complexity. Numerical evidence supports the theory in diagonal and non-diagonal settings.

A fast method based on Dynamic Mode Decomposition for radiative heat transfer in participating media

The radiative transfer equation (RTE) is an integro-differential equation and solving it is time-consuming except in a few specific cases. A fast method based on dynamic mode decomposition (DMD) is introduced for solving the RTE in an absorbing-emitting and scattering medium. First, some parameters are considered as independent variables. The RTE is solved for different values of these parameters (known input vectors) using the discrete ordinates method (S6 approximation), and the system responses generate the snapshot matrix. Then using the DMD technique, the dynamic modes are constructed, so the degree of freedom of the system is decreased. The reduced-order model (ROM), called DMD-RBF, is generated by combining the DMD and the radial basis functions. Two cases, radiative equilibrium and medium with known temperature (isothermal and non-isothermal), are considered. The accuracy of the model is investigated using random input vectors. The results show that the DMD-RBF has a good agreement with the numerical solutions. Comparison between the ROM and numerical CPU times shows the high efficiency of the ROM. The results also show that the problem complexity does not affect the computational cost. For all cases, the CPU time of the ROM is of the order of 0.01 seconds.

Digital Image Compression Using Approximate Addition

This paper analyzes the usefulness of approximate addition for digital image compression. Discrete Cosine Transform (DCT) is an important operation in digital image compression. We used accurate addition and approximate addition individually while calculating the DCT to perform image compression. Accurate addition was performed using the accurate adder and approximate addition was performed using different approximate adders individually. The accurate adder and approximate adders were implemented in an application specific integrated circuit (ASIC)-type design environment using a 32–28 nm complementary metal oxide semiconductor (CMOS) standard cell library and in a field programmable gate array (FPGA)-based design environment using a Xilinx Artix-7 device. Error analysis was performed to calculate the error parameters of various approximate adders by applying one million random input vectors. It is observed that the approximate adders help to better reduce the file size of compressed images than the accurate adder. Simultaneously, the approximate adders enable reductions in design parameters compared to the accurate adder. For an ASIC-type implementation using standard cells, an optimum approximate adder achieved 27.1% reduction in delay, 46.4% reduction in area, and 50.3% reduction in power compared to a high-speed accurate carry look-ahead adder. With respect to an FPGA-based implementation, an optimum approximate adder achieved 8% reduction in delay and 19.7% reduction in power while requiring 47.6% fewer look-up tables (LUTs) and 42.2% fewer flip-flops compared to the native accurate FPGA adder.

Chaos-Based Mutual Synchronization of Three-Layer Tree Parity Machine: A Session Key Exchange Protocol Over Public Channel

In this paper, a chaos-based triple-layer tree parity machine (TLTPM)-guided neural synchronization has been proposed for the development of the public key exchange protocol. A special neural network structure called tree parity machine (TPM) is used for neural synchronization. Two TPMs accept the common input and different weight vectors and update the weights using the neural learning rule by exchanging their output. In some steps, it results in complete synchronization, and the weights of the two TPMs become identical. These identical weights serve as a secret key. There is, however, hardly any investigation to investigate the randomness of the common input vector used in the synchronization process. In this paper, logistic chaos system-based TLTPM is proposed. For faster synchronization, this proposed TLTPM model uses logistic chaos-generated random common input vector. This proposed TLTPM model is faster and has better security than TPM with the same input, output, and hidden neurons. This proposed technique has been passed through a series of parametric tests. The results have been compared with some recent techniques. The results of the proposed technique have shown effective and robust potential.

Deep Learning Guided Double Hidden Layer Neural Synchronization Through Mutual Learning

In this paper, a Double Hidden Layer Neural Networks synchronization mechanism using Generative Adversarial Network (GAN) and mutual learning is used for the development of the cryptographic key exchange protocol. This protocol is used to exchange sensitive information through a public channel. At the time of exchanging sensitive information, an intruder can easily attack the vital information/signals by sniffing, spoofing, phishing, or Man-In-The-Middle attack. There is, however, hardly some investigation to investigate the randomness of the common input vector in the synchronization of two neural networks. This proposed technique provides GAN generated random input vectors for neural synchronization which are very sensitive to the seed value. To enhance the security of the synchronization process, GAN generates the best random sequence of the input vector. Two neural networks use GAN generated input vector and different random weight vector and swap their output. In some steps, it results in complete synchronization by setting the discrete weights according to the common learning rule. The synchronized weight vector serves as a session key at the end of the neural synchronization process. An increase in the weight range increases the complexity of a successful attack exponentially but the effort to build the neural key decreases over the polynomial time. The proposed technique offers synchronization and authentication steps in parallel. It is difficult for the attacker to distinguish between synchronization and authentication steps. This proposed technique has been passed through different parametric tests. The results have shown effective and robust potential. Simulations of the process show effectiveness in terms of cited results in the paper.

Secure exchange of information using artificial intelligence and chaotic system guided neural synchronization

In this paper, a chaos-based neural synchronization has been proposed for the development of the public-key exchange protocol. A special neural network structure called Tree Parity Machine (TPM) is used for neural synchronization. Two TPMs accept the common input and different weight vector and update the weights using neural learning rule by exchanging their output. In some steps, it results in complete synchronization, and the weights of the two TPMs become identical. These identical weights serve as a secret key. There is, however, hardly some investigation to investigate the randomness of the common input vector used in the synchronization process. In this paper, logistic Chaos system based Tree Parity Machine (CTPM) is proposed. For faster synchronization, this proposed CTPM model uses logistic chaos generated random common input vector. This proposed CTPM model is faster and has better security than TPM with the same input, output, and hidden neurons. This proposed technique has been passed through a series of parametric tests. The results have been compared with some recent techniques. The results of the proposed technique have shown effective and robust potential.

Improved sampling strategies for ensemble-based optimization

We are concerned with the efficiency of stochastic gradient estimation methods for large-scale nonlinear optimization in the presence of uncertainty. These methods aim to estimate an approximate gradient from a limited number of random input vector samples and corresponding objective function values. Ensemble methods usually employ Gaussian sampling to generate the input samples. It is known from the optimal design theory that the quality of sample-based approximations is affected by the distribution of the samples. We therefore evaluate six different sampling strategies to optimization of a high-dimensional analytical benchmark optimization problem, and, in a second example, to optimization of oil reservoir management strategies with and without geological uncertainty. The effectiveness of the sampling strategies is analyzed based on the quality of the estimated gradient, the final objective function value, the rate of the convergence, and the robustness of the gradient estimate. Based on the results, an improved version of the stochastic simplex approximate gradient method is proposed based on UE(s2) sampling designs for supersaturated cases that outperforms all alternative approaches. We additionally introduce two new strategies that outperform the UE(s2) designs previously suggested in the literature.

GlyphGAN: Style-consistent font generation based on generative adversarial networks

In this paper, we propose GlyphGAN: style-consistent font generation based on generative adversarial networks (GANs). GANs are a framework for learning a generative model using a system of two neural networks competing with each other. One network generates synthetic images from random input vectors, and the other discriminates between synthetic and real images. The motivation of this study is to create new fonts using the GAN framework while maintaining style consistency over all characters. In GlyphGAN, the input vector for the generator network consists of two vectors: character class vector and style vector. The former is a one-hot vector and is associated with the character class of each sample image during training. The latter is a uniform random vector without supervised information. In this way, GlyphGAN can generate an infinite variety of fonts with the character and style independently controlled. Experimental results showed that fonts generated by GlyphGAN have style consistency and diversity different from the training images without losing their legibility.

SquASH: Approximate Square-Accumulate With Self-Healing

Approximate computing strives to achieve the highest performance-, area-, and power-efficiency for a given quality constraint and vice versa. Conventional approximate design methodology restricts the introduction of errors to avoid a high loss in quality. However, this limits the computing efficiency and the number of pareto-optimal design alternatives for a quality-efficiency tradeoff. This paper presents a novel self-healing (SH) methodology for an approximate square-accumulate (SAC) architecture. SAC refers to a hardware architecture that computes the inner product of a vector with itself. SH exploits the algorithmic error resilience of the SAC structure to ensure an effective quality-efficiency tradeoff, wherein the squarer is regarded as an approximation stage, and the accumulator as a healing stage. We propose to deploy an approximate squarer mirror pair , such that the error introduced by one approximate squarer mirrors the error introduced by the other, i.e., the errors generated by the approximate squarers are approximately the additive inverse of each other. This helps the healing stage (accumulator) to automatically average out the error originated in the approximation stage, and thereby to minimize the quality loss. For random input vectors, SH demonstrates up to 25% and 18.6% better area and power efficiency, respectively, with a better quality output than the conventional approximate computing methodology. As a case study, SH is applied to one of the computationally expensive components (SAC) of the radio astronomy calibration application, where it shows up to 46.7% better quality for equivalent computing efficiency as that of conventional methodology.

Robustness regions for measures of risk aggregation

Abstract One of risk measures’ key purposes is to consistently rank and distinguish between different risk profiles. From a practical perspective, a risk measure should also be robust, that is, insensitive to small perturbations in input assumptions. It is known in the literature [14, 39], that strong assumptions on the risk measure’s ability to distinguish between risks may lead to a lack of robustness. We address the trade-off between robustness and consistent risk ranking by specifying the regions in the space of distribution functions, where law-invariant convex risk measures are indeed robust. Examples include the set of random variables with bounded second moment and those that are less volatile (in convex order) than random variables in a given uniformly integrable set. Typically, a risk measure is evaluated on the output of an aggregation function defined on a set of random input vectors. Extending the definition of robustness to this setting, we find that law-invariant convex risk measures are robust for any aggregation function that satisfies a linear growth condition in the tail, provided that the set of possible marginals is uniformly integrable. Thus, we obtain that all law-invariant convex risk measures possess the aggregation-robustness property introduced by [26] and further studied by [40]. This is in contrast to the widely-used, non-convex, risk measure Value-at-Risk, whose robustness in a risk aggregation context requires restricting the possible dependence structures of the input vectors.

Optimum design of preform geometry and forming pressure in tube hydroforming using the equi-potential lines method

The quality of a tube-hydroformed component as well as the tooling cost and processing time involved in the process are notably affected by the component’s preform. Hence, it is necessary to produce a proper preform shape for the successful hydroforming from the initial tube to final shape. In this paper, the notion of equi-potential lines (EPLs) is used to find an appropriate preform shape in the tube hydroforming process for the first time. The EPLs generated between two conductors of different voltages show minimum work paths between the initial and final shapes. Based on this similarity, the EPLs method is utilized for preform shape design. Next, the forming pressure of the preform is determined using finite element analysis. Finally, the computationally expensive procedure introduced above is significantly facilitated by employing a multi-layer perceptron neural network which is trained using results from application of the procedure to a set of uniformly distributed random input vectors. Real-world examples are presented to demonstrate the applicability and efficiency of the proposed approach.

New Neural Networks Strategy Used to Improve Wind Speed Forecasting

Wind speed forecasting is critical for wind energy conversion systems since it greatly influences the issues such as the scheduling of a power system, and the dynamic control of the wind turbine. The wind forecast problem aims to find an estimate f( t + k) of the wind vector y( t + k) based on the previous n measurements. Artificial neural networks ANN is a technique basically used to map random input vector(s) to the corresponding random output vector without pre-assuming any fixed relationship between them. Different network structures, learning rates, and inputs are believed to result in different forecast accuracies. However, in literature it was discovered that, different inputs and learning rates, as well as model structures, directly influence the forecast accuracy. In this paper, we present a robust and reliable forecast method by applying a new learning Strategy. This new method allows a renewal learning data in time. A simple multilayer perceptron (MLP) with Levenberg-Marquardt learning algorithm technique is used for predicting the wind speed. For our algorithm a neural network is developed to estimate just one value f( t + 1), then it is taken up with a new set of learning enriched by data freshly measured. The wind data used are the hourly mean wind speed collected at an observation sites in Ksar El chellala, (Algeria). Simulation results are reported, showing that the estimated wind speed values, predicted by the proposed learning algorithm technique, are in good agreement with the experimental measured values. The present paper deals with the development of an adaptive neural network model for the hourly forecasting of wind speed.

Resolution tests revisited: the power of random numbers

Abstract We propose a simple method where the inversion of synthetic data, corresponding to a zero-mean random input vector, is used to infer the average horizontal and vertical resolution lengths of tomographic models. The method works well if the resolution operator has a diagonally dominant structure. This assumption, although often verified in seismic tomography, can be tested by simply cross-correlating the input with the output of the synthetic simulation. The method is as efficient as a single checkerboard test, but reveals more easily interpretable information.

Statistical full-chip total power estimation considering spatially correlated process variations

In this paper, we propose an efficient statistical full-chip total power estimation method considering process variations with spatial correlation. Traditionally, dynamic power and leakage power were computed separately as leakage power is more susceptible to process variations. But in the end, it is total power that designers will be concerned with. We propose a new method to compute the statistical total power via circuit level simulation under realistic input testing vectors. To consider the process variations with spatial correlation, we first apply principle factor analysis method (PFA) or its weighted version (wPFA) to transform the correlated variables into uncorrelated ones and meanwhile reduce the number of resulting random variables. Afterwards, Hermite orthogonal polynomials and sparse grid techniques are used to estimate total power distribution in a sampling way. The proposed method has no restrictions on models of statistical distributions for total powers. The method works well when strong spatial correlation exists among random variables in the chip. Experimental results show that the proposed method has 100X times speedup than the Monte Carlo method under fixed input vector and 20X times speedup than the Monte Carlo method considering both random input vectors and process variations with spatial correlation.

Subsets of Primary Input Vectors in Sequential Test Generation for Single Stuck-at Faults

The complexity of deterministic sequential test generation for a target fault in a circuit with <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> primary inputs is determined by the need to explore a search space that consists of 2 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> primary input vectors at every time unit. This paper studies the possibility of reducing the complexity of deterministic sequential test generation by using subsets of primary input vectors of limited sizes during test generation for target faults. It considers a test generation procedure that uses subsets of primary input vectors of size <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> , for increasing values of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> starting with <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> =1 . The subsets consist of primary input vectors from the test sequence already generated, and of random primary input vectors. The results indicate that all or most of the detectable single stuck-at faults in benchmark circuits can be detected using small subsets of primary input vectors.

Flexible Simulation e-Learning Environment for Studying Digital Circuits and Possibilities for it Deployment as Semantic Web Service

In this article we present a partially realized project for building a distributed learning environment for studying digital circuits Test and Diagnostics at TU-Sofia. We describe the main requirements for this environment, substantiate the developer platform choice, and present our simulation and circuit parameter calculation tools. Administrative, Demo, and Service tools are fully realized and presented in the article. Serial fault simulator and ATPG with random input vectors are also presented. Some tools for fault diagnosis are developed and presented in the article. We discuss and compare modern semantic technologies for publishing functionalities of our application as semantic web services to make them easily searchable and usable from the internet. Initial version of ontology, conceptualizing valuable domain and semantic web service terminology is developed and conceptual model, using this ontology for dynamic service discovery and composition is presented and discussed.

Random Test Generation With Input Cube Avoidance

Test generation procedures attempt to assign values to the inputs of a circuit so as to detect target faults. We investigate a complementary view whereby the goal is to avoid the assignment of certain input values in order not to prevent faults from being detected. We describe a procedure for computing input cubes (or incompletely specified input vectors) that should be avoided during test generation for target faults. We demonstrate that avoiding such input cubes leads to the detection of target faults after the application of limited numbers of random input vectors. This indicates that explicit test generation is not necessary once certain input values are precluded. Other potential uses of the computed input cubes are in a deterministic test generation procedure to reduce the search space, and during built-in test generation to preclude input vectors that will not lead to the detection of target faults. We consider stuck-at faults in full-scan circuits. We also extend the discussion to four-way bridging faults.