Low-dimensional Set Research Articles

A fast calculation method for dynamic topology optimization based on hybrid spectral element method

In this study, a Hybrid Spectral Element Method (HSEM) integrated with Equivalent Static Load (ESL) in the frequency domain is suggested. This integration aims to enhance the computational efficiency of dynamic topology optimization. In comparison with existing techniques, the proposed HSEM transforms the governing equation of dynamic analysis into a spectral element equation within the frequency domain by utilizing the Fast Fourier Transform (FFT) algorithm. This approach enables the representation of both structural displacements and external loads in spectral forms, potentially leading to a reduction in the number of dimensions compared to traditional time-interval-based methods. By using spectral representation, a low-dimensional ESL set can be constructed in the frequency domain for model reduction. To validate the effectiveness of the suggested proposed method, extensive analyses and comparisons using various two-dimensional (2D) and three-dimensional (3D) examples are carried out. The obtained results demonstrate a substantial improvement in computational efficiency, both during the dynamic analysis phase and the quasi-static topology optimization phase, while maintaining high levels of accuracy. Moreover, even as the scale of the model increases, our method maintains its advantage in computational efficiency. In the test examples, a maximum speedup ratio of up to 6.54 times was observed, indicating the significant potential of the proposed HSEM-ESL approach in enhancing the performance of dynamic topology optimization tasks.

High-dimensional expensive optimization by Kriging-assisted multiobjective evolutionary algorithm with dimensionality reduction

Surrogate-assisted multi-objective evolutionary algorithms (SA-MOEAs) have made significant progress in solving expensive multi- and many-objective optimization problems. However, most of them perform well in low-dimensional settings but often struggle with high-dimensional problems. The main reason is that some techniques used in SA-MOEAs, like the Kriging model, are ineffective in exploring high-dimensional search spaces. As a result, this research investigates frameworks incorporating dimensionality reduction techniques to conduct modeling and optimization tasks on dimensionality reduction decision spaces. This article uses a singular value decomposition method to map the high-dimensional decision space into a low-dimensional one, then employs a feature fusion strategy to combine low-dimensional features with high-dimensional ones for better representation. Subsequently, these low-dimensional features are used to train the Kriging-based surrogates to select promising solutions within a limited number of function evaluations. In addition, this article provides two types of evolutionary modes to balance exploration and exploitation. Experimental results demonstrate the effectiveness of the proposed SA-MOEA compared to several state-of-the-art algorithms.

Geometric quantum complexity of bosonic oscillator systems

According to the pioneering work of Nielsen and collaborators, the length of the minimal geodesic in a geometric realization of a suitable operator space provides a measure of the quantum complexity of an operation. Compared with the original concept of complexity based on the minimal number of gates required to construct the desired operation as a product, this geometrical approach amounts to a more concrete and computable definition, but its evaluation is nontrivial in systems with a high-dimensional Hilbert space. The geometrical formulation can more easily be evaluated by considering the geometry associated with a suitable finite-dimensional group generated by a small number of relevant operators of the system. In this way, the method has been applied in particular to the harmonic oscillator, which is also of interest in the present paper. However, subtle and previously unrecognized issues of group theory can lead to unforeseen complications, motivating a new formulation that remains on the level of the underlying Lie algebras for most of the required steps. Novel insights about complexity can thereby be found in a low-dimensional setting, with the potential of systematic extensions to higher dimensions as well as interactions. Specific examples include the quantum complexity of various target unitary operators associated with a harmonic oscillator, inverted harmonic oscillator, and coupled harmonic oscillators. The generality of this approach is demonstrated by an application to an anharmonic oscillator with a cubic term.

Representation learning with unconditional denoising diffusion models for dynamical systems

Abstract. We propose denoising diffusion models for data-driven representation learning of dynamical systems. In this type of generative deep learning, a neural network is trained to denoise and reverse a diffusion process, where Gaussian noise is added to states from the attractor of a dynamical system. Iteratively applied, the neural network can then map samples from isotropic Gaussian noise to the state distribution. We showcase the potential of such neural networks in proof-of-concept experiments with the Lorenz 1963 system. Trained for state generation, the neural network can produce samples that are almost indistinguishable from those on the attractor. The model has thereby learned an internal representation of the system, applicable for different tasks other than state generation. As a first task, we fine-tune the pre-trained neural network for surrogate modelling by retraining its last layer and keeping the remaining network as a fixed feature extractor. In these low-dimensional settings, such fine-tuned models perform similarly to deep neural networks trained from scratch. As a second task, we apply the pre-trained model to generate an ensemble out of a deterministic run. Diffusing the run, and then iteratively applying the neural network, conditions the state generation, which allows us to sample from the attractor in the run's neighbouring region. To control the resulting ensemble spread and Gaussianity, we tune the diffusion time and, thus, the sampled portion of the attractor. While easier to tune, this proposed ensemble sampler can outperform tuned static covariances in ensemble optimal interpolation. Therefore, these two applications show that denoising diffusion models are a promising way towards representation learning for dynamical systems.

Low and high dimensional wavelet thresholds for matrix-variate normal distribution

The matrix-variate normal distribution is a probability distribution that is a generalization of the multivariate normal distribution to matrix-valued random variables. In this paper, we introduce a wavelet shrinkage estimator based on Stein’s unbiased risk estimate (SURE) threshold for matrix-variate normal distribution. We find a new SURE threshold for soft thresholding wavelet shrinkage estimator under the reflected normal balanced loss function in low and high dimensional cases. Also, we obtain the restricted wavelet shrinkage estimator based on non-negative sub matrix of the mean matrix. Finally, we present a simulation study to test the validity of the wavelet shrinkage estimator and two real examples for low and high dimensional data sets.

A comparison of hyperparameter tuning procedures for clinical prediction models: A simulation study.

Tuning hyperparameters, such as the regularization parameter in Ridge or Lasso regression, is often aimed at improving the predictive performance of risk prediction models. In this study, various hyperparameter tuning procedures for clinical prediction models were systematically compared and evaluated in low-dimensional data. The focus was on out-of-sample predictive performance (discrimination, calibration, and overall prediction error) of risk prediction models developed using Ridge, Lasso, Elastic Net, or Random Forest. The influence of sample size, number of predictors and events fraction on performance of the hyperparameter tuning procedures was studied using extensive simulations. The results indicate important differences between tuning procedures in calibration performance, while generally showing similar discriminative performance. The one-standard-error rule for tuning applied to cross-validation (1SE CV) often resulted in severe miscalibration. Standard non-repeated and repeated cross-validation (both 5-fold and 10-fold) performed similarly well and outperformed the other tuning procedures. Bootstrap showed a slight tendency to more severe miscalibration than standard cross-validation-based tuning procedures. Differences between tuning procedures were larger for smaller sample sizes, lower events fractions and fewer predictors. These results imply that the choice of tuning procedure can have a profound influence on the predictive performance of prediction models. The results support the application of standard 5-fold or 10-fold cross-validation that minimizes out-of-sample prediction error. Despite an increased computational burden, we found no clear benefit of repeated over non-repeated cross-validation for hyperparameter tuning. We warn against the potentially detrimental effects on model calibration of the popular 1SE CV rule for tuning prediction models in low-dimensional settings.

Fast deep mixtures of Gaussian process experts

AbstractMixtures of experts have become an indispensable tool for flexible modelling in a supervised learning context, allowing not only the mean function but the entire density of the output to change with the inputs. Sparse Gaussian processes (GP) have shown promise as a leading candidate for the experts in such models, and in this article, we propose to design the gating network for selecting the experts from such mixtures of sparse GPs using a deep neural network (DNN). Furthermore, a fast one pass algorithm called Cluster–Classify–Regress (CCR) is leveraged to approximate the maximum a posteriori (MAP) estimator extremely quickly. This powerful combination of model and algorithm together delivers a novel method which is flexible, robust, and extremely efficient. In particular, the method is able to outperform competing methods in terms of accuracy and uncertainty quantification. The cost is competitive on low-dimensional and small data sets, but is significantly lower for higher-dimensional and big data sets. Iteratively maximizing the distribution of experts given allocations and allocations given experts does not provide significant improvement, which indicates that the algorithm achieves a good approximation to the local MAP estimator very fast. This insight can be useful also in the context of other mixture of experts models.

Evaluating variable selection methods for multivariable regression models: A simulation study protocol.

Researchers often perform data-driven variable selection when modeling the associations between an outcome and multiple independent variables in regression analysis. Variable selection may improve the interpretability, parsimony and/or predictive accuracy of a model. Yet variable selection can also have negative consequences, such as false exclusion of important variables or inclusion of noise variables, biased estimation of regression coefficients, underestimated standard errors and invalid confidence intervals, as well as model instability. While the potential advantages and disadvantages of variable selection have been discussed in the literature for decades, few large-scale simulation studies have neutrally compared data-driven variable selection methods with respect to their consequences for the resulting models. We present the protocol for a simulation study that will evaluate different variable selection methods: forward selection, stepwise forward selection, backward elimination, augmented backward elimination, univariable selection, univariable selection followed by backward elimination, and penalized likelihood approaches (Lasso, relaxed Lasso, adaptive Lasso). These methods will be compared with respect to false inclusion and/or exclusion of variables, consequences on bias and variance of the estimated regression coefficients, the validity of the confidence intervals for the coefficients, the accuracy of the estimated variable importance ranking, and the predictive performance of the selected models. We consider both linear and logistic regression in a low-dimensional setting (20 independent variables with 10 true predictors and 10 noise variables). The simulation will be based on real-world data from the National Health and Nutrition Examination Survey (NHANES). Publishing this study protocol ahead of performing the simulation increases transparency and allows integrating the perspective of other experts into the study design.

Research on Improved Particle Swarm Computational Intelligence Algorithm and Its Application to Multi-Objective Optimisation

Abstract Due to the pervasive generalization challenges in optimization technology, there is a noticeable trend toward planning and diversifying optimization techniques. This paper focuses on particle swarm optimization algorithms, particularly their application in multi-objective optimization scenarios. Initially, the study examines basic particle swarm, standard particle swarm, and particle swarm algorithms with a shrinkage factor. Subsequently, an enhanced particle swarm optimization algorithm is proposed, incorporating a hybridization model and a convergence factor model tailored to the specific characteristics of particle swarm algorithms. This improved algorithm is then applied to multi-objective optimization problems, establishing a novel algorithm based on the fusion of the enhanced particle swarm approach with constrained optimization. Simulation experiments conducted on this model reveal significant findings. In low-dimensional settings, the algorithm achieves a 100% optimization success rate, marking an average improvement of 53.80%, 40.78%, and 24.76% over competing algorithms. Moreover, in multi-objective optimization simulation experiments, this algorithm generates 142 and 135 optimal solutions, outperforming traditional algorithms by 112 and 107 solutions, respectively. These results validate the efficiency and enhanced performance of the improved particle swarm-based multi-objective optimization algorithm, demonstrating its potential as an effective tool for addressing real-world optimization challenges.

A comparative analysis of prognostic regression models and machine learning algorithms in surgical decision-making of cardial submucosal tumors

Background and aimsNon-tunneling and submucosal tunneling endoscopic resection (STER) techniques are the most frequent treatments for cardial submucosal tumor (SMT). Here, we analyzed common machine learning (ML) algorithms and compared them with traditional regression models in surgical decision-making for cardial SMTs. MethodsUsing key baseline predictive factors, ML algorithms and logistic regression (LR) were conducted in 246 patients. For the ML algorithms, gradient boosting machines (GBM), artificial neural networks (ANN), random forests (RF), and support vector machines (SVM), were included. For small sample-sized data, a technique for k-fold cross-validation was exploited to avoid over-fitting. Meanwhile, we tuned the parameters through several replications. Then, we quantified the discrimination (area under the curve, AUC) and predictive ability (Brier score, F1 score, specificity, sensitivity, and accuracy) of models. We divided patients (n ​= ​246) into STER-treated (n ​= ​97) and non-tunneling endoscopic resection (NTER)-treated (n ​= ​149) groups. ResultsLR outperformed among all groups (Brier score ​= ​0.1398, F1 score ​= ​0.7391, AUC ​= ​0.8729, and predictive accuracy ​= ​80.65 ​%). In comparison to ML algorithms, an outperformance of the traditional regression approach was also found in a low-dimensional setting for surgical decision prediction of cardial SMTs. ConclusionsThe traditional regression approach outperformed ML algorithms for the prediction of the best surgical method in patients with SMTs.

Riemannian frameworks for the harmonization of resting-state functional MRI scans

Magnetic Resonance Imaging provides unprecedented images of the brain. Unfortunately, scanners and acquisition protocols can significantly impact MRI scans. The development of statistical methods able to reduce this variability without altering the relevant information in the scans, often coined harmonization methods, has been the topic of an increasing research effort supported by the recent growth of publicly available neuroimaging data sets and new possibilities for combining them to achieve greater statistical power. In this work, we focus on the challenges specifically raised by the harmonization of resting-state functional MRI scans. We propose to harmonize resting-state fMRI scans by reducing the impact of covariates such as scanner differences and scanning protocols on their associated functional connectomes and then propagating the changes back to the rs-fMRI time series. We use Riemannian geometric frameworks to preserve the mathematical properties of functional connectomes during their harmonization, and we demonstrate how state-of-the-art harmonization methods can be embedded within these frameworks to reduce covariates effects while preserving the relevant clinical information associated with aging or brain disorders. During our experiments, a large set of synthetic data was generated and processed to compare eighty variants of the proposed approach. The framework achieving the best harmonization was then applied to three low-dimensional data sets made of 712 sets of fMRI time series provided by the ABIDE consortium and two high-dimensional data sets obtained by processing 1527 rs-fMRI scans provided by the Human Connectome Project, the Framingham Heart Study and the Genetics of Brain Structure and Function study. These experiments established that our new framework could successfully harmonize low-dimensional connectomes and voxelwise functional time series and confirmed the need for preserving connectomes properties during their harmonization.

Reduced-order model-based variational inference with normalizing flows for Bayesian elliptic inverse problems

We propose a reduced-order model-based variational inference method with normalizing flows for Bayesian elliptic inverse problems. The coefficient of the elliptic PDE is represented by a finite number of parameters. We aim to estimate the posterior distributions of these parameters in the framework of variational inference, and the approximation of the posterior distribution is constructed through a normalizing flow. Moreover, as data of inputs and outputs of the forward problem are accumulated during the training of the normalizing flow, we can naturally exploit the low-dimensional intrinsic structure of the forward elliptic PDE using reduced-order models based on these data, in which information of the true posterior is incorporated. We construct a low-dimensional set of data-driven basis functions in the solution space using proper orthogonal decomposition (POD) and train a neural network that maps the parameters to the coefficients of these data-driven basis functions. The surrogate forward map, which is the combination of the reduced-order model and the parameter-to-coefficient neural network, is then applied to the Bayesian elliptic inverse problem, where in each iteration the forward problem is evaluated in the space spanned by the POD basis functions using the surrogate forward map. Thus the inversion will be significantly accelerated as the surrogate forward map is essentially a low-dimensional model. We present numerical examples to show the accuracy and efficiency of the proposed method.

Pumping the brakes on RNA velocity by understanding and interpreting RNA velocity estimates.

RNA velocity analysis of single cells offers the potential to predict temporal dynamics from gene expression. In many systems, RNA velocity has been observed to produce a vector field that qualitatively reflects known features of the system. However, the limitations of RNA velocity estimates are still not well understood. We analyze the impact of different steps in the RNA velocity workflow on direction and speed. We consider both high-dimensional velocity estimates and low-dimensional velocity vector fields mapped onto an embedding. We conclude the transition probability method for mapping velocity estimates onto an embedding is effectively interpolating in the embedding space. Our findings reveal a significant dependence of the RNA velocity workflow on smoothing via the k-nearest-neighbors (k-NN) graph of the observed data. This reliance results in considerable estimation errors for both direction and speed in both high- and low-dimensional settings when the k-NN graph fails to accurately represent the true data structure; this is an unknown feature of real data. RNA velocity performs poorly at estimating speed in both low- and high-dimensional spaces, except in very low noise settings. We introduce a novel quality measure that can identify when RNA velocity should not be used. Our findings emphasize the importance of choices in the RNA velocity workflow and highlight critical limitations of data analysis. We advise against over-interpreting expression dynamics using RNA velocity, particularly in terms of speed. Finally, we emphasize that the use of RNA velocity in assessing the correctness of a low-dimensional embedding is circular.

Charting Nanocluster Structures via Convolutional Neural Networks.

A general method to obtain a representation of the structural landscape of nanoparticles in terms of a limited number of variables is proposed. The method is applied to a large data set of parallel tempering molecular dynamics simulations of gold clusters of 90 and 147 atoms, silver clusters of 147 atoms, and copper clusters of 147 atoms, covering a plethora of structures and temperatures. The method leverages convolutional neural networks to learn the radial distribution functions of the nanoclusters and distills a low-dimensional chart of the structural landscape. This strategy is found to give rise to a physically meaningful and differentiable mapping of the atom positions to a low-dimensional manifold in which the main structural motifs are clearly discriminated and meaningfully ordered. Furthermore, unsupervised clustering on the low-dimensional data proved effective at further splitting the motifs into structural subfamilies characterized by very fine and physically relevant differences such as the presence of specific punctual or planar defects or of atoms with particular coordination features. Owing to these peculiarities, the chart also enabled tracking of the complex structural evolution in a reactive trajectory. In addition to visualization and analysis of complex structural landscapes, the presented approach offers a general, low-dimensional set of differentiable variables that has the potential to be used for exploration and enhanced sampling purposes.

High-amplitude network co-fluctuations linked to variation in hormone concentrations over the menstrual cycle.

Many studies have shown that the human endocrine system modulates brain function, reporting associations between fluctuations in hormone concentrations and brain connectivity. However, how hormonal fluctuations impact fast changes in brain network organization over short timescales remains unknown. Here, we leverage a recently proposed framework for modeling co-fluctuations between the activity of pairs of brain regions at a framewise timescale. In previous studies we showed that time points corresponding to high-amplitude co-fluctuations disproportionately contributed to the time-averaged functional connectivity pattern and that these co-fluctuation patterns could be clustered into a low-dimensional set of recurring "states." Here, we assessed the relationship between these network states and quotidian variation in hormone concentrations. Specifically, we were interested in whether the frequency with which network states occurred was related to hormone concentration. We addressed this question using a dense-sampling dataset (N = 1 brain). In this dataset, a single individual was sampled over the course of two endocrine states: a natural menstrual cycle and while the subject underwent selective progesterone suppression via oral hormonal contraceptives. During each cycle, the subject underwent 30 daily resting-state fMRI scans and blood draws. Our analysis of the imaging data revealed two repeating network states. We found that the frequency with which state 1 occurred in scan sessions was significantly correlated with follicle-stimulating and luteinizing hormone concentrations. We also constructed representative networks for each scan session using only "event frames"-those time points when an event was determined to have occurred. We found that the weights of specific subsets of functional connections were robustly correlated with fluctuations in the concentration of not only luteinizing and follicle-stimulating hormones, but also progesterone and estradiol.

Nonlinear model order reduction of resonant piezoelectric micro-actuators: An invariant manifold approach

This paper presents a novel derivation of the direct parametrisation method for invariant manifolds able to build simulation-free reduced-order models for nonlinear piezoelectric structures, with a particular emphasis on applications to Micro Electro Mechanical Systems. The constitutive model adopted accounts for the hysteretic and electrostrictive response of the piezoelectric material by resorting to the Landau-Devonshire theory of ferroelectrics. Results are validated with full-order simulations operated with a harmonic balance finite element method to highlight the reliability of the proposed reduction procedure. Numerical results show a remarkable gain in terms of computing time as a result of the dimensionality reduction process over low dimensional invariant sets. Results are also compared with experimental data to highlight the remarkable benefits of the proposed model order reduction technique.

Evidence of synergy coordination patterns of upper-limb motor control in stroke patients with mild and moderate impairment.

Objectives: Previous studies showed that the central nervous system (CNS) controls movements by recruiting a low-dimensional set of modules, usually referred to as muscle synergies. Stroke alters the structure and recruitment patterns of muscle synergies, leading to abnormal motor performances. Some studies have shown that muscle synergies can be used as biomarkers for assessing motor function. However, coordination patterns of muscle synergies in post-stroke patients need more investigation to characterize how they are modified in functional movements. Methods: Thirteen mild-to-moderate stroke patients and twenty age-matched healthy subjects were recruited to perform two upper-limb movements, hand-to-mouth movement and reaching movement. Muscle synergies were extracted with nonnegative matrix factorization. We identified a set of reference synergies (i.e., averaged across healthy subjects) and typical synergies (i.e., averaged across stroke subjects) from the healthy group and stroke group respectively, and extracted affected synergies from each patient. Synergy similarity between groups was computed and analyzed. Synergy reconstruction analysis was performed to verify synergy coordination patterns in post-stroke patients. Results: On average, three synergies were extracted from both the healthy and stroke groups, while the mild impairment group had a significantly higher number of synergies than the healthy group. The similarity analysis showed that synergy structure was more consistent in the healthy group, and stroke instead altered synergy structure and induced more variability. Synergy reconstruction analysis at group and individual levels showed that muscle synergies of patients often showed a combination of healthy reference synergies in the analyzed movements. Finally, this study associated four synergy coordination patterns with patients: merging (equilibrium and disequilibrium), sharing (equilibrium and disequilibrium), losing, and preservation. The preservation was mainly represented in the mild impairment group, and the moderate impairment group showed more merging and sharing. Conclusion: This study concludes that stroke shows more synergy variability compared to the healthy group and the alterations of muscle synergies can be described as a combination of reference synergies by four synergy coordination patterns. These findings deepen the understanding of the underlying neurophysiological mechanisms and possible motor control strategies adopted by the CNS in post-stroke patients.

Variable selection in linear regression models: Choosing the best subset is not always the best choice.

We consider the question of variable selection in linear regressions, in the sense of identifying the correct direct predictors (those variables that have nonzero coefficients given all candidate predictors). Best subset selection (BSS) is often considered the "gold standard," with its use being restricted only by its NP-hard nature. Alternatives such as the least absolute shrinkage and selection operator (Lasso) or the Elastic net (Enet) have become methods of choice in high-dimensional settings. A recent proposal represents BSS as a mixed-integer optimization problem so that large problems have become computationally feasible. We present an extensive neutral comparison assessing the ability to select the correct direct predictors of BSS compared to forward stepwise selection (FSS), Lasso, and Enet. The simulation considers a range of settings that are challenging regarding dimensionality (number of observations and variables), signal-to-noise ratios, and correlations between predictors. As fair measure of performance, we primarily used the best possible F1-score for each method, and results were confirmed by alternative performance measures and practical criteria for choosing the tuning parameters and subset sizes. Surprisingly, it was only in settings where the signal-to-noise ratio was high and the variables were uncorrelated that BSS reliably outperformed the other methods, even in low-dimensional settings. Furthermore, FSS performed almost identically to BSS. Our results shed new light on the usual presumption of BSS being, in principle, the best choice for selecting the correct direct predictors. Especially for correlated variables, alternatives like Enet are faster and appear to perform better in practicalsettings.

A LINEAR-PROGRAMMING PORTFOLIO OPTIMIZER TO MEAN–VARIANCE OPTIMIZATION

In the Markowitz mean–variance portfolio optimization problem, the estimation of the inverse covariance matrix is not trivial and can even be intractable, especially when the dimension is very high. In this paper, we propose a linear-programming portfolio optimizer (LPO) to solve the Markowitz optimization problem in both low-dimensional and high-dimensional settings. Instead of directly estimating the inverse covariance matrix [Formula: see text], the LPO method estimates the portfolio weights [Formula: see text] through solving an [Formula: see text]-constrained optimization problem. Moreover, we further prove that the LPO estimator asymptotically yields the maximum expected return while preserving the risk constraint. To offer a practical insight into the LPO approach, we provide a comprehensive implementation procedure of estimating portfolio weights via the Dantzig selector with sequential optimization (DASSO) algorithm and selecting the sparsity parameter through cross-validation. Simulations on both synthetic data and empirical data from Fama–French and the Center for Research in Security Prices (CRSP) databases validate the performance of the proposed method in comparison with other existing proposals.

Artificial intelligence enabled Luong Attention and Hosmer Lemeshow Regression Window‐based attack detection in 6G

SummaryRegardless of the developments of networking and communication technologies, security is without exception a predominant feature to ensure network reliability. The future sixth‐generation (6G) network is anticipated to be carried out with artificial intelligence (AI) powered communication via machine learning (ML), post‐quantum cryptography, and so on. AI‐powered communication has been in recent years utilized in enhancing network traffic performance with respect to resource management, optimal frequency spectrum design, security, and latency. The studies of modern wireless communications and anticipated features of 6G networks revealed a prerequisite for designing a trustworthy attack detection mechanism. In this work, a method called, Luong Attention and Hosmer Lemeshow Regression Window‐based (LA‐HLRW) attack detection in 6G is proposed. Initially, with the raw Botnet Attack dataset obtained as input, preprocessing is performed to normalize network traffic features. Next, the dimensionality of network traffic feature of large‐scale network traffic data is reduced using the Luong Attention integrated with Long Short Term Memory (LSTM)‐based Feature extraction model. Finally, with the objective of classifying network traffic samples for attack detection in 6G, we analyze the low dimensional network traffic feature set produced by Luong Attention integrated with LSTM using the Hosmer Lemeshow Logistic Regression Window‐based Attack Detection model. Extensive experiments are performed with the Botnet Attack dataset to validate the efficiency of the proposed LA‐HLRW method by using different parameters such as attack detection accuracy, attack detection time, precision, and recall. The overall analysis of proposed LA‐HLRW results significantly reduced the attack detection time by 24%, and additionally improved attack detection accuracy, precision, and recall by 5%, 5%, and 6% as compared to existing attack detection methods respectively.