Rectified Linear Unit Research Articles

TanhReLU -based convolutional neural networks for MDD classification.

Major Depression Disorder (MDD), a complex mental health disorder, poses significant challenges in accurate diagnosis. In addressing the issue of gradient vanishing in the classification of MDD using current data-driven electroencephalogram (EEG) data, this study introduces a TanhReLU-based Convolutional Neural Network (CNN). By integrating the TanhReLU activation function, which combines the characteristics of the hyperbolic tangent (Tanh) and rectified linear unit (ReLU) activations, the model aims to improve performance in identifying patterns associated with MDD while alleviating the issue of model overfitting and gradient vanishing. Experimental results demonstrate promising outcomes in the task of MDD classification upon the publicly available EEG data, suggesting potential clinical applications.

Chordal measurement of phase fraction distribution in a static gas-liquid system using collimated gamma-ray densitometer and artificial neural networks

Two-phase flow occurs in various industries, as in the production of oil and gas. A collimated gamma-ray densitometer is applied for the study of a static gas-liquid system that simulates a stratified flow pattern. It stands out for its non-intrusive measurement capacity, its high sensitivity to density variations and its good spatial resolution. Chordal phase fraction distributions are obtained in a tube containing water and air at room conditions, with the water level varied between 25%, 50% and 75%. The results obtained highlight the usefulness of the collimated gamma-ray densitometer to determine phase fraction distributions along the pipe’s cross section. Furthermore, this study suggests the use of an artificial neural network (ANN) model for predicting holdup in pipeline systems using a dataset of 110 experimental data points. The ANN model considers factors such as absorbed intensity, water cut percentage, and dimensionless h/D ratio. The adopted configuration includes the use of the Adam solver, Rectified Linear Unit (ReLU) activation function, a batch size of 3, two hidden layers (60 neurons each), and a learning rate of 0.001. The model achieves good accuracy, with a minimum mean square error (MSE) of 0.3% and a low mean absolute error (MAE) of 0.028.

Stability Analysis of Feedback Systems with ReLU Nonlinearities via Semialgebraic Set Representation

This paper is concerned with the stability/instability analysis problem of feedback systems with rectified linear unit (ReLU) nonlinearities. Such feedback systems arise when we model dynamical (recurrent) neural networks (NNs) and NN-driven control systems where all the activation functions of NNs are ReLUs. In this study, we focus on the semialgebraic set representation characterizing the input-output properties of ReLUs. This allows us to employ a novel copositive multiplier in the framework of the integral quadratic constraint and, thus, to derive a new linear matrix inequality (LMI) condition for the stability analysis of the feedback systems. However, the infeasibility of this LMI does not allow us to obtain any conclusion on the system's stability due to its conservativeness. This motivates us to consider its dual LMI. By investigating the structure of the dual solution, we derive a rank condition on the dual variable certificating that the system at hand is unstable. In addition, we construct a hierarchy of dual LMIs allowing for improved instability detection. We illustrate the effectiveness of the proposed approach by several numerical examples.

Usage of Statistical Techniques to Monitor the Performance of Wind Turbines

Calculating the yearly energy output, which keeps the balance between both the generation and consumption of electricity, is made easier with the use of wind energy production estimates for grid interfaces. Effective wind speed forecasting is crucial for achieving this goal. In this research, linear statistical models of prediction Generalized Autoregressive Score (GAS), GAS model with exogenous variable x (GASX), and Autoregressive Integrated Moving Average (ARIMA) are the models used to estimate wind speed accurately. Additionally, the modeling of non-linear time-series data has been done using the Non-Linear GASX (NLGASX) statistical predictive modeling method. Additionally, the REctified Linear Unit (RELU), Softmax, Hyperbolic Tangent (TANH), and Sigmoid modeling approaches are used to optimize the suggested NLGASX model. In comparison to existing models, the suggested optimized NLGASX approach performs significantly better. In order to anticipate wind power, the wind power curve modeling additionally takes wind speed as an input. The estimated wind power has been used to determine the yearly energy

Gradient Correction for White-Box Adversarial Attacks.

Deep neural networks (DNNs) play key roles in various artificial intelligence applications such as image classification and object recognition. However, a growing number of studies have shown that there exist adversarial examples in DNNs, which are almost imperceptibly different from the original samples but can greatly change the output of DNNs. Recently, many white-box attack algorithms have been proposed, and most of the algorithms concentrate on how to make the best use of gradients per iteration to improve adversarial performance. In this article, we focus on the properties of the widely used activation function, rectified linear unit (ReLU), and find that there exist two phenomena (i.e., wrong blocking and over transmission) misguiding the calculation of gradients for ReLU during backpropagation. Both issues enlarge the difference between the predicted changes of the loss function from gradients and corresponding actual changes and misguide the optimized direction, which results in larger perturbations. Therefore, we propose a universal gradient correction adversarial example generation method, called ADV-ReLU, to enhance the performance of gradient-based white-box attack algorithms such as fast gradient signed method (FGSM), iterative FGSM (I-FGSM), momentum I-FGSM (MI-FGSM), and variance tuning MI-FGSM (VMI-FGSM). Through backpropagation, our approach calculates the gradient of the loss function with respect to the network input, maps the values to scores, and selects a part of them to update the misguided gradients. Comprehensive experimental results on ImageNet and CIFAR10 demonstrate that our ADV-ReLU can be easily integrated into many state-of-the-art gradient-based white-box attack algorithms, as well as transferred to black-box attacks, to further decrease perturbations measured in the l2 -norm.

A note about why deep learning is deep: A discontinuous approximation perspective

AbstractDeep learning has achieved unprecedented success in recent years. This approach essentially uses the composition of nonlinear functions to model the complex relationship between input features and output labels. However, a comprehensive theoretical understanding of why the hierarchical layered structure can exhibit superior expressive power is still lacking. In this paper, we provide an explanation for this phenomenon by measuring the approximation efficiency of neural networks with respect to discontinuous target functions. We focus on deep neural networks with rectified linear unit (ReLU) activation functions. We find that to achieve the same degree of approximation accuracy, the number of neurons required by a single‐hidden‐layer (SHL) network is exponentially greater than that required by a multi‐hidden‐layer (MHL) network. In practice, discontinuous points tend to contain highly valuable information (i.e., edges in image classification). We argue that this may be a very important reason accounting for the impressive performance of deep neural networks. We validate our theory in extensive experiments.

Enhanced SSD framework for detecting defects in cigarette appearance using variational Bayesian inference under limited sample conditions.

In high-speed cigarette manufacturing industries, occasional minor cosmetic cigarette defects and a scarcity of samples significantly hinder the rapid and accurate detection of defects. To tackle this challenge, we propose an enhanced single-shot multibox detector (SSD) model that uses variational Bayesian inference for improved detection of tiny defects given sporadic occurrences and limited samples. The enhanced SSD model incorporates a bounded intersection over union (BIoU) loss function to reduce sensitivity to minor deviations and uses exponential linear unit (ELU) and leaky rectified linear unit (ReLU) activation functions to mitigate vanishing gradients and neuron death in deep neural networks. Empirical results show that the enhanced SSD300 and SSD512 models increase the model's detection accuracy mean average precision (mAP) by up to 1.2% for small defects. Ablation studies further reveal that the model's mAP increases by 1.5%, which reduces the computational requirements by 5.92 GFLOPs. The model also shows improved inference in scenarios with limited samples, thus highlighting its effectiveness and applicability in high-speed, precision-oriented cigarette manufacturing industries.

Approximate Policy Iteration With Deep Minimax Average Bellman Error Minimization.

In this work, we investigate the utilization of deep approximate policy iteration (DAPI) in estimating the optimal action-value function Q* within the context of reinforcement learning, employing rectified linear unit (ReLU) ResNet as the underlying framework. The iterative process of DAPI incorporates the minimax average Bellman error minimization principle. It employs ReLU ResNet to estimate the fixed point of the Bellman equation, which is aligned with the estimated greedy policy. Through error propagation, we derive nonasymptotic error bounds between Q* and the estimated Q function induced by the output greedy policy in DAPI. To effectively control the Bellman residual error, we address both the statistical and approximation errors associated with the α -mixing dependent data derived from Markov decision processes, using the techniques of empirical process and deep approximation theory, respectively. Furthermore, we present a novel generalization bound for ReLU ResNet in the presence of dependent data, as well as an approximation bound for ReLU ResNet within the Hölder class. Notably, this approximation bound contributes to a significant improvement in the dependence on the ambient dimension, transitioning from an exponential relationship to a polynomial one. The derived nonasymptotic error bounds explicitly depend on factors such as the sample size, the ambient dimension (in polynomial terms), and the width and depth of the neural networks. Consequently, these bounds serve as valuable theoretical guidelines for appropriately setting the hyperparameters, thereby enabling the achievement of the desired convergence rate during the training process of DAPI.

Revolutionizing Breast Cancer Detection: Enhanced Mammogram Analysis with Modified Xception and Self-Attention

In the realm of precision medicine, the intersection of state-of-the-art technology and disease identification has ushered in a new era of accuracy in healthcare diagnostics. This paper reviews a groundbreaking research endeavor aiming to enhance breast cancer detection in mammograms through the synergistic application of transfer learning, architectural modifications, and advanced optimization techniques.
 At the core of this research is the concept of transfer learning, leveraging insights gained from one domain to illuminate another. The study extends this paradigm to the Xception architecture, renowned for its proficiency in discerning intricate patterns within images. However, the novelty lies in the intelligent modification of Xception to be specifically attuned to breast cancer detection. By fine-tuning the network's final layers, the model's innate ability to understand features is harmonized with the complexities of mammographic images, ensuring sensitivity to nuanced markers of potential malignancy.
 A distinctive aspect of this research is the incorporation of a self-attention mechanism, mirroring human visual processing. This mechanism dynamically highlights crucial regions within mammograms, transforming the model into an active interpreter capable of identifying subtle textures, shapes, and edges indicative of breast cancer. This adaptive approach enhances the model's finesse in navigating diverse breast cancer cases effectively.
 Throughout the training phase, optimization is pivotal for steering the research towards success. The utilization of the Adam optimizer, known for its adaptability in learning rates and moment estimations, guides the process, ensuring precise gradient descent through complex patterns. The integration of the rectified linear unit (ReLU) activation function further empowers the model to capture intricate relationships within data, enhancing its ability to identify subtle cancer markers. This review comprehensively explores the innovative strides made in breast cancer detection, shedding light on the nuanced interplay of transfer learning, architectural adjustments, self-attention mechanisms, and advanced optimization techniques. The modified Xception model emerges as a promising tool in the pursuit of accurate and sensitive breast cancer diagnostics.

Gibbs Artifacts Removal with Nonlinearity.

Gibbs artifacts, appearing as oscillations or ringing around sharp edges or boundaries, are frequently encountered in image processing. They arise when the image's frequency components are adjusted, such as in image deblurring and sharpening. Linear methods are ineffective in reducing Gibbs artifacts; nonlinear methods may be more effective. One such nonlinear method is the use of neural networks. This paper applies a simple convolutional neural network (CNN) to an image sharpening task and observes the effects of Gibbs artifacts. This network has only one convolutional layer, which consists of four channels. The well-known rectified linear unit (ReLU) is used as the nonlinear activation function. For simple one-dimensional (1D) and two-dimensional (2D), unrealistic case studies, the Gibbs artifacts are completely removed. The reason why the artifacts can be removed is explained. This simple case study illustrates the power of nonlinear functions and the use of multiple channels. In fact, this task can be achieved without using a neural network.

PREDIKSI HASIL PERTANDINGAN SEPAK BOLA LIGA PREMIER INGGRIS DENGAN ARTIFICIAL NEURAL NETWORK BACKPROPAGATION

This study aims to enhance the accuracy of predicting English Premier League football match outcomes by utilizing a partially updated Artificial Neural Network (ANN) model based on match outcome data from the period 2017 to 2021. In this research, various statistical features such as the number of goals scored in the first half and the number of shots on target were incorporated as inputs to the ANN model. The match outcome data was normalized to improve the model's performance. The ANN model employed multiple hidden layers with ReLU (Rectified Linear Unit) activation functions and was trained using the Backpropagation algorithm. Throughout the training process, the model was periodically updated to reflect changes in match patterns over time. The research findings reveal that the ANN model with partial updates can predict football match outcomes with an accuracy of 77.89% in the final iteration, with a Mean Squared Error (MSE) of 0.769 and a Mean Absolute Error (MAE) of 0.689. Additionally, the prediction results are visualized in the form of a distribution graph comparing actual match outcomes with the predictions from the final iteration, providing a visual representation of the model's performance. This study makes a significant contribution to the development of modeling techniques for forecasting football match outcomes and underscores the importance of partial updates in adapting to changes in match patterns over time, offering potential for improvements in football match analysis and prediction in the future

Nowcasting of Chili Pepper (Capsicum frutescens L.) Prices in East Java Province Using Multi-Layer Perceptron Method

The aims of study is to predict the price of chili pepper at the provincial level in East Java by looking for the best input variable from three types of input variables, price of chili pepper at the regency and city levels, natural factors, and word search index on Google Trends as an approach to the causes of chili pepper price fluctuations. The Multi-Layer Perceptron method, accompanied by a search for the best combination of model parameters is selected to get the model with the best nowcasting ability. The result shows that the best model for nowcasting is characterized by: the input variable is price of chili pepper at the regency and city levels with three hidden layers and 32, 45, and 51 neurons in each hidden layer, maximum iteration is 200 iterations, maximum iteration when the model not increase in performance for applying early stopping is 20 iterations, non-linear activation used is RELU (Rectified Linear Unit), and optimization function used is ADAM optimizer. The accuracy of nowcasting in this study is highly accurated with MAPE smaller than 10%.

A deep convolutional neural network architecture for breast mass classification using mammogram images

<p>Breast cancer is one of the second most common cancer occurring worldwide. Early identification of the disease is a major interest that promises to propose several diagnostic procedures to prevent further surgical interventions. This research paper aims to develop a breast mass classifier system using deep learning to differentiate breast mass images from normal mammographic images. The benchmark mammographic datasets CBIS-DDSM, INbreast, and mini-MIAS are used for constructing the proposed model DELU-BM-CNN. The region of interest is identified by applying image processing techniques (median filter, binarization and dilation) and the images are enhanced and sharpened using adaptive histogram equalization and unsharp masking techniques. The pre-processed images are trained with a minimum of five deep convolutional layers activated by an Exponential Linear Unit (ELU) which is developed from scratch for feature learning and classifying the given whole mammographic images. Dropout, Data normalization, and Global average pooling are some of the regularization techniques adopted to prevent the model from over-fitting. The proposed models are able to classify CBIS-DDSM images with an accuracy of 96.60%, INbreast images with 96.20% and MIAS images with 97.40%. The experimental results are also compared with conventional Rectified Linear Unit (ReLU) and Leaky ReLU activation function that promises the proposed model as a good prognosticator than the state-of-art models for cancer diagnosis using mammogram images as input.</p>

Neural networks with ReLU powers need less depth

Despite the widespread success of deep learning in various applications, neural network theory has been lagging behind. The choice of the activation function plays a critical role in the expressivity of a neural network but for reasons that are not yet fully understood. While the rectified linear unit (ReLU) is currently one of the most popular activation functions, ReLU squared has only recently been empirically shown to be pivotal in producing consistently superior results for state-of-the-art deep learning tasks (So et al., 2021). To analyze the expressivity of neural networks with ReLU powers, we employ the novel framework of Gribonval et al. (2022) based on the classical concept of approximation spaces. We consider the class of functions for which the approximation error decays at a sufficiently fast rate as network complexity, measured by the number of weights, increases. We show that when approximating sufficiently smooth functions that cannot be represented by sufficiently low-degree polynomials, networks with ReLU powers need less depth than those with ReLU. Moreover, if they have the same depth, networks with ReLU powers can have potentially faster approximation rates. Lastly, our computational experiments on approximating the Rastrigin and Ackley functions with deep neural networks showed that ReLU squared and ReLU cubed networks consistently outperform ReLU networks.

A Thermo-Structural Analysis of Die-Sinking Electrical Discharge Machining (EDM) of a Haynes-25 Super Alloy Using Deep-Learning-Based Methodologies

The most effective and cutting-edge method for achieving a 0.004 mm precision on a typical material is to employ die-sinking electrical discharge machining (EDM). The material removal rate (MRR), tool wear rate (TWR), residual stresses, and crater depth were analyzed in the current study in an effort to increase the productivity and comprehension of the die-sinking EDM process. A parametric design was employed to construct a two-dimensional model, and the accuracy of the findings was verified by comparing them to prior research. Experiments were conducted utilizing the EDM machine, and the outcomes were assessed in relation to numerical simulations of the MRR and TWR. A significant temperature disparity that arises among different sections of the workpiece may result in the formation of residual strains throughout. As a consequence, a structural model was developed in order to examine the impacts of various stress responses. The primary innovations of this paper are its parametric investigation of residual stresses and its use of Haynes 25, a workpiece material that has received limited attention despite its numerous benefits and variety of applications. In order to accurately forecast the output parameters, a deep neural network model, more precisely, a multilayer perceptron (MLP) regressor, was utilized. In order to improve the precision of the outcomes and guarantee stability during convergence, the L-BFGS solver, an adaptive learning rate, and the Rectified Linear Unit (ReLU) activation function were integrated. Extensive parametric studies allowed us to determine the connection between key inputs, including the discharge current, voltage, and spark-on time, and the output parameters, namely, the MRR, TWR, and crater depth.

Modifying Kohlrausch's Law to Describe Nonaqueous Electrolytes for Lithium-Ion Batteries.

To develop next-generation lithium-ion batteries with enhanced stability and safety, it is crucial to understand the physicochemical principles of nonaqueous electrolytes. Kohlrausch's law describes a linear decrease in the molar conductivity (Λ) with respect to the square root of the molarity of strong electrolytes at lower concentrations. This empirical law explains the impeded ionic mobility at higher concentrations due to ionic interactions, i.e., relaxation and asymmetric effects. However, this law does not hold at higher concentrations due to the ionic association that alleviates the ionic interactions and retards the decrease in the Λ. Especially, the anomalously stagnant decrease in the Λ near the solubility limit has not been clearly explained, calling for the consideration of other concentration-dependent factors such as the mean activity coefficient (γ±), viscosity (η), and dielectric constant (ε). Herein, we develop a systematic method to modify Kohlrausch's law. First, we install the ionic association constant, and the theoretical estimation is compared with the experimental results to induce the correction function that is related with the previously neglected concentration-dependent factors. Thus, the induced correction function was close to the rectified linear unit (ReLU) function, which has been widely used in the field of artificial intelligence. The modified Kohlrausch's law with the ReLU-type correction function provides a highly precise and reliable data fitting, and the fitted parameters showed clear concentration dependency and straightforward interpretability. As a result, this method effectively generalized Kohlrausch's law for nonaqueous electrolytes at higher concentrations up to the solubility limit of 3.0-3.5 M. Moreover, the modified Kohlrausch's law inspired us to discover the physical origins of the anomalously stagnant Λ profiles near the solubility limit; and the most relevant physical origin of the anomaly was the concentration dependency of the γ± and η, which grow exponentially above a critical concentration.

A Multi-Input Convolutional Neural Networks Model for Earthquake Precursor Detection Based on Ionospheric Total Electron Content

Earthquakes occur all around the world, causing varying degrees of damage and destruction. Earthquakes are by their very nature a sudden phenomenon and predicting them with a precise time range is difficult. Some phenomena may be indicators of physical conditions favorable for large earthquakes (e.g., the ionospheric Total Electron Content (TEC)). The TEC is an important parameter used to detect pre-earthquake changes by measuring ionospheric disturbances and space weather indices, such as the global geomagnetic index (Kp), the storm duration distribution (Dst), the sunspot number (R), the geomagnetic storm index (Ap-index), the solar wind speed (Vsw), and the solar activity index (F10.7), have also been used to detect pre-earthquake ionospheric changes. In this study, the feasibility of the 6th-day earthquake prediction by the deep neural network technique using the previous five consecutive days is investigated. For this purpose, a two-staged approach is developed. In the first stage, various preprocessing steps, namely TEC signal improvement and time-frequency representation-based TEC image construction, are performed. In the second stage, a multi-input convolutional neural network (CNN) model is designed and trained in an end-to-end fashion. This multi-input CNN model has a total of six inputs, and five of the inputs are designed as 2D and the sixth is a 1D vector. The 2D inputs to the multi-input CNN model are TEC images and the vector input is concatenated space weather indices. The network branches with the 2D inputs contain convolution, batch normalization, and Rectified Linear Unit (ReLU) activation layers, and the branch with the 1D input contains a ReLU activation layer. The ReLU activation outputs of all the branches are flattened and then concatenated. And the classification is performed via fully connected, softmax, and classification layers, respectively. In the experimental work, earthquakes with a magnitude of Mw5.0 and above that occurred in Turkey between 2012 and 2019 are used as the dataset. The TEC data were recorded by the Turkey National Permanent GNSS Network-Active (TNPGN-Active) Global Navigation Satellite System (GNSS) stations. The TEC data five days before the earthquake were marked as “precursor days” and the TEC data five days after the earthquake were marked as “normal days”. In total, 75% of the dataset is used to train the proposed method and 25% of the dataset is used for testing. The classification accuracy, sensitivity, specificity, and F1-score values are obtained for performance evaluations. The results are promising, and an 89.31% classification accuracy is obtained.

MAGNETIC RESONANCE IMAGE DENOIZING USING A DUAL-CHANNEL DISCRIMINATIVE DENOIZING NETWORK

Magnetic Resonance Imaging (MRI) provides detailed information about soft tissues, which is essential for disease analysis. However, the presence of Rician noise in MR images introduces uncertainties that challenge medical practitioners during analysis. The objective of our research paper is to introduce an innovative dual-channel deep learning (DL) model designed to effectively denoize MR images. The methodology of this model integrates two distinct pathways, each equipped with unique normalization and activation techniques, facilitating the creation of a wide range of image features. Specifically, we employ Group Normalization in combination with Parametric Rectified Linear Units (PRELU) and Local Response Normalizations (LRN) alongside Scaled Exponential Linear Units (SELU) within both channels of our denoizing network. The outcomes of our proposed network exhibit clinical relevance, empowering medical professionals to conduct more efficient disease analysis. When evaluated by experienced radiologists, our results were deemed satisfactory. The network achieved a noteworthy improvement in performance metrics without requiring retraining. Specifically, there was a (6.65 ± 0.03)% enhancement in Peak Signal-to-Noise Ratio (PSNR) values and a (3.9 ± 0.02)% improvement in Structural Similarity Index (SSIM) values. Furthermore, when evaluated on the dataset on which the network was initially trained, the increase in PSNR and SSIM values was even more pronounced, with a (7.5 ± 0.02)% improvement in PSNR and a (4.3 ± 0.01)% enhancement in SSIM. Evaluation metrics, such as SSIM and PSNR, demonstrated a notable enhancement in the results obtained using our network. The statistical significance of our findings is evident, with p-values consistently less than 0.05 (p < 0.05). Importantly, our network demonstrates exceptional generalizability, as it performs remarkably well on different datasets without the need for retraining.

Application of Machine Learning in Estimating Milk Yield According to the Phenotypic and Pedigree Data of Holstein-Friesian Cattle in Serbia

Summary This paper presents a deep neural network (DNN) approach designed to estimate the milk yield of Holstein-Friesian cattle. The DNN comprised stacked dense (fully connected) layers, each hidden layer followed by a dropout layer. Various configurations of the DNN were tested, incorporating 2 and 3 hidden layers containing 8 to 54 neurons. The experiment involved testing the DNN with different activation functions such as the sigmoid, tanh, and rectified linear unit (ReLU). The dropout rates ranging from 0 to 0.3 were employed, with the output layer using a linear activation function. The DNN models were trained using the Adam, SGD, and RMSprop optimizers, with the root mean square error serving as the loss metric. The training dataset comprised information from a unique database containing records of dairy cows in the Republic of Serbia, totaling 3,406 cows. The input parameters (a total of 27) for the DNN included breeding and milk yield data from the cow’s mother, as well as the father’s ID, whereas the output parameters (a total of 8) consisted of milk yield parameters (a total of 3) and breeding parameters of the cow (a total of 5). Training iterations were conducted using a batch size of 8 over 500, 1000, and 5000 epochs.

Understanding Deep MIMO Detection

Incorporating deep learning (DL) into multiple-input multiple-output (MIMO) detection has been deemed as a promising technique for future wireless communications. However, most of the DL-based MIMO detection algorithms are lack of interpretation on internal mechanisms. In this paper, we analyze the performance of the DL-based MIMO detection to better understand its strengths and weaknesses. We investigate and compare two different models: data-driven DL detector with neural networks activated by rectifier linear unit (ReLU) function and model-driven DL detector based on traditional detection algorithms. We show that the data-driven DL detector asymptotically approaches to the maximum a posterior (MAP) detector in various scenarios but requires a large amount of training samples to converge in time-varying channels. On the other hand, the model-driven DL detector utilizes the expert knowledge to alleviate the impact of channels and achieves relatively high detection accuracy with a small set of training data. Simulation results confirm our analytical results and demonstrate the effectiveness of the DL-based MIMO detection for both linear and nonlinear signal systems.