The EEG data for this study were obtained from a local hospital. The GAD group consisted of 80 patients diagnosed with GAD, and the HC group included 39 HC. Patients with GAD were diagnosed by psychiatric experts using structured clinical interviews according to the Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition (DSM-5) criteria, and anxiety severity was assessed using the HAM-A. The HAM-A consists of 14 items, each scored on a 0–4 ordinal scale, yielding a total score ranging from 0 to 56; higher scores indicate greater anxiety severity. In this study, the HAM-A total score was used as the reference standard for model training and evaluation. HC scores were retained as observed labels and included to represent the lower end of the continuous severity spectrum, without additional near-zero remapping. Detailed demographic information is presented in Table 1. As shown, there were no significant differences in age or sex between the two groups (age: p = 0.06; sex: p = 0.87), whereas the HAM-A scores showed a significant difference between the two groups (p = 1.14 × 10⁻²⁴). To ensure data accuracy and reliability, all participants were required to meet specific inclusion criteria. First, all participants with GAD were first-time clinic visitors and had not taken any medications at the time of EEG acquisition. Furthermore, any participant with a current of using psychoactive medications (including but not limited to benzodiazepines, antidepressants, antipsychotics, or stimulants) was excluded. Second, all participants were right-handed, and individuals with epilepsy, neurodegenerative diseases, stroke, schizophrenia, or other psychiatric disorders were excluded. Additionally, participants with severe cardiopulmonary dysfunction, significant hepatic or renal impairment, malignant tumors, or autoimmune diseases were not eligible. These conditions and their treatments may influence cerebral oxygenation, metabolic status, inflammatory status, and neurophysiological activity, thereby potentially altering EEG rhythms and FC. To minimize potential confounding factors, participants were instructed to maintain adequate sleep the night before data collection and to refrain from smoking, as well as from consuming coffee or strong tea, within 8 hours prior to testing. Furthermore, individuals with a history of substance or alcohol abuse were excluded from the study. Lastly, participants were required to have no prior history of brain injury. This study was approved by the Ethics Committee of Zhejiang Normal University. Written informed consent was obtained from all participants prior to their involvement in the study.

All EEG recordings were conducted in a specialized EEG acquisition room within the hospital to ensure a high-quality and standardized data collection process. Participants were instructed to stay awake, keep their eyes closed, and remain relaxed during each session, which lasted 10 min to record resting-state EEG signals. EEG data were acquired using a Nicolet EEG TS215605 system, with electrodes placed according to the international 10–20 system. A total of 16 electrodes were selected, specifically FP1, FP2, F3, F4, C3, C4, P3, P4, O1, O2, F7, F8, T3, T4, T5, and T6, with bilateral mastoids serving as reference electrodes. To ensure signal precision, the sampling rate was set to 250 Hz, allowing for the capture of subtle variations in EEG signals. Furthermore, electrode impedance was maintained below 5 kΩ to minimize signal interference and enhance data reliability.

The acquired EEG data underwent a series of preprocessing steps to ensure data quality and reliability: (1) Downsampling and Filtering: The raw EEG data were downsampled to 125 Hz and processed using a fourth-order Butterworth bandpass filter, restricting the frequency range to 4–30 Hz to remove unwanted low- and high-frequency noise. (2) Fast independent component analysis was employed to effectively remove artifacts, including eye blinks, electrocardiographic interference, and electromyographic noise, ensuring the extraction of clean EEG signals reflective of genuine neural activity. (3) Segmentation: The continuous EEG recordings were segmented into shorter epochs to capture distinct neural activity patterns and facilitate subsequent feature extraction. (4) Frequency Band Extraction: EEG signals were decomposed into distinct frequency bands to analyze different neural oscillations, including theta (4–8 Hz), alpha1 (8–10 Hz), alpha2 (10–13 Hz), and beta (13–30 Hz) rhythms. These preprocessing steps ensured that the EEG data were clean, reliable, and suitable for further analysis and research.

In this study, PLI was extracted as a key feature for the quantitative assessment of anxiety severity in GAD patients. Compared to other time-domain and nonlinear features, PLI was considered more reliable in terms of stability. Time-domain features may exhibit fluctuations across different time points, leading to inconsistencies. Nonlinear features are highly susceptible to signal noise, affecting their robustness. PLI has been widely recognized for its advantages in assessing FC in brain networks (37, 38). Unlike time-domain features that can fluctuate with time and nonlinear features that are sensitive to noise, PLI focuses on the phase relationship between signals, which is more stable and reliable for quantifying synchronization between different brain regions (39). The utilization of PLI features helps minimize instability-related noise, thus enabling a more accurate representation of EEG activity.

Given two preprocessed EEG signals, x1(t) and x2(t), the instantaneous phase information is first obtained using the Hilbert Transform, as shown in Equation 1:

Here, j  represents the imaginary unit, and P.V.  denotes the Cauchy principal value. At each time point t, PLI can be used to assess the phase synchronization between  Φ1(t)  and  Φ2(t)  by computing the phase difference. The phase difference is calculated as shown in Equation 2:

Here, arg  denotes the phase angle of a complex number. Subsequently, the signum function of the phase difference is defined as shown in Equation 3:

Finally, the PLI is defined as shown in Equation 4:

Here, |·| denotes the mean operation, while  〈·〉 represents the absolute value. The PLI value ranges from 0 to 1, indicating the degree of phase synchronization between brain regions. A PLI value close to 0 suggests an absence of phase synchronization, whereas a value approaching 1 indicates strong phase synchronization.

In this study, four frequency bands were analyzed: theta (4–8 Hz), alpha1 (8–10 Hz), alpha2 (10–13 Hz), and beta (13–30 Hz). For each frequency band, PLI was calculated for all possible electrode pair combinations, yielding N × (N - 1)/2 features, where N = 16 in this study. Consequently, a total of  4×120=480 features were extracted across the four frequency bands.

This section introduces the Conv_gMLP model, an innovative approach proposed for predicting the severity of GAD. The inspiration for Conv_gMLP originates from the gMLP module, which has demonstrated strong performance in image and natural language processing tasks (40). Given its frequent application in tabular data tasks, it is commonly referred to as tab_gMLP. In this study, the gMLP architecture is refined and extended to create the Conv_gMLP model. This novel gMLP model uses PLI features derived from quantitative EEG analysis as input. The Conv_gMLP model consists of three key components: channel expansion convolution module, the gMLP module, and feature aggregation. As illustrated in Figure 1, the Conv_gMLP Model architecture is constructed by stacking N identical gMLP blocks of the same structure and size. All projection operations within the model are linear, where ⊗ represents element-wise multiplication (linear gating) and ⊕ denotes element-wise addition (residual connection). Additionally, ablation experiments were conducted on different gMLP model architectures to evaluate the effectiveness of Conv_gMLP in predicting GAD severity.

To compare the performance of the Conv_gMLP model, several ML and DL models were selected for this regression task. For all models, the n×480 PLI features were used as input. For n samples, each containing 480 PLI features, 80% of the data was used for training, and 20% was used for testing. The predictions were compared to the true values using the HAM-A score, and the MAE was calculated to assess the performance.

ML and DL models contain numerous hyperparameters, and different combinations of these parameters yield varying training outcomes. Since hyperparameter selection significantly impacts model performance and generalization ability, optimizing these parameters helps mitigate the risks of overfitting or underfitting, thereby enhancing predictive accuracy and robustness. This study employ ed the Tree-structured Parzen Estimator (TPE) algorithm to search for the optimal hyperparameter configuration and improve model performance. Compared with traditional grid search or random search methods, TPE leverages historical data to accelerate the optimization process, offering lower time complexity and efficiently identifying superior hyperparameter sets in less time.

The TPE algorithm, implemented in the Hyperopt Python library, is a powerful method for hyperparameter optimization, comprising three key steps to ensure an effective and practical process. First, defining the objective function is fundamental to the TPE algorithm. The optimization target in this study is the MAE between the model’s predictions on the test set and the ground truth. Second, defining the hyperparameter search space is crucial. The hyperparameter search space used in this study is detailed in Tables 3–8, with the selection of ML optimization parameters and their respective ranges based on the AutoGluon automated ML framework. Finally, setting the number of search iterations controls the optimization process, with a maximum of 30 iterations specified. Through the systematic integration of these three steps, the TPE algorithm efficiently explores the hyperparameter space, enhancing both the performance and generalization capability of ML and DL models.

In this study, repeated 5-fold cross-validation was employed to reduce estimation bias and improve the robustness of model evaluation. For ML models, four subsets of the data were used for training, while the remaining subset was used for testing to evaluate model performance. For DL models, 10% of the training data was further randomly selected for validation to prevent overfitting. All models underwent three rounds of repeated 5-fold cross-validation, and the final results were obtained by averaging the performance across all test sets. Model performance was assessed using the MAE, where a lower MAE indicates better model performance. The calculation formula is provided in Equation 11:

Model interpretability has long been a critical research focus in the fields of artificial intelligence and ML. In this study, Gradient-weighted Regression Activation Mapping (Grad-RAM) is utilized to interpret the decision-making process of DL models. Grad-RAM builds upon Class Activation Mapping (CAM) and Gradient-weighted Class Activation Mapping (Grad-CAM), offering an advanced visualization technique.

CAM generates class-specific activation heatmaps by leveraging the feature maps from the last convolutional layer of a CNN with weights derived from the global average pooling layer, thereby revealing the key activation regions in the input signals. However, CAM struggles to capture detailed spatial information within feature maps. Grad-CAM addresses this limitation by incorporating gradient information to weight the heatmap, thereby improving the precision of interpretability and deepening insights into model decisions. This enables clear visualization of the regions critical to the model’s classification decisions. Consequently, Grad-CAM significantly enhances model interpretability, fostering a better understanding of DL model decision-making and increasing their reliability. Its mathematical formulation is detailed in Equations 12, 13:

Here, yc represents the score predicted by the network for class c (before applying softmax activation), Aijk denotes the data at position (ij) in channel k of the feature layer A, and Z refers to the width and height of the feature layer multiplied together.

Here, A represents a feature layer (the output of the last convolutional layer is taken in this study), k denotes the k-th channel in feature layer A, c represents the target class, Ak refers to the data in the k-th channel of feature layer A, and αkc represents the weight of the k-th channel in feature layer A for class c.

Grad-RAM is an improved version of Grad-CAM designed for the interpretability of regression tasks. For regression models, the gradient is defined as the derivative of the inverse of the prediction bias, where a smaller bias leads to a larger gradient. Specifically, LGrad-RAMe is derived from Equation 14, with the weight of each channel αke calculated using Equation 15. The probability yc in Grad-CAM is replaced by ye, which is computed from Equation 16, where ŷ is the predicted target value and y is the predicted value. LGrad-RAMe changes according to the variation in the error bias.

This study demonstrates that the Conv_gMLP model significantly outperforms other models in predicting the severity of GAD, owing to its innovative architectural design and optimized feature extraction strategy. Two key factors drive its superior performance: the optimization of the time window and the innovative structure of the Conv_gMLP model.

First, the selection of the optimal time window is critical for enhancing model performance. Previous studies have indicated that the selection of sliding time windows influences the quantification of brain network stability and detection performance, suggesting that optimizing this parameter can enhance predictive accuracy (41). Furthermore, it has been confirmed that a time window of approximately 10 s is most suitable for automatic EEG feature extraction and emotion state recognition, effectively capturing emotion-related oscillatory characteristics (42). This duration aligns with the principles of neurophysiology, as EEG signals can capture dynamic neural network activities. For instance, the beta rhythm oscillations, which are highly sensitive to anxiety levels (43), reflect the heightened brain alertness and arousal in GAD patients (44). Moreover, human emotional states, including anxiety, typically last for 10 s or longer (45). By systematically varying the sliding-window length, a 10-s epoch yielded optimal performance, with the ensemble learner attaining 98.1% accuracy for GAD-severity grading under this temporal window (24). Thus, the 10-second window effectively captures these oscillatory features, providing a biologically grounded explanation for the model’s superior performance.

Second, the Conv_gMLP architecture leverages neurobiological insights to improve GAD severity prediction. Anxiety disorders are associated with aberrant large-scale functional network patterns, characterized by enhanced connectivity between the insula and thalamus and reduced activity within the frontoparietal network—patterns that provide insight into the underlying pathophysiological changes in anxiety disorders (46). Notably, Chu et al. observed that GAD patients exhibit significantly stronger high-beta-band FC between brain regions than HC, and that this hyper-connectivity becomes more pronounced with longer illness duration (47). Functional networks are collections of brain regions with closely coordinated activity during both resting-state and cognitive tasks, each supporting distinct aspects of cognition. The Conv_gMLP model integrates quantitative EEG analysis with the gMLP framework (40), enabling precise identification of EEG activity patterns in GAD patients by extracting PLI features from EEG signals. This design reflects a deep understanding of both the data structure and the underlying neural mechanisms. In conclusion, the Conv_gMLP model successfully predicts the severity of GAD, owing to its optimized time window selection and innovative architectural design. These aspects not only enhance the model’s technical performance but also strengthen its alignment with the neurophysiological basis of anxiety. Future research should focus on refining this model and exploring its potential in clinical applications.

This study investigates the neurophysiological underpinnings of GAD severity, emphasizing the roles of brain regions, beta rhythms, and FC in characterizing the condition. Persistent excessive worry in GAD is strongly associated with structural and functional brain alterations (48), and identifying these functional changes may uncover disruptions in neural circuits and emotional regulation. Using the Grad-RAM method for feature weight analysis, this study suggests that severity-relevant features are primarily concentrated in the frontal and temporal lobes. Mechanistically, the prominence of frontal and temporal regions may reflect the involvement of large-scale networks supporting cognitive control, affective processing, and their interaction, which are broadly relevant to anxiety symptom expression. Studies indicate that the frontal cortex plays a crucial role in emotional cognition (14, 49). FC analysis further confirms aberrant prefrontal network connectivity in anxiety disorders (46) and highlights abnormalities in the temporal region of patients with GAD (25). Further studies reveal that most brain regions in GAD patients exhibit elevated correlation dimension (D2) values, particularly in the left prefrontal and right temporal lobes (50). Because correlation dimension is a nonlinear measure reflecting the complexity of EEG dynamics and information processing, such elevations in these regions may indicate altered cortical dynamics associated with greater anxiety severity. This finding further reinforces that key brain signals for assessing GAD severity primarily originate from the prefrontal and temporal lobes, consistent with our results.

Moreover, EEG rhythms encode extensive neural activity information and have been widely applied in both research and clinical assessments of GAD (51, 52). The EEG features of beta rhythms are significantly correlated with brain activity levels, with increased beta-band activity closely associated with anxiety symptoms (52, 53). Multiple studies have demonstrated that beta rhythm power is significantly elevated in GAD patients (53–55), strongly associated with brain alertness and arousal states (56), and more easily detectable under anxiety conditions (57). Mechanistically, heightened beta power may reflect persistently increased arousal and reduced network flexibility, which could make beta-band FC particularly informative for continuous severity estimation. Beta rhythm EEG features have been quantitatively utilized in GAD assessment. Recent evidence demonstrates significantly elevated beta power together with aberrant long-range fronto-temporal FC in patients relative to HC (43). This convergence may reflect stronger long-range coupling that supports sustained arousal, which could be relevant to severity estimation. Our study identifies beta rhythms as the most critical among EEG rhythm features, further confirming their value in evaluating GAD severity and providing a plausible biological basis for the observed predictive contributions.

Finally, the study suggests that EEG-based FC may serve as a valuable biomarker for distinguishing individuals with GAD (47). FC reflects the coordination and interactions among different brain regions, with alterations observable even in unconscious states. Variations in FC indicate alterations in brain region coordination and cognitive function, capturing specific traits of GAD (58). These connectivity disruptions are especially pronounced in GAD, where frontal-temporal connectivity strength is strongly associated with cognitive function. Overall, this study confirms the impact of brain regions and beta rhythms on GAD severity. It also underscores the importance of FC in brain coordination and cognition, suggesting its potential as a biomarker for assessing GAD severity.

Although this study offers new evidence supporting a novel approach to quantifying the severity of GAD, several limitations should be acknowledged. First, the sample size was relatively small, and the sex distribution was uneven. Therefore, the generalizability of the proposed EEG-based severity estimation framework across sexes should be interpreted cautiously. Future studies should aim to increase the number of participants and ensure balanced sample sizes across groups. Second, the HAM-A was used as the reference standard for quantifying GAD severity. However, because the HAM-A is a clinician-rated and ordinal measurement instrument, it is subject to measurement variability, which may partly manifest as label noise in the model training data. Accordingly, the model’s prediction error reflects not only the potential gap between EEG-derived neurophysiological features and symptom severity, but also the intrinsic uncertainty of the clinical reference standard itself. Conceptually, our model learned a mapping between EEG features and the contemporaneous clinical consensus on severity. Future work should integrate multimodal assessments and longitudinal outcomes to establish a more robust composite standard, thereby further improving the validity and clinical applicability of objective severity evaluation. Third, the cross-sectional design limits the ability to evaluate the model’s performance in longitudinal monitoring or in predicting treatment responses. Prospective studies with repeated EEG measurements over time are necessary to determine the model’s utility in tracking disease progression. Finally, the current model was trained using data from a single clinical center, which may introduce regional bias and restrict its generalizability. Future research should prioritize multicenter validation to ensure the model’s robustness across diverse populations and healthcare settings.