Forewarned Is Forearmed: The Single- and Dual-Brain Mechanisms in Detectors from Dyads of Varying Social Distance during Deceptive Outcome Evaluation

Statistical analysis: group homogeneity and manipulation checks

Participants whose ratings of context realism for both gain and loss contexts were below 5 (on a 9 Likert scale, ranging from 1 to 9) were excluded to ensure task engagement. Subsequently, we tested for baseline equivalence across social distance dyads (friend vs stranger) on key demographic and individual difference variables, including age, gender, academic year, monthly disposable income, and detector scores on the SVS and HAS scales. Group matching was confirmed across demographics and trait scales using χ² and t tests. Friend dyads were defined as 6–18 months of acquaintance with closeness ratings between 3 and 5 (Zhang et al., 2025).

Statistical analysis: behavioral data

In this study, senders were free to decide whether to deceive, resulting in two behavioral types: honesty and deception. If the detector's final decision resulted in greater gain (or less loss) for the sender, the deception was considered successful (successful deception). Conversely, if the detector's decision led to greater gain (or reduced loss) for themselves, the deception attempt was considered unsuccessful (failed deception).

We computed three primary behavioral indices: (1) honesty rate—the proportion of trials in which the sender provided truthful information favorable to the detector. To avoid potential biases in subsequent comparisons and INS calculations due to the limited number of deception trials, dyads with honesty rates above 85% were excluded from the analysis (Chen et al., 2020). (2) Deception rate—the proportion of trials in which the sender provided information that was disadvantageous to the detector across the entire experiment. (3) Successful deception rate—the proportion of deceptive trials in which the detector ended up with a lower gain or greater loss. A two-way mixed ANOVA with Bonferroni’s correction was used. The significance threshold was set at p < 0.05. Effect sizes were reported using partial eta squared (ηp2) .

Statistical analysis: fNIRS data analysis

Neural data were analyzed using the same statistical procedures described above, Statistical analysis: behavioral data, except that multiple comparisons were corrected using the false discovery rate (FDR) method (Benjamini and Hochberg, 1995). Results were visualized via BrainNet Viewer (Xia et al., 2013). Additionally, since this study focuses primarily on analyzing the neural response patterns of the detector during deception evaluation, the neural analysis concentrates mainly on trials where the sender chooses to deceive.

Preprocessing. fNIRS data were preprocessed using the Homer2 toolbox in MATLAB. Low-quality channels were removed using enPruneChannels. Dyads with >50% bad channels were excluded (Zhao et al., 2023). Principal component analysis (PCA) was applied to extract task-related signals and reduce systemic noise, including motion artifacts and global physiological oscillations (Pan et al., 2017). A fifth-order Butterworth bandpass filter (0.01–0.5 Hz) was applied for temporal and frequency-domain preprocessing. Optical density (OD) signals were converted into concentrations of oxygenated (HbO) and deoxygenated hemoglobin (HbR) using the modified Beer–Lambert law (Strangman et al., 2002). Given the higher signal-to-noise ratio of HbO, only HbO signals were analyzed in the present study.

Intrabrain function connectivity. To comprehensively elucidate the neural mechanisms underlying interpersonal deception, it is essential to investigate both the intraindividual cognitive processing and the interindividual synchronization patterns. Accordingly, this study employed WTC to construct an analytical framework capable of assessing both intrabrain FC (within the detector's key regions) and INS between dyad members.

WTC was applied to calculate pairwise coherence between all channels within the same probe, thereby assessing intrahemispheric FC within the PFC (Grinsted et al., 2004). To isolate task-related neural dynamics and exclude noncognitive interference, we compared the coherence values during the resting state and task state to identify the task-relevant frequency range (Grinsted et al., 2004). The mean WTC value within this frequency band during successful deception trials was computed and used as the FC index between channel pairs (Fig. 6A). The WTC method offers a temporal resolution of 0.1 s and a frequency resolution of ∼0.01 Hz. All WTC computations were performed using the MATLAB toolbox (available at http://noc.ac.uk/using-science/crosswavelet-wavelet-coherence).

INS: task-level. INS between dyad members was estimated using the WTC method, which is consistent with our approach to computing FC. The WTC is defined as follows:WTC(t,s)=|⟨s−1Wij(t,s)⟩|2|⟨s−1Wi(t,s)⟩|2|⟨s−1Wj(t,s)⟩|2. To identify the task-relevant frequency band, we employed a data-driven approach by comparing INS values across the full 0.01–0.5 Hz frequency range between the statement (task) and resting phases (Zhao et al., 2023). After FDR correction, the 0.024–0.040 Hz band showed significantly higher synchrony during the task phase and was therefore selected as the frequency of interest (see Fig. 7A). The resulting interbrain synchrony time series were Fisher Z-transformed, and INS change (ΔINS = INS_Task−INS_Rest) was calculated during the successful deception phase.

INS validity testing. To verify that the observed increase in INS was attributable to true interpersonal interaction rather than shared task structure or data characteristics, we conducted a permutation test involving 1,000 iterations (Frossard and Renaud, 2021). In each iteration, dyad pairings were randomly shuffled and INS recomputed. The resulting values were submitted to the same two-way mixed ANOVA, and FDR-corrected p values were compared with those from the original dyads to assess the robustness of task-specific neural synchrony.

Trial-level △INS prediction of deception outcomes. To systematically investigate the dynamic predictive ability of INS in the deceptive information evaluation process, this study calculates INS for each trial based on fNIRS signals. It predicts the outcome of deception behavior in the current trial. Given that near-infrared signals are highly susceptible to noise at the single-trial level, we adapted the methods developed by Klein and Kranczioch (2019) to improve signal quality and ensure the stable extraction of INS features. This adaptation includes (1) applying a bandpass filter (0.01–0.1 Hz) to the raw OD signals to retain task-relevant low–frequency neural oscillations and filter out high-frequency physiological noise, (2) using the wavelet minimum description length (wavelet-MDL) algorithm to correct for motion artifacts, and (3) applying drift correction based on the baseline segment (5 s before stimulus) for each trial. Additionally, to further eliminate systematic errors, we employed the global component removal method to remove cross-channel covarying systematic components. After preprocessing, fNIRS data were segmented according to time markers, and the signal during the verbal interaction phase (1–15 s) of each trial was extracted for subsequent INS calculations.

Previous studies have indicated that trial-level data exhibit substantial variability (Brigadoi and Cooper, 2015; Pfeifer et al., 2018). Therefore, we selected channels that showed significant enhancement in interpersonal synchrony for analysis, aiming to improve the stability and explanatory validity of trial-level analyses. Trial-level INS was computed using the same WTC method as in the task-level analysis, with ΔINS extracted separately for each successful and failed deception trial. To control the risk of overfitting due to redundant features, the trial-level INS features were first Fisher Z-transformed and then reduced in dimensionality using PCA, retaining principal components that explained >85% of the cumulative variance for modeling (van Aert, 2023).

During the model construction phase, the deception outcome of each trial (binary, successful deception 0, failed deception 1) was treated as the dependent variable. At the same time, the trial-level △INS feature vectors served as the independent variables. Classification models were built to predict the trial-level deception outcomes. Given that the focus of this study is the real-time predictive function of trial-level INS in interpersonal interactions, we initially selected logistic regression as the primary modeling approach. This method aims to assess the linear predictive ability of △INS features for the success or failure of deception and provides a more interpretable baseline model. Additionally, to examine whether there is a nonlinear relationship between trial-level △INS and current deception outcomes, we conducted a comparative analysis using SVM models. All models were trained and tested using the leave-one-subject-out cross-validation strategy to ensure robust cross-subject generalization of the prediction results (Xu and Huang, 2012). Model performance was primarily evaluated using three metrics: (1) accuracy, which measures the overall proportion of correct predictions; (2) area under the receiver operating characteristic curve (ROC–AUC), which evaluates the model's ability to distinguish between successful and failed deception trials; (3) F₁ score, which reflects the model's balance between precision and recall in successful deception trials. Additionally, to test whether the model's performance was significantly better than chance, a permutation test with 1,000 label shuffles was conducted.

Trial-level △INS time-series process analysis. To further explore the dynamic process characteristics of attitude or behavior changes during the evaluation of deceptive information, we conducted a time-series process analysis of trial-level △INS for both successful and failed deception. The method used for trial-level △INS computation is consistent with previous research (Jiang et al., 2015). △INS was computed separately for successful and failed deception trials under different conditions, with each condition containing coherence values from 15 time points. Subsequently, paired-sample t tests were applied to the △INS at each time point, yielding a series of p values (15 in total). These p values were then subjected to multiple testing correction using the FDR method.

Statistical analysis: brain–behavior correlation

Two-tailed Pearson's correlation analyses were conducted to examine the relationship between ΔINS during deception and the behavior outcome. Specifically, correlations were calculated separately for conditions of successful deception and failed deception, allowing for a more nuanced evaluation of the predictive value of INS under different outcome contexts.

Statistical analysis: regression analysis

Multiple regression analysis. To investigate whether neural indicators predict detectors’ outcomes of deceptive information evaluation—whether deception succeeds—and to isolate the contribution of Interpersonal perspective (△INS) to this predictive power, we performed multiple regression analyses. At the intrabrain level, the dependent variable was the successful deception rate, and the independent variables were the WTC-FC from three predefined regions of interest (ROIs) in the detector's brain during successful deceptive trials. At the interbrain level, the same dependent variable was regressed on two ΔINS indices that showed significant differences during the successful deception phase. This approach allowed us to evaluate the distinct contribution of INS beyond individual-level neural dynamics.

Hierarchical linear regression. To evaluate whether INS offers superior predictive power relative to demographic and subjective self-report variables, we conducted a hierarchical linear regression analysis. This method assessed whether dyadic ΔINS in the DLPFC and OFC could significantly enhance the model's ability to predict deception outcomes beyond other known factors. Predictors were entered in blocks: in Step 1, demographic variables (e.g., gender, education background) were entered; in Step 2, subjective self-report measures were entered into the model, including perceived Intimacy (rang of 1–7), SVS scores, and HAS scores; finally, Step 3–4 introduced the ΔINS variables, first from failed deception phase and then for successful deception phase. Model fit improvements were examined at each stage to determine whether INS provided incremental explanatory power over and above demographic and subjective factors, thus confirming its unique predictive value.

ML model-based evaluation of INS for predicting successful deception

To comprehensively reveal the relationship between brain and behavior, this study employed both trial-level and task-level INS measures in the preliminary analysis. At the trial level, we examined whether the fluctuations in INS during each interaction were associated with the outcome of deception in that trial, aiming to reveal the immediate predictive value of INS. However, since trial-level signals are influenced by various factors such as individual state fluctuations and dynamic interaction changes, they tend to have lower signal-to-noise ratios and less stable correlations (Brigadoi and Cooper, 2015). Additionally, due to the larger number of features, these signals are more prone to model overfitting, limiting their generalizability in predictive modeling. In contrast, task-level INS features are averaged across multiple trials, providing higher stability and statistical robustness (Dale and Buckner, 1997; Tanaka, 2020), and better reflecting the overall neural coordination pattern of the detector under specific social distance and gain/loss conditions. Therefore, in the prediction modeling phase, we selected task-level INS measures as input variables to enhance the generalizability and practical applicability of behavioral predictions.

We implemented a data-driven ML approach to predict the probability of detectors being deceived under varying conditions. Independent predictive models were constructed for each of the four experimental conditions (friend/stranger × gain/loss), using the ΔINS from channel pairs showing significant differences during successful deception as input variables and deception success rate as the output variable. The algorithms employed included SVR, LDA, logistic regression, KNN, naive Bayes, and SVM. To enhance model generalizability and mitigate overfitting, all model hyperparameters were automatically tuned using Bayesian optimization via Optuna (rather than manual specification). Model performance was evaluated on held-out samples using leave-one-out cross-validation, whereby each sample served once as the test set and the remainder as the training set. To address class imbalance, we incorporated class weights into model training, improving sensitivity to minority outcomes. All modeling procedures were conducted in a Python 3.9 environment using Spyder 5.2.2. ML models were implemented via scikit-learn.

Hyperparameter optimization process. Hyperparameters are parameters in machine learning models that must be set before training and remain fixed during the learning process; they are not automatically learned from the training data but are manually specified by the researcher or selected through optimization methods (Wu et al., 2019). In this study, to ensure optimal predictive performance, we employed a Bayesian optimization approach based on the Optuna framework to tune the hyperparameters of the models. Bayesian optimization is a method that incrementally approaches the global optimum of a target function by constructing a surrogate model, such as a Gaussian process (Jenkins and Gerstoft, 2022; Lu et al., 2022). Within the Optuna framework, dynamic search space adjustment mechanisms and efficient sampling strategies enable the rapid identification of the best hyperparameter configurations (Almarzooq and Waheed, 2024). Specifically, we defined a reasonable candidate range within the hyperparameter search space (e.g., learning rate, regularization parameters, kernel type). Then we used Optuna's Bayesian optimization algorithm to efficiently explore potential hyperparameter combinations. By minimizing the loss function on the validation set or maximizing classification accuracy as the optimization objective, the surrogate model was iteratively updated to identify the global optimal hyperparameter configuration. Below, we detail the hyperparameter optimization process for each algorithm used in this study.

Support vector regression (SVR). In this study, SVR was implemented using the SVR module. Given the high sensitivity of SVR to hyperparameter settings, we systematically optimized several key hyperparameters, including the kernel type [e.g., linear, radial basis function (rbf), polynomial], regularization parameter C (which controls the trade-off between model complexity and training error), epsilon (ε; which defines the width of the ε-insensitive margin), and gamma (for rbf and polynomial kernels, determining the influence range of individual data points). Hyperparameter tuning was performed using a combination of grid search and fivefold cross-validation to minimize prediction error (mean squared error, MSE) and maximize model performance. The final optimal hyperparameter values are reported in Table 1.

LDA. LDA computations were performed using the LinearDiscriminantAnalysis library in this study. As LDA has relatively few tunable hyperparameters compared with more complex models, we primarily focused on optimizing the solver parameter (which determines the algorithm used for model fitting, such as “svd,” “lsqr,” or “eigen”) and the shrinkage parameter (which can be set to None, “auto,” or a float value and controls the regularization strength when using solvers that support shrinkage, such as “lsqr” or “eigen”). We determined the optimal hyperparameter configuration through grid search combined with cross-validation, aiming to maximize classification accuracy while enhancing the model's generalization ability. The final optimal hyperparameter settings for LDA are reported in Table 2.

Logistic regression. Logistic regression (Davis and Offord, 1997) computations were performed using the Logistic Regression Classifier library in this study. During model training, we optimized several key hyperparameters, including the penalty type (e.g., L1, L2, or ElasticNet, which controls model complexity and helps prevent overfitting), the regularization strength (C; the inverse of the regularization coefficient, determining the penalty applied to significant coefficients), and the solver (e.g., “liblinear,” “lbfgs,” or “saga,” which selects different optimization algorithms suited to the data size and penalty type). Hyperparameter optimization was conducted using grid search combined with fivefold cross-validation to maximize classification accuracy and F₁ score while ensuring the model's generalization capacity and stability. The final optimal hyperparameter settings are reported in Table 3.

KNN. In this study, KNN (Ertuğrul and Tagluk, 2017) computations were performed using the K-Neighbors Classifier library. During model training, we primarily optimized the number of neighbors (n_neighbors; which determines how many nearest neighbors participate in the voting process), the weights parameter (e.g., “uniform” or “distance,” which determines how neighbor votes are weighted), and the distance metric (e.g., Euclidean distance or Manhattan distance, used to compute similarity between samples). Hyperparameter optimization was conducted using grid search combined with fivefold cross-validation to maintain high classification accuracy while reducing sensitivity to noisy data and enhancing model generalization. The final optimal hyperparameter settings are reported in Table 4.

Random forest (RF). Depending on the specific prediction task, RF computations were conducted using the RandomForestClassifier and RandomForestRegressor libraries. Hyperparameter optimization focused on several key parameters: the number of trees (n_estimators; which determines the size of the ensemble), the maximum tree depth (max_depth; which controls the depth and capacity of individual decision trees), the minimum number of samples required to split an internal node (min_samples_split; which determines when a node should be further split), and the maximum number of features considered at each split (max_features; which introduces randomness and helps reduce overfitting risk). We employed randomized search combined with cross-validation to efficiently explore the hyperparameter space, aiming to achieve the best balance between predictive accuracy and generalization performance. The final optimized hyperparameter settings are reported in Table 5.

SVM. In this study, SVM (Steinwart and Christmann, 2008) were used with both linear kernels and nonlinear (rbf) kernels. Computations were performed using the Linear Support Vector Classification and SVM libraries. During model training, hyperparameter optimization focused on several key aspects: for linear kernel SVM, we primarily tuned the regularization parameter C (which controls the trade-off between model complexity and classification margin); for rbf kernel SVM, we further optimized both the kernel parameter gamma (which defines the influence range of individual data points) and the C parameter to balance accurate data fitting with the prevention of overfitting. The final optimal hyperparameter settings are reported in Table 6.

This approach has been extensively explored and refined in many prior studies, as it helps identify the optimal model and effectively reduces overfitting across models. Notably, our hyperparameter configurations align with those reported in numerous published studies (Bergstra et al., 2015; Morales-Hernández et al., 2023; Saputra et al., 2023; Sorato et al., 2024).

Model evaluation. The model evaluation metrics include accuracy, precision, recall, F₁ score, and Matthews correlation coefficient (MCC). MCC quantifies the correlation between predicted and observed labels, accounting for all values in the confusion matrix, and is particularly suitable for imbalanced classification problems, with a range from −1 (inverse prediction) to +1 (perfect prediction) and 0 indicating chance-level performance.

Model generalization verification. To assess model performance at a continuous level, we further calculated the Pearson's correlation coefficient (r) between predicted deception outcomes and actual behavioral outcomes. Statistical significance of the observed r values was tested via permutation testing using 5,000 label shuffles, generating a null distribution to assess whether the true r value exceeded the chance level (Zhang et al., 2025).

Model training overfitting/underfitting test. We plotted the learning curves of the six models under the different conditions to examine whether overfitting occurred. Our observations confirmed that none of the models exhibited overfitting.