Impact of Collective Learning Atmosphere on Student Psychological Safety: A Multi-Scale Visual Analysis via Group Behavior Segmentation and Fine-Grained Expression Recognition

The DCCG framework proposed in this paper takes the classroom surveillance video stream $I \in \mathrm{R}^{T \times H \times W \times 3}$ as input and outputs the student psychological safety score $P S \in[0,100]$ through three deeply coupled modules, where the single-frame input size is denoted as $H_0=480, W_0=640$. The design of the framework follows a progressive logic from visual parsing to semantic reasoning: Module 1 is responsible for pixel-level semantic segmentation of group behaviors. Through DSADC and a geometric boundary adversarial mechanism, the input image is mapped to a multi-channel probability map $M \in \mathrm{R}^{C_g \times H \times W}$ ($C_g=8$ behavior categories). At the same time, the spatial bounding box $B_i=\left(x_i, y_i, w_i, h_i\right)$ and head pose angles of each student $\Theta_i=\left(\right. yaw _i, pitch_i, roll_i\left.\right)$ are extracted from the segmentation results, providing precise spatial priors and pose constraints for subsequent individual-level analysis. Module 2 uses the $B_i$ and $\Theta_i$ output by Module 1 as guidance to perform pose affine normalization on each student's face region, and then extracts fine-grained expression features through a difference-driven multi-scale disentangled attention mechanism, outputting emotional coordinates $\left(V_i(t), A_i(t)\right)$, where $V_i \in[-1,1]$ is valence and $A_i \in[-1,1]$ is arousal, thus completing the scale descent from group segmentation to individual emotion. Module 3 incorporates the outputs of the first two modules into a graph learning framework, constructing a heterogeneous fully-connected graph $G=(V, \mathrm{E})$ containing group field nodes $V_g$ (corresponding to a $4 \times 4$ spatial grid, totaling 16 nodes) and individual particle nodes $V_i$. Through dual-path cross-attention message passing, bidirectional collaborative inference is achieved between the macroscopic group field and microscopic emotional particles, and finally the psychological safety score is output through a regressor. The three modules are jointly optimized during end-to-end training, and the overall loss function is:

$L_{\text {total}}=L_{\text {seg}}+L_{\text {expr}}+L_{P S}+\eta L_{\text {sparse}}$         (1)

where, $L_{\text {seg}}$ is the group segmentation loss, including Dice loss, Focal loss, and geometric boundary adversarial loss; $L_{\text {expr}}$ is the expression recognition loss, i.e., the mean squared error of valence and arousal and temporal smooth contrastive regularization; $L_{P S}$ is the Huber loss for psychological safety regression, $L_{\text {sparse}}$ is the attention sparse regularization term, and $\eta$ is the balance coefficient. The following sections elaborate on the mathematical mechanisms and engineering implementation details of the three modules in turn.

2.1 Module 1: Group behavior semantic segmentation based on dynamic receptive field decoupling and boundary adversarial learning

Group behavior semantic segmentation aims to assign behavior category labels to each pixel in classroom scenarios, while providing precise spatial priors for downstream individual analysis. This module adopts ResNet-50 as the backbone network to construct a feature pyramid, extracting four-level semantic features $C_2, C_3, C_4, C_5$, whose spatial resolutions are 1/4, 1/8, 1/16, and 1/32 of the input image, respectively. On top of this backbone structure, the module faces two core challenges: first, the scales of student faces and limbs in the classroom vary drastically from the front row to the back row, and convolution operations with fixed receptive fields are difficult to simultaneously adapt to the feature extraction requirements of distant small targets and proximal large targets; second, boundaries between adjacent students in densely seated scenarios are often blurred due to occlusion, and general segmentation losses struggle to guarantee the geometric coherence of individual masks. To address the above problems, this paper provides solutions from two aspects: dynamic receptive field modulation and boundary adversarial supervision. Figure 1 illustrates the architecture of group behavior semantic segmentation based on dynamic receptive field decoupling and boundary adversarial learning.

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Figure 1. Architecture of group behavior semantic segmentation based on dynamic receptive field decoupling and boundary adversarial learning

For DSADC, to address the limitation of fixed dilation rates in traditional dilated convolution, a spatially adaptive mechanism is introduced. Given the input feature map $F \in \mathrm{R}^{C \times H \times W}$, the gating network first generates a dilation rate offset for each spatial position $p$. The network consists of two $1 \times 1$ convolutions and a GELU activation function, and the output is normalized by Sigmoid and then mapped to an integer dilation rate:

$\Delta(p)=\left|\sigma\left(\operatorname{Conv}_{1 \times 1}\left(\operatorname{GELU}\left(\operatorname{Conv}_{1 \times 1}(F(p))\right)\right)\right) \cdot \Delta_{\max}\right|$            (2)

where, F(p) is the feature vector at position p, $\sigma(~)$ is the Sigmoid function, which normalizes the output to the interval [0,1]. Δ_max = 6 is the upper limit of the maximum dilation rate, and the rounding operation ensures that the dilation rate is an integer. Since rounding is non-differentiable in backpropagation, this module adopts the Straight-Through Estimator to maintain gradient approximation. The convolution output expression is:

$Y(p)=\sum_{k_x=-1}^{1} \sum_{k_y=-1}^{1} W\left(k_x, k_y\right) \cdot F\left(p_x+\Delta(p) k_x, p_y+\Delta(p) k_y\right)$     (3)

where, $W \in \mathrm{R}^{C_{{out}} \times C \times 3 \times 3}$ is the learnable convolution kernel weight, the convolution kernel size is fixed at $3 \times 3$, while the actual sampling positions are dynamically regulated by $\Delta(p)$, and $C_{{out}}$ is the number of output channels. To suppress feature aliasing caused by sampling point drift, spatial interpolation adopts a bilinear kernel B( ) for weighting:

$F(p+\Delta \cdot k)=\sum_q F(q) \cdot B(q-(p+\Delta \cdot k))$         (4)

where, $q$ traverses all integer coordinate positions on the feature map, $\Delta$ is the shorthand for the dilation rate offset, and B( ) is the bilinear interpolation weight function, whose input is the coordinate offset between the sampling point and the integer grid point. This mechanism enables spatial positions of back-row small targets to obtain larger dilation rates, thereby aggregating a wider range of contextual discriminative signals; front-row large targets maintain smaller dilation rates, preserving local texture details to maintain boundary precision.

Boundary adhesion is the primary quality issue of segmentation results in dense classroom scenarios. This module introduces a boundary discriminator $D_{{edge}}$ to explicitly supervise the geometric boundaries of predicted masks. Its structure consists of five convolutional layers, with channel numbers of 64, 128, 256, 512, and 1 in sequence, each followed by Instance Normalization and LeakyReLU activation. The input to the discriminator is the boundary response map of the predicted mask $B_{{pred}}=\left\|\nabla M_{{pred}}\right\|_2$ and the ground truth boundary map $B_{g t}$, where ∇ is the Sobel operator, and $M_{{pred}}$ is the hard label obtained by applying argmax to the multi-channel probability map output by the segmentation network. The adversarial loss is defined as:

$L_{G B A}=E_{B \sim B_{{gt}}}\left[\log D_{{edge}}(B)\right]+E_{B \sim B_{{pred}}}\left[\log \left(1-D_{{edge}}(B)\right)\right]$       (5)

This loss drives the segmentation network to simultaneously optimize two objectives at the decoder end: semantic classification and boundary geometric consistency. During training, the discriminator adopts R1 gradient penalty to stabilize the adversarial process:

$L_{G P}=\gamma \cdot E_{\widetilde{B} \sim \mathrm{P}_{\widetilde{B}}}\left[\left\|\nabla_{\widetilde{B}} D_{{edge}}(\widetilde{B})\right\|_2^2\right]$      (6)

where, $\widetilde{B}$ is a random interpolation point between the predicted boundary and the ground truth boundary, and $\gamma=10.0$ is the penalty coefficient. This regularization term constrains the gradient norm of the discriminator near the data manifold, thereby avoiding training oscillation.

The segmentation network outputs a multi-channel probability map $M \in \mathrm{R}^{C_g \times H \times W}$, where the number of behavior categories is $C_g=8$. Based on the segmentation results, the module extracts three types of group field features to describe the spatial structure of the collective learning atmosphere. The regional attention entropy $H_{{region}}(r)$ divides the image into a $4 \times 4$ grid, and calculates the normalized entropy value of the pixel proportions of listening and interacting categories for each grid:

$H_{{region}}(r)=-\sum_{c \in\{{listen,interact}\}} p_{r, c} \log p_{r, c}, p_{r, c}=\frac{{count}_{r, c}}{\sum_c {count}_{r, c}}$            (7)

where, $r$ is the grid index, $p_{r, c}$ is the pixel proportion of category $c$ in the $r$-th grid, and $count_{r,c}$ is the pixel count of category $c$ in that grid. This metric reflects the concentration degree of effective participation behaviors in each region. The interaction density field $\rho_{{inter}}$ generates a spatially continuous heatmap by performing Gaussian kernel density estimation on the centroids of pixels of discussion and hand-raising behaviors. The behavior distribution uniformity $U_{{behav}}$ characterizes the balance of pixel proportions of various behaviors from a global perspective:

$U_{{behav}}=1-\frac{1}{N_g} \sum_c\left(\frac{N_c}{N_{\text {total}}}-\frac{1}{C_g}\right)^2$       (8)

where, $N_c$ is the total number of pixels of behavior category $c$, $N_{{total}}$ is the sum of valid pixels, and $C_g=8$ is the total number of behavior categories. Meanwhile, the module performs instance-level parsing on each connected domain in the segmentation results, outputting the individual spatial bounding box $B_i=\left(x_i, y_i, w_i, h_i\right)$, and feeds the segmentation mask into a lightweight pose regression branch to estimate head pose angles $\Theta_i=\left(\right.yaw_i,pitch_i,roll_i\left.\right)$. This branch consists of two fully connected layers and outputs three-dimensional Euler angles. It shares backbone encoder parameters with the segmentation network, thus adding almost no extra computational cost.

The total loss function of this module integrates two objectives: semantic supervision and boundary geometric supervision:

$L_{{seg}}=L_{{Dice}}+\lambda_1 L_{{GBA}}+\lambda_2 L_{{Focal}}+\lambda_{{GP}} L_{{GP}}$       (9)

where, $L_{{Dice}}$ is the Dice loss and $L_{{Focal}}$ is the Focal loss, both jointly responsible for pixel-level semantic classification. $\lambda_1=0.5$ and $\lambda_2=1.0$ are the weight coefficients for the Geometric Boundary Adversarial (GBA) loss and Focal loss, respectively. Through the above design, the segmentation module not only provides high-precision behavior semantic maps, but also outputs necessary spatial priors and pose constraints for subsequent individual expression recognition and cross-scale collaborative inference.

2.2 Module 2: Fine-grained individual expression spatiotemporal recognition based on pose decoupling and difference-driven learning

The core difficulty of individual expression recognition lies in the small face scale, drastic pose variations, and frequent occlusions in classroom scenarios. The spatial bounding box $B_i=\left(x_i, y_i, w_i, h_i\right)$ and head pose angles $\Theta_i=\left(\right.yaw_i,pitch_i,roll_i\left.\right)$ output by Module 1 provide precise spatial localization and pose priors for this module, enabling expression feature extraction to focus on amplifying micro-expression residual signals on the basis of pose normalization. The design of this module follows a progressive logic from spatial alignment to feature decoupling and then to temporal constraints: first, pose angles are used to guide affine transformation to eliminate the interference of head deflection on texture encoding; then, common identity-related bases and emotion-related difference residuals are separated in multi-scale feature space; finally, temporal contrastive constraints are applied to utilize the continuity between video frames to suppress abnormal jitter in single-frame predictions. Figure 2 illustrates the architecture of fine-grained expression spatiotemporal recognition based on pose decoupling and difference-driven learning.

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Figure 2. Architecture of fine-grained expression spatiotemporal recognition based on pose decoupling and difference-driven learning

For the $i$-th student, the bounding box output $B_i$ by Module 1 crops the face region $R_i \in \mathrm{R}^{3 \times h_i \times w_i}$ from the original image. A rotation matrix $R\left(\Theta_i\right) \in \mathrm{R}^{2 \times 3}$ is constructed based on the head pose angles $\Theta_i$, which affine-transforms the original face image to a standard frontal pose, keeping both eyes horizontal and the bridge of the nose at the facial midline. The transformed face image is uniformly normalized to $112 \times 112$ pixels through grid sampling:

$\widetilde{R}_i={GridSample}\left(R_i, R\left(\Theta_i\right)\right), \widetilde{R}_i \in \mathrm{R}^{3 \times 112 \times 112}$      (10)

where, GridSample is a bilinear interpolation sampling function, and $R\left(\Theta_i\right)$ is composed of a rotation matrix and a translation vector, specifically calculated from the three Euler angles yaw, pitch, and roll. The core function of this spatial normalization operation is to completely strip pose variations from the mapping relationship that the network needs to learn, so that the entire parameter capacity of the subsequent feature extraction network can be used to encode texture details related to emotion, without additionally allocating parameters to cope with pose diversity. This strategy is particularly critical in classroom small-scale face scenarios: when the facial region only occupies $32 \times 32$ pixels, any parameter overhead for pose robustness will significantly weaken the model's sensitivity to subtle expression changes.

The pose-normalized face image $\widetilde{R}_i$ is fed into a lightweight feature pyramid to extract multi-scale representations. This pyramid reuses the low-level parameters of the backbone network of Module 1, but blocks the backpropagation of gradients from the segmentation task during training to avoid interference from the segmentation objective on expression features. The pyramid outputs feature maps at three scales: $F_1 \in \mathrm{R}^{256 \times 28 \times 28}$ corresponds to $1 / 4$ scale of the input image, $F_2 \in \mathrm{R}^{512 \times 14 \times 14}$ corresponds to $1 / 8$ scale, and $F_3 \in \mathrm{R}^{1024 \times 7 \times 7}$ corresponds to 1/16 scale. This paper takes $F_2$ at 1/8 scale as the consensus anchor $F_m$, which achieves the best balance between receptive field and spatial resolution, and is suitable for carrying the identity information of the face and the common base of basic expressions. The consensus feature $F_{{base}}$ is obtained by feeding $F_m$ into a channel attention module, which adopts the Squeeze-and-Excitation structure to recalibrate the channel dimension and strengthen the common response patterns that are discriminative for expression classification.

Difference feature extraction is a key link in distinguishing fine-grained emotional changes. For the large-scale branch $F_1$ and the small-scale branch $F_3$, the feature difference between each and the consensus anchor is calculated respectively. Since the number of channels at each scale is inconsistent, they are first uniformly mapped to 512 dimensions through $1 \times 1$ convolution, and then element-wise subtraction is performed:

$F_{{diff,} s}=\phi_s\left(F_s\right)^{\ominus} \psi_s\left(F_m\right), s \in\{1,3\}$          (11)

where, $\phi_s$ and $\psi_s$ are both $1 \times 1$ convolutional layers, $\ominus$ denotes element-wise subtraction, and s is the scale index. The essence of this difference operation is to filter out the identity information shared with the consensus base at each scale, and retain the residual signals inconsistent with the consensus, which exactly correspond to the subtle deformations in micro-expressions involving areas such as the corners of the mouth, the corners of the eyes, and the brow ridge. However, not all difference features at all scales are beneficial for emotion classification; differences at some scales may originate from residual errors of illumination or pose normalization. To this end, a dynamic gating mechanism is introduced to adaptively evaluate the importance of difference features through global average pooling and a two-layer Multilayer Perceptron (MLP):

$g_s=\sigma\left(M L P\left(A v g P o o l\left(F_{\text {diff,}s}\right)\right)\right) \in[0,1]^{512}$       (12)

where, AvgPool is the global average pooling operation, which compresses the spatial dimension to $1 \times 1$. The MLP structure is $512 \rightarrow 128 \rightarrow 512$, with the ReLU activation in the middle layer, and $\sigma$ is the Sigmoid function that restricts the output to $[0,1]$. Each dimension of the gating coefficient $g_s$ corresponds to a channel of the difference feature, controlling the contribution ratio of that channel in the final fusion. The final fused feature is expressed as:

$F_{\text {expr}}=F_{\text {base}}+g_1 \odot F_{\text {diff}, 1}+g_3 \odot F_{\text {diff}, 3} \in \mathrm{R}^{512}$        (13)

where, ⊙ is the Hadamard product. This fusion strategy allows the model to selectively inject differentiated emotional residuals from different scales while preserving the consensus base. Large-scale differences are responsible for capturing local texture changes, and small-scale differences are responsible for encoding global configuration shifts, and the two complement each other under the gating mechanism.

The emotional states of adjacent frames in classroom surveillance video should maintain temporal continuity, while frames separated by a farther distance should have distinguishable representations. To utilize this temporal redundancy to improve the noise resistance of single-frame recognition, this paper applies temporal smooth contrastive constraints in the feature embedding space. Let the fused feature of the t-th frame be mapped to a 128-dimensional embedding vector $z_t=\operatorname{Projector}\left(F_{\text {expr}, t}\right)$ through a projection head, which consists of a two-layer MLP. The temporal contrastive loss is defined as:

$L_{T S C}=\frac{1}{T-1} \sum_{t=1}^{T-1} \max \left(0,\left\|z_t-z_{t+1}\right\|_2^2-\left\|z_t-z_{t+K}\right\|_2^2+\delta\right)$          (14)

where, $T$ is the total number of frames in the video clip, $K=5$ is the far-frame interval, $\delta=0.5$ is the margin hyperparameter, and $\|$ $\|_2^2$ is the square of the Euclidean distance. The physical meaning of this loss function is clear: if the distance between adjacent frame features in Euclidean space minus the distance between features separated by frames plus the margin is still greater than zero, a positive loss is generated, driving the model to pull adjacent frames closer and push far frames apart; otherwise, no gradient update is produced. This design does not rely on any label information, and the supervisory signal is purely provided by the temporal structure of the video data itself. Finally, $F_{\text {expr}}$ passes through a classification head $512 \rightarrow 256 \rightarrow 2$ to output the two-dimensional emotional coordinates of the current frame $\left(V_i(t), A_i(t)\right)$, where $V_i \in[-1,1]$ is valence and $A_i \in[-1,1]$ is arousal. The total loss of the module is:

$L_{\text {expr}}=L_V+L_A+\lambda_3 L_{T S C}$       (15)

where, $L_V$ and $L_A$ are both mean squared error losses, supervising the regression of valence and arousal respectively, and $\lambda_3=0.1$ is the weight coefficient of the temporal contrastive loss.

2.3 Module 3: Psychological safety mapping based on cross-scale graph neural collaborative inference

The first two modules respectively complete the pixel-level parsing of group behaviors and the fine-grained extraction of individual expressions. However, in existing classroom analysis systems, these two are often treated as independent processing pathways. The semantic gap between them causes the quantification of the collective learning atmosphere to lack the support of individual emotional states, while the inference of psychological safety lacks the constraint of group field information. This module aims to establish a bidirectional collaborative inference mechanism between the group field and individual emotional particles, unifying macroscopic spatial distribution features and microscopic emotional temporal signals into a graph learning framework for joint inference, thereby completing the final mapping from visual appearance to psychological safety scores. Figure 3 illustrates the principle of dual-path cross-scale graph neural collaborative inference and psychological safety mapping.

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Figure 3. Dual-path cross-scale graph neural collaborative inference and psychological safety mapping

The construction of the heterogeneous fully-connected graph is the foundation of cross-scale collaborative inference. Let the graph be $G=(V, \mathrm{E})$, the node set $V=V_g \cup V_i$ contains two types of nodes. There are 16 group nodes $V_g$, corresponding to the $4 \times 4$ grid divided in the image space. The initial feature $h^{(r)}{ }_g \in \mathrm{R}^{16}$ of the $r$-th node is formed by concatenating five parts: the pixel proportion distribution of 8 behavior categories within the grid, the regional attention entropy $H_{\text {region}}(r)$, the interaction density $\rho_{\text {inter}}(r)$, the global behavior uniformity $U_{\text {behav}}$, and the historical moving average of the first 4 frames. The number $N$ of individual node $V_i$ dynamically changes with the number of students detected in the scene. The initial feature $h_{i \nu}^{(i)} \in \mathrm{R}^{14}$ of the $i$-th node includes the current frame's emotional valence $V_i(t)$ and arousal $A_i(t)$, the temporal differences $\Delta V_i$ and $\Delta A_i$ of the first 5 frames ( 5 dimensions each), and the normalized spatial coordinates $\left(x_i / H_0, y_i / W_0\right)$, where $H_0=480$ and $W_0=640$ are the height and width of the input image. The edge set E contains two types of connections: fully-connected edges between group nodes and individual nodes, realizing the cross-scale information pathway; and spatial proximity edges between individual nodes, connecting only individual pairs whose Euclidean distance is less than $15 \%$ of the image width, used to characterize local peer effects. Connections are not established between group nodes to prevent macroscopic features from over-smoothing across the grid and losing spatial heterogeneity.

Message passing on the graph adopts a dual-path cross-attention mechanism to establish bidirectional interaction between the group field and individual particles. In the top-down path, group nodes aggregate the emotional and spatial information of individual nodes to revise the understanding of the group field. For each group node r, the attention weight with all individual nodes is calculated as:

$\alpha_{r t \leftarrow i}=\operatorname{softmax}\left(\frac{\left(W_Q h_g^{(r)}\right)^{\top}\left(W_K h_i^{(i)}\right)}{\sqrt{d_k}}\right)$       (16)

where, $W_Q, W_K \in \mathrm{R}^{d_k \times d}$ are the projection matrices for the query and key, $d=128$ is the hidden dimension of node features, $d_k=128$ is the projection dimension for query and key, and the number of heads for multi-head attention is set to 4. $\alpha_{r \leftarrow i}$ is the normalized attention weight of the $r$-th group node for the $i$-th individual node, and softmax is calculated along the individual dimension. Subsequently, the group node updates its representation via a residual connection:

$h_g^{(r)} \leftarrow h_g^{(r)}+\operatorname{MLP}\left(\sum_i \alpha_{k \leftarrow i} \cdot\left(W_V h_i^{(i)}\right)\right)$    (17)

where, $W_V \in \mathrm{R}^{d_v \times d}$ is the projection matrix for the value, $d_v=128$, and MLP is a two-layer fully connected network with a hidden layer dimension of 256 . This path enables each spatial grid to dynamically adjust its representation of the group atmosphere based on the emotional states of the students within it. The bottom-up path executes the opposite direction of information flow, where individual nodes aggregate the field features of all group nodes to correct their own emotional representation:

$\beta_{i \leftarrow r}=\operatorname{softmax}\left(\frac{\left(W^{'}_Q h_i^{(i)}\right)^{\top}\left(W^{'}_K h_g^{(r)}\right)}{\sqrt{d_k}}\right), h_i^{(i)} \leftarrow h_i^{(i)}+M L P\left(\sum_r \beta_{i \leftarrow r} \cdot\left(W^{'}_V h_g^{(r)}\right)\right)$            (18)

where, $W^{'}_Q, W^{'}_K, W^{'}_V$ are independently learned projection matrices for the bottom-up path, and $\beta_{i \leftarrow r}$ is the normalized attention weight of the i-th individual node for the r-th group node. The physical meaning of this path is that when a student is in a high-interaction-density area, their own low-arousal state may be corrected by the group field information, thereby avoiding emotional misjudgment caused by single-frame occlusion or pose deflection. The two paths each execute two rounds of iterative updates, and all nodes are updated synchronously after each round.

After two rounds of message passing, the node features have fully integrated cross-scale collaborative information. Average pooling and max pooling are applied to the updated features of all individual nodes to extract the central tendency and extreme responses of the individual set, respectively; average pooling is applied to the group node features to obtain the global field summary. The three are concatenated to form the collaborative fusion feature:

$F_{{collab}}=Concat\left(\begin{array}{l}{AvgPool}\left(\left\{h_i^{(i)}\right\}\right), \\ \underline{{MaxPool}\left(\left\{h_{i}^{(i)}\right\}\right),} \\ {AvgPool}\left(\left\{h_g^{(r)}\right\}\right)\end{array}\right) \in \mathrm{R}^{272}$            (19)

where, $AvgPool\left(\left\{h_{i}^{(i)}\right\}\right)\in\mathrm{R}^{128}$ is the mean vector of individual node features, ${MaxPool}\left(\left\{h_i^{(i)}\right\}\right) \in \mathrm{R}^{128}$ is the element-wise maximum value, and $AvgPool\left(\left\{h_{i}^{(i)}\right\}\right)\in\mathrm{R}^{16}$ is the mean vector of group node features. $F_{{collab}}$ is mapped to a scalar via the regressor $M L P_{{reg}}$, whose structure is $272 \rightarrow 128 \rightarrow 64 \rightarrow 1$, with a Dropout rate of 0.3 and ReLU activation inserted between layers. The output is normalized by Sigmoid and scaled to the [0,100] interval:

$\widehat{P S}=\operatorname{sigmoid}\left(M L P_{{reg}}\left(F_{{collab}}\right)\right) \times 100$        (20)

The training supervision signal is the measured score from the Edmondson scale $P S_{{label}}$. The Huber loss is adopted to balance the accuracy of the squared error and the robustness of the absolute error to outliers:

$L_{P S}(y, \hat{y})=\left\{\begin{array}{c}\frac{1}{2}(y-\hat{y})^2,|y-\hat{y}| \leq \delta \\ \delta|y-\hat{y}|-\frac{1}{2} \delta^2, {otherwise}\end{array}\right.$            (21)

where, $y$ is the measured scale score $P S_{{label}}, \hat{y}$ is the model prediction $\widehat{P S}$, and $\delta=5.0$ is the threshold parameter of the Huber loss, controlling the division point between squared loss and linear loss. To further enhance the interpretability of model decisions, this paper applies sparse regularization to the attention weights, constraining the cross-scale attention distribution in the top-down path to deviate from a uniform distribution $\alpha_{i \leftarrow r}:$

$L_{{sparse}}=\sum_r K L\left(\alpha_{r \leftarrow} . \|\right. Uniform)=\sum_r \sum_i \alpha_{r\leftarrow i} \log \left(N \cdot \alpha_{r \leftarrow i}\right)$            (22)

where, ${{K L( } \|})$ is the Kullback-Leibler divergence, Uniform is the uniform distribution with value 1/N, N is the total number of individual nodes, and r traverses the 16 group nodes. This regularization term encourages the attention of each group node to focus on a few key individuals, making the prediction of psychological safety traceable to specific spatial regions and student groups.

The DCCG framework adopts end-to-end joint training. The overall loss function is:

$L_{{total}}=L_{{seg}}+L_{{expr}}+L_{P S}+\eta L_{{sparse}}$       (23)

where, $L_{{seg}}$ is the segmentation loss of Module $1, L_{{expr}}$ is the expression recognition loss of Module 2, $L_{P S}$ is the Huber loss for psychological safety regression, and $\eta=0.01$ is the weight coefficient of the sparse regularization term. The training uses the AdamW optimizer, with an initial learning rate set to $1 \times 10^{-4}$, a weight decay of $5 \times 10^{-4}$, and a batch size of 8 . Since the loss functions of the three modules share the computation graph during backpropagation, the gradient information is naturally coupled, eliminating the need to design additional strategies to balance the convergence speed of each module. Through the above design, Module 3 completes the complete inference chain from heterogeneous information fusion of the group field and individual emotional particles to quantitative regression of psychological safety.