Nonlinear Adaptive Optimization of Multi-Modal Learning Paths Using Graph Convolutional Networks and Reinforcement Learning for Intelligent Educational Systems

Collaborative filtering (CF) is a foundational technique in recommendation systems, leveraging user-item interaction matrices to predict user preferences. Matrix factorization techniques, such as singular value decomposition (SVD) and non-negative matrix factorization (NMF), have demonstrated strong performance in static recommendation tasks[8].However, CF methods encounter significant limitations in educational recommendations:

1) Cold-Start Problem: CF struggles to generate accurate recommendations for new users or newly introduced resources due to sparse interaction data[9].

Recent research has addressed these limitations by incorporating contextual features (e.g., learning background and goals) or integrating knowledge graph-based methods. However, these enhancements still fall short in dynamic modeling and multimodal resource processing.

Deep learning has significantly advanced recommendation systems by enabling non-linear feature modeling. Representative models include:

1) Neural Collaborative Filtering (NCF): Replacing traditional linear inner-product operations with multi-layer perceptrons (MLPs), NCF captures complex user-item interactions[2].

Despite their success in general applications, these models face challenges in education, such as processing heterogeneous learning resources (e.g., textbooks, instructional videos, and experimental code) and capturing the dynamic temporal aspects of user learning behaviors.

Knowledge graphs (KG) have seen increasing adoption in educational recommendations, enabling semantic representation of course chapters, knowledge points, and their dependencies. Recent advancements include:

1) Knowledge Graph Embeddings: Techniques like TransE and DistMult map entities and relationships into low-dimensional vector spaces, enhancing semantic representation[5].

While these methods have shown promise, they often lack robust support for temporal dynamics and multimodal data integration.

Modern educational resources are inherently multimodal, encompassing textual content, videos, and programming exercises. Recent efforts to model multimodal data include:

1) Multi-Gate Mixture-of-Experts (MMoE): This framework dynamically assigns weights to different modalities, reflecting their varying importance in learning tasks[7].

Despite these innovations, challenges remain in dynamically adjusting modality weights to reflect changes in learning stages and effectively integrating the semantics of heterogeneous data sources.

Temporal modeling plays a crucial role in capturing the dynamic nature of user learning behaviors. Key techniques include:

1) Long Short-Term Memory (LSTM): LSTM networks excel in capturing long-term dependencies in sequential data[22].

Attention mechanisms have emerged as a key solution for addressing challenges in multimodal fusion and temporal modeling. By focusing on critical features and time points, attention mechanisms significantly enhance the performance of recommendation systems [23].

Reinforcement learning (RL) optimizes recommendation strategies based on real-time user interactions. Deep reinforcement learning (DRL) extends RL capabilities with deep neural networks, achieving notable success in domains such as e-commerce and video streaming [14].

In education, RL enables dynamic adjustment of learning paths to accommodate evolving student needs, offering a promising direction for personalized recommendations [15].

Reward signal design is critical in RL, particularly in education, where multi-objective optimization (e.g., learning completion, knowledge coverage, and resource diversity) is essential. Multi-objective reward functions provide theoretical foundations for dynamic recommendation strategies [16].

This study introduces a gating mechanism combined with reinforcement learning to achieve dynamic weighting of multimodal features, such as textbooks, instructional videos, and experiments, effectively addressing varying learning stage requirements.

A novel framework integrating graph convolutional networks (GCN), temporal modeling, and reinforcement learning is proposed. This framework captures interdependencies among knowledge points, dynamically adjusts recommendation paths, and represents a paradigm shift in personalized educational recommendations.

In summary, recent studies on educational recommendation systems have made significant progress, yet notable research gaps remain in the generation of dynamic learning paths, the integration of multimodal data, and the modeling of temporal and knowledge associations. This paper comprehensively reviews recent advancements, highlighting the strengths and limitations of traditional collaborative filtering methods, deep learning-based recommendation techniques, and knowledge graph-driven models in educational contexts. Additionally, it explores the latest developments in multimodal learning and temporal modeling, as well as the potential of reinforcement learning for personalized recommendations [7],[13]. Based on this foundation, the paper proposes an innovative framework for personalized learning recommendation systems that integrates graph convolutional networks (GCN)[1],[2],[20], attention mechanisms, dynamic weighting of multimodal features, and reinforcement learning, offering a novel technical pathway to address these challenges.

The Computer Networks course is a critical component of computer science education, characterized by unique learning needs and recommendation challenges. These include: diverse learning objectives, encompassing both fundamental theories (e.g., network protocols, layered architectures) and practical exercises (e.g., network simulations, socket programming); personalized learning paths, requiring the system to dynamically adapt to students' varying learning levels, interests, and mastery of knowledge; and temporal dependency, indicating that students' learning needs are often sequential, such as studying foundational knowledge (e.g., TCP/IP protocols) before advancing to hands-on practices[16].

This study proposes a dynamic personalized learning recommendation system tailored to the Computer Networks course. The system is designed to recommend multimodal learning resources, such as textbooks, instructional videos, lab projects, and code repositories[13],[17]. By modeling user learning behaviors and employing temporal sequence analysis, the system dynamically adjusts recommendation strategies, enabling students to construct efficient learning paths. To achieve this, the architecture leverages a combination of Graph Convolutional Networks (LightGCN)[2], attention mechanisms [5], and reinforcement learning[8][23] to optimize recommendations, while incorporating domain-specific input features to capture the unique aspects of the Computer Networks course[17].

The proposed dynamic personalized learning recommendation system is structured as illustrated in Figure 1, which outlines the hierarchical workflow of the system, from input processing to recommendation generation and feedback optimization. This framework includes five key modules: the Input Layer, the Multimodal Data Fusion Layer[7], the Temporal Modeling Module, the Recommendation Engine Module, and the Feedback Module[18].

Figure 1.

Infrastructure components of the designed system

Figure 1 provides a detailed view of how the various components of the system are interconnected, including data flow and the roles of specific technologies. For instance, the Input Layer processes raw user data and extracts features via a shared embedding network, feeding them into subsequent layers. The Multimodal Data Fusion Layer[7], as depicted, employs a gated mechanism enhanced by reinforcement learning to integrate multi-modal information dynamically. This layered design ensures the system's ability to adaptively recommend learning materials tailored to individual students' needs, particularly within the context of a Computer Networks course[18].

The proposed system consists of five key components:

1) Input Layer: Collects user learning behavior data (e.g., resource clicks, dwell time), course content features (e.g., textbook sections, code snippets), and temporal features (e.g., learning stages) while performing feature engineering and preprocessing.

The resources for the computer networks course are highly diverse, encompassing textbooks (text), videos (dynamic visualizations), and code examples (hands-on practice). These modalities significantly influence students’ learning behaviors and progress. However, the heterogeneous nature of these modalities presents challenges in directly fusing them, as this could result in information loss or imbalanced contributions from different modalities. To address these challenges, we design a dynamic multi-modal fusion strategy tailored for computer networks course resources. This strategy leverages a gating mechanism and reinforcement learning to dynamically adjust the weights of modalities, ensuring precise modeling of students’ learning needs.

To dynamically adjust the importance of different modalities, the gating mechanism incorporates user behavior features A_m, such as click rate, video watch duration, and interaction frequency. The fusion formula is defined as: (6) Ffused =∑m=1MαmFm \[{{\text{F}}_{\text{fused }\!\!~\!\!\text{ }}}=\sum\nolimits_{\text{m}=1}^{\text{M}}{{{\alpha }_{\text{m}}}{{\text{F}}_{\text{m}}}}\]

where the modality weight α_m is computed as: (7) αm=exp(g(Fm,Am))∑j=1Mexp(g(Fj,Aj)) \[{{\alpha }_{\text{m}}}=\frac{\exp \left( \text{g}\left( {{\text{F}}_{\text{m}}},{{\text{A}}_{\text{m}}} \right) \right)}{\sum\nolimits_{\text{j}=1}^{\text{M}}{\exp \left( \text{g}\left( {{\text{F}}_{\text{j}}},{{\text{A}}_{\text{j}}} \right) \right)}}\]

Here, g(·) is a nonlinear function (e.g., an MLP) that outputs an importance score based on the modality feature F_m and behavior feature A_m.

Weight Design for Computer Networks Course:For chapter-based content (e.g., link layer, network layer, application layer), the weights of different modalities are dynamically adjusted. For example:

Textbooks are assigned higher weights during topics like the "Link Layer" to emphasize theoretical understanding.

The reinforcement learning optimization strategy, as described in Figure 1, enhances this gating mechanism by dynamically learning optimal weights during the recommendation process. The reward function used for reinforcement learning is defined as Formula (8): (8) R=λ1⋅ Learning Progress +λ2⋅ Engagement Level \[\text{R}={{\lambda }_{1}}\cdot ~\text{Learning Progress}~+{{\lambda }_{2}}\cdot ~\text{Engagement Level }\!\!~\!\!\text{ }\]

where Learning Progress measures the completion of learning tasks, and Engagement Level evaluates student interactions with the recommended resources.

The multi-modal fusion process is modeled as a Markov Decision Process (MDP), where the state s_t represents the modality features in the current learning phase, and the action a_t adjusts the modality weights α_m. The objective of reinforcement learning is to maximize the cumulative reward RR: (9) ℒRL=E[ ∑t=1TγtRt ] \[{{\mathcal{L}}_{\text{RL}}}=\mathbb{E}\left[ \sum\nolimits_{\text{t}=1}^{\text{T}}{{{\gamma }^{\text{t}}}{{\text{R}}_{\text{t}}}} \right]\]

where γ is the discount factor. A Deep Q-Network (DQN) is utilized as the policy network, which takes the state s_t as input and outputs the optimal action a_t.The iterative optimization ensures that the system adapts to students’ evolving learning behaviors over time.

As highlighted in Figure 1, the reinforcement learning strategy works in tandem with the gating mechanism to dynamically adjust the fusion strategy during training. This approach not only maximizes learning efficiency but also ensures resource diversity in the recommendations.

The Input Layer (highlighted in blue in Figure 1 is responsible for collecting and preprocessing user data. For the Computer Networks course, the input data consists of the following components:

1) Behavioral Data: Captures students' interactions with learning resources, including:

(1) Click behaviors: Frequency and duration of clicks on textbooks, videos, and labs.

To adapt multimodal input data, the following preprocessing steps are performed:

The shared embedding network maps multi-modal features (text, code, and temporal) into a unified feature space, generating the final input vector: (6) h=σ(W1zb1) \[h=\sigma \left( {{\text{W}}_{1}}z{{b}_{1}} \right)\]

where h represents the user’s multi-modal feature representation, and σ is an activation function (e.g., ReLU).

In the Computer Networks course, knowledge points exhibit a strong sequential and dependency relationship. For instance, learning the "Network Layer" relies on foundational knowledge from the "Link Layer." To model this dependency, a dependency matrix D is defined as follows: (10) Dij={ 1, if chapterj is a prerequisite for chapter i 0,otherwise. \[{{\text{D}}_{\text{ij}}}=\left\{ \begin{matrix} 1,~\text{if chapterj is a prerequisite for chapter i }\!\!~\!\!\text{ } \\ \begin{array}{*{35}{l}} \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} 0, & {} \\ \end{matrix} & {} & {} \\ \end{matrix} & {} & \text{otherwise}. \\ \end{matrix} & {} & {} \\ \end{matrix} & {} & {} \\ \end{array} \\ \end{matrix} \right.\]

In the LSTM, the hidden state update formula is modified to incorporate the dependency relationship: (11) ht=σ(Whxt+Uhht−1+Dt⋅ht−1+bh) \[{{\text{h}}_{\text{t}}}=\sigma \left( {{\text{W}}_{\text{h}}}{{\text{x}}_{\text{t}}}+{{\text{U}}_{\text{h}}}{{\text{h}}_{\text{t}-1}}+{{\text{D}}_{\text{t}}}\cdot {{\text{h}}_{\text{t}-1}}+{{\text{b}}_{\text{h}}} \right)\]

where D_t·h_t–1 explicitly represents the influence of the current knowledge point's prerequisite dependencies on the hidden state.

As shown in Figure 1, this dependency modeling is embedded in the Temporal Modeling Layer, enabling the system to accurately capture the hierarchical structure of knowledge points in the course. The dependency matrix enhances the temporal dynamics modeled by LSTM by introducing explicit representations of prerequisite relationships.

The temporal sequence data X = [x₁,x₂, … , x_T] represents the student's learning behavior sequence, where each x_t is the feature vector of learning activities at time step t LSTM is employed to capture the temporal dependencies in this sequence. The core equations of LSTM are as follows: (12) it=σ(Wixt+Uiht−1+bi),ft=σ(Wfxt+Ufht−1+bf),ot=σ(Woxt+Uoht−1+bo),ct=ft⊙ct−1+it⊙tanh(Wcxt+Ucht−1+bc),ht=ot⊙tanh(ct),

where σ(·)is the sigmoid activation function and ⊙denotes element-wise multiplication.

As depicted in Figure 1, the Temporal Modeling Layer applies LSTM to the processed input sequence from the Multimodal Data Fusion Layer, effectively learning long-term and short-term dependencies in students' learning behaviors. This facilitates capturing the sequential nature of knowledge acquisition in the course.

To enhance the modeling of the importance of course knowledge points, an attention mechanism is introduced to compute the significance weight of each time step: (13) βt=exp(qTtanh(Waht+ba))∑j=1Texp(qTtanh(Wahj+ba)) \[{{\beta }_{\text{t}}}=\frac{\exp \left( {{\text{q}}^{\text{T}}}\tanh \left( {{\text{W}}_{\text{a}}}{{\text{h}}_{\text{t}}}+{{\text{b}}_{\text{a}}} \right) \right)}{\sum\nolimits_{\text{j}=1}^{\text{T}}{\exp \left( {{\text{q}}^{\text{T}}}\tanh \left( {{\text{W}}_{\text{a}}}{{\text{h}}_{\text{j}}}+{{\text{b}}_{\text{a}}} \right) \right)}}\]

The final weighted representation of the temporal sequence is then computed as: (14) Hattn=∑t=1Tβtht. \[{{\text{H}}_{\text{attn}}}=\sum\nolimits_{\text{t}=1}^{\text{T}}{{{\beta }_{\text{t}}}{{\text{h}}_{\text{t}}}.}\]

This attention mechanism, as visualized in Figure 1, enhances the LSTM's output by focusing on critical knowledge points in the sequence. The weights βt\beta_t can be further adjusted according to chapter importance, enabling the system to prioritize more impactful sections of the course material.

Beyond the attention mechanism, reinforcement learning is utilized to optimize the temporal modeling of students' learning behaviors. A reward function is designed to encourage students to follow the dependency chain of knowledge points sequentially: (15) Rt=λ1⋅ Correctness t+λ2⋅ Completion t \[{{\text{R}}_{\text{t}}}={{\lambda }_{1}}\cdot ~\text{Correctness}{{~}_{\text{t}}}+{{\lambda }_{2}}\cdot ~\text{Completion}{{\text{ }\!\!~\!\!\text{ }}_{\text{t}}}\]

where:

Correctness_t evaluates the accuracy of the learning content at the current time step,

As shown in Figure 1, this reinforcement learning framework is integrated into the Feedback Module and linked back to the Temporal Modeling Layer. The dynamic reward strategy ensures that the model adapts to individual students' progress and learning goals, enhancing both personalization and temporal alignment in recommendations.

The code snippet shown in the Figure 2 represents a core part of the dynamic personalized learning recommendation system described in the paper. The snippet outlines the process for multi-modal data fusion and temporal modeling for user representation generation, which are crucial for the proposed model. Here's a brief breakdown:

Figure 2.

Pseudo code of the “Multimodal Data Fusion and Temporal Modeling”Algorithm

Step 1: Multi-modal Data Fusion:

This step combines multiple data sources (e.g., text, images, or other features) using a weighted fusion technique. Each modality's contribution to the final representation is computed based on the softmax function, which normalizes the weights across different modalities.

Step 2: Temporal Modeling with LSTM

In this step, the Long Short-Term Memory (LSTM) model is used to process the time sequence data. LSTM is commonly used for sequential data and helps capture temporal dependencies in user behavior (e.g., learning patterns over time).

Step 3: Attention Mechanism for Temporal Features

This step applies an attention mechanism to the temporal features, which allows the model to focus more on important time steps in the sequence. The attention mechanism uses learned weights β_t to assign different attention scores to each time step.

Step 4: Final User Representation

Finally, the outputs of the multi-modal fusion and temporal modeling (i.e., the fused feature vectors and attention-modulated time steps) are concatenated to form the final user representation, which is then used for personalized recommendations.

This code showcases an efficient method to fuse multi-modal data and account for temporal dependencies in user behavior, key for the personalized learning recommendations the paper addresses.

For the recommendation task in the Computer Networks course, we constructed not only a user-resource interaction graph G = (V, E), representing the relationships between users and learning resources (e.g., textbook chapters, experimental videos, code projects), but also an extended knowledge-point graph G_kn = (V_kn, E_kn). The components of the graphs are defined as follows:

V_kn: A set of knowledge points (e.g., key topics such as the Link Layer, Network Layer, and Transport Layer).

As illustrated in Figure 1, the Graph Construction step within the Recommendation Engine Module integrates both interaction and knowledge-point graphs. This dual-graph modeling approach combines users’ learning behaviors with the knowledge structure of the course, thereby enriching the embeddings used in subsequent recommendation generation.

In the recommendation generation process, the user's progress in learning specific course resources is incorporated into the scoring computation. The recommendation score s_u,i for user u and resource i is calculated as: (17) su,i=Attention(hu,hi)+γ⋅Progress(u,i) \[{{s}_{u,i}}=\text{Attention}\left( {{h}_{u}},{{h}_{i}} \right)+\gamma \cdot \text{Progress}(u,i)\]

where:

Attention(h_u, h_i): The compatibility score between the user and the learning resource, calculated as: (18) Attention(hu,hi)=qTtanh(Wuhu+Wihi+b) \[\text{Attention}\left( {{\text{h}}_{\text{u}}},{{\text{h}}_{\text{i}}} \right)={{\text{q}}^{\text{T}}}\tanh \left( {{\text{W}}_{\text{u}}}{{\text{h}}_{\text{u}}}+{{\text{W}}_{\text{i}}}{{\text{h}}_{\text{i}}}+\text{b} \right)\]

with W_u, W_i, and q^T as learnable parameters.

As depicted in Figure 1, the Recommendation Engine Module combines embeddings from the Feature Propagation step (via LightGCN) with user-progress information to produce personalized recommendations. By incorporating user progress, the system ensures that recommended resources align with the user's current learning stage, providing a dynamic and context-aware recommendation experience.

In the Computer Networks course, the hierarchical structure of knowledge (e.g., progressing from the Link Layer to the Application Layer) plays a crucial role in ensuring effective learning. To respect this hierarchical progression, the recommendation system prioritizes incomplete but essential chapters or experimental projects. The re-ranking mechanism dynamically adjusts recommendation results by combining the user's personalized compatibility score with the prerequisite importance of the learning resources. The re-ranking score for resource iii is defined as: (19) Rank(i)=su,i⋅PrerequisiteScore(i) \[\text{Rank}(\text{i})={{s}_{u,i}}\cdot \text{PrerequisiteScore}(i)\]

where:

s_u,i : The compatibility score between user uand resource i, computed in the recommendation process (see 3.5.2 Progress-Aware Recommendation Generation for details).

The PrerequisiteScore is derived using the knowledge-point dependencies modeled in the Graph Construction step (depicted in Figure 1) and is calculated based on the criticality and completion status of the resource's prerequisite nodes. For example, if a student has not completed the foundational chapters in the "Link Layer," these chapters are assigned higher priority in the re-ranking process, ensuring that subsequent topics (e.g., "Network Layer") are not recommended prematurely.

In the recommendation task for the Computer Networks course, the learning state of a user must comprehensively represent the current progress and the remaining tasks. The state s_t at time step t is defined as: (20) st=(hu,Ccompleted ,Cremaining ) \[{{s}_{\text{t}}}=\left( {{\text{h}}_{\text{u}}},{{\text{C}}_{\text{completed }\!\!~\!\!\text{ }}},{{\text{C}}_{\text{remaining }\!\!~\!\!\text{ }}} \right)\]

where:

(h_u : The embedding representation of the user.

As depicted in Figure 1, the Feedback Module (green block) processes this state to generate a reward signal R_t, which reflects the user's learning engagement, progress, and diversity in the recommended resources. This detailed representation ensures that the system effectively tracks and adapts to the user’s learning trajectory, aligning recommendations with both completed and pending knowledge points.

The reward signal is tailored to the learning scenario, incorporating user interactions, knowledge point progress, and course completion rate. The composite reward function is defined as: (21) Rt=λ1⋅ Engagement +λ2⋅ Learning Progress +λ3⋅ CompletionRate \[{{\text{R}}_{\text{t}}}={{\lambda }_{1}}\cdot ~\text{Engagement}~+{{\lambda }_{2}}\cdot ~\text{Learning Progress}~+{{\lambda }_{3}}\cdot \text{ }\!\!~\!\!\text{ CompletionRate}~\]

where:

Engagement: Measures the user's interaction with the recommended resources, calculated as: (22) Engagement = Interactions Total Resources . \[\text{ }\!\!~\!\!\text{ Engagement}~=\frac{\text{ }\!\!~\!\!\text{ Interactions }\!\!~\!\!\text{ }}{\text{ }\!\!~\!\!\text{ Total Resources }\!\!~\!\!\text{ }}.\]

As illustrated in Figure 1, the reward signal computation is tightly integrated with the Feedback Module. This module dynamically adjusts the reward by monitoring the user’s progress along the knowledge graph, captured in the Knowledge Graph Propagation step (purple block).

To encourage recommendation diversity, a diversity score based on the distribution of knowledge points is incorporated into the reward signal. The diversity score is defined as: (24) Diversity =1−∑i,j∈ssim(hi,hj)|S|⋅(|S|−1) \[~\text{Diversity}~=1-\frac{\sum\limits_{\text{i},\text{j}\in \text{s}}{\text{sim}\left( {{\text{h}}_{\text{i}}},{{\text{h}}_{\text{j}}} \right)}}{|\text{S}|\cdot (|\text{S}|-1)}\]

where:

S: The set of recommended resources.

where λ₄ is the weight of the diversity score. As depicted in Figure 1, the diversity-enhanced reward signal is processed in the Reward Signal block of the Feedback Module, ensuring that the recommendations are not only personalized but also varied, encouraging exploration and comprehensive learning.

Below is the pseudocode that integrates knowledge graph propagation, dynamic user progress adjustment, recommendation generation, and reinforcement learning-based optimization.

As illustrated in Figure 1, the algorithm relies on distinct modules, including the Knowledge Graph Propagation (purple block), Multi-modal Data Fusion (pink block), and the Feedback Module (green block), to achieve personalized, adaptive, and effective recommendations.

To highlight the characteristics of the Computer Networks course, we analyze the complexity added by knowledge dependencies and dynamic user progress updates.

Considering the characteristics of the knowledge-point graph and course modules, the space complexity is:

1) Embedding Storage: For user and module embeddings:O(N_u·d_g + N_m·d_g).

The experimental data is derived from the 2016 to 2022 cohorts of Computer Science students from the School of Information Engineering, who have participated in the Computer Networks course. The dataset comprises 486 students, divided into two groups:

To comprehensively evaluate the performance of the model, the following metrics were used:

1) Recommendation Accuracy :

• Precision@K: The proportion of relevant items in the top K recommended items[2].

where |S| is the size of the recommendation set, and Sim(·)is the cosine similarity.

The performance of the proposed framework was compared against the following methods:

1) Baseline Models:Collaborative Filtering (CF);Matrix Factorization (MF) .

We use Precision@K, Recall@K, and NDCG@K as the primary metrics for recommendation accuracy. The results are shown in Figure 3:

Figure 3.

Recommendation Accuracy with primary metrics

Analysis:

1) The proposed GCN-Attention-RL model achieves the best performance across all metrics. Compared to the strong baseline LightGCN, Precision@5 improves by 5.9%, Recall@5 by 5.6%, and NDCG@5 by 5.0% [2].

The results of time series modeling using RMSE (Root Mean Square Error) are shown in Figure 4:

Figure 4.

The results of time series modeling using RMSE

Analysis:

1) The GCN-Attention-RL model achieves the best RMSE score, reducing error by 20.3% compared to LSTM and by 13.4% compared to TCN[5].

We evaluate recommendation diversity and user learning outcomes, including course completion rate and average experimental scores. The results are presented in Figure 5:

Figure 5.

Diversity and Learning Outcome Analysis Result

Analysis:

1) Recommendation Diversity: The diversity metric for GCN-Attention-RL reaches 0.698, a 10.1% improvement compared to LightGCN [4]. This improvement is due to:

(1) Diversity-oriented reinforcement learning reward functions: Encourages diverse recommendation outcomes.

To further quantify the practical impact of the GCN-Attention-RL framework on learning behavior, we compare the experimental group (using the proposed framework) with the control group (using traditional methods) on several key metrics. Results are summarized in Figure 6:

Figure 6.

Experimental Group vs. Control Group Analysis

The Multi-modal Fusion Module has a linear complexity with respect to the number of modalities MM and feature dimension d_m, making it relatively efficient. The Temporal Modeling Module using LSTM and attention mechanisms exhibits quadratic complexity concerning the sequence length T, where sparse attention can help mitigate the computational overhead. The Reinforcement Learning Module adds linear complexity for each time step T, making it suitable for real-time recommendation when implemented efficiently.

Table 5 provides the space complexity of each module in the proposed framework

The User and Resource Embedding Module has a space complexity linear in the number of users N_u and resources N_m, scaled by the embedding dimension d_g Reducing d_g without compromising feature representation can alleviate memory consumption. Additionally, the Knowledge Graph Storage Module, which stores dependencies between learning modules, can be optimized using sparse representations to manage the large-scale storage efficiently.

This detailed complexity analysis ensures the proposed model remains scalable for real-world applications, particularly in the context of personalized learning recommendation systems.