Drug-target interaction prediction via hierarchical gated attention and information bottleneck

2.1. Graph computational method-based DTI prediction

Early DTI prediction methods framed the task as link prediction on heterogeneous networks, learning topology-preserving embeddings. DTINet^[14] integrated multimodal features via random walks followed by dimensionality reduction. With the rise of GNNs^[15], NeoDTI^[16] jointly modeled structural and attribute information through neighborhood aggregation, while GCN-DTI^[17] and EEG-DTI^[18] used graph convolutional networks (GCNs) to extract drug and protein features separately. However, these approaches rely on simplistic aggregation (e.g., mean or sum pooling), failing to capture fine-grained local structural characteristics. To better exploit semantic dependencies, researchers have introduced attention mechanisms and meta-paths. IMCHGAN^[19] employed hierarchical attention to distinguish meta-path semantics, and AMGDTI^[20] adaptively fused multi-view features from multiple meta-paths. DHGT-DTI^[21] further proposed a dual-view heterogeneous graph to capture local and global interaction patterns. Nevertheless, naïve fusion of multi-view features often leads to information redundancy, and high-dimensional heterogeneous structures introduce noise, degrading representation compactness^[22]. More recent methods adopt contrastive learning and causal inference to enhance model robustness and address data sparsity. CE-DTI^[23] incorporated causal inference to mitigate bias; SGCL-DTI^[24] and SHGCL-DTI^[25] applied structure-aware contrastive learning to maximize mutual information between local and global views; DSS-DTI^[26] used a dual-scale spatiotemporal framework; and MIDTI^[27] employed multi-view interaction modeling. Despite these advances, balancing fine-grained local substructure extraction with global semantic redundancy reduction remains a key challenge, motivating a framework that integrates structural gating with information compression.

2.2. Graph attention network-based applications

The attention mechanism, inspired by human visual cognition, enables models to focus on salient input features while suppressing irrelevant information. Graph Attention Networks (GATs)^[28] extend this paradigm to non-Euclidean domains. Attention mechanisms were first introduced to address long-range dependencies in machine translation. The Transformer relies entirely on self-attention to capture global dependencies, outperforming recurrent neural networks (RNNs). Attention mechanisms also capture spatial relationships and regions of interest. Non-local neural networks^[29] used self-attention to model pixel-level long-range dependencies, overcoming convolution’s receptive field limits. Vision Transformers^[30] further demonstrate that purely attention-based architectures excel at image recognition. Moreover, biological data (e.g., molecular structures, protein interaction networks) naturally lend themselves to graph representations. AlphaFold^[31] heavily utilizes attention to predict 3D protein structures by modeling pairwise residue relationships. For molecular property prediction, GATs learn molecular fingerprints by attending to critical atoms and functional groups^[32]. In protein-protein interaction (PPI) prediction, attention identifies key interface residues by weighting biologically active regions. These successes underscore the ability of graph attention mechanisms to capture both local structural details and global functional dependencies in biomedical data.

3.1. Overall framework

The proposed HGMAIB model comprises four core modules [Figure 1]. (1) Node representation initialization: Node2Vec^[33] generates low-dimensional embeddings for drug and protein nodes as informative input features; (2) Adaptive meta-path selection: Automatically identifies discriminative semantic paths to guide high-order semantic information propagation and aggregation; (3) Multi-semantic structural modeling: Employs a multi-step graph convolutional framework with weighted residual connections to capture deep semantic dependencies while mitigating gradient vanishing and feature over-smoothing. A hierarchical gated multi-head attention mechanism further learns node-level local structural patterns and integrates multi-perspective semantic information. (4) IB: Compresses redundant information and extracts task-relevant joint embeddings, enhancing discriminative power and generalization.

Figure 1. (A) Overall architecture of HGMAIB: (a) Node representation initialization - Node2Vec extracts drug and target features. (b) Adaptive meta-path search - A dynamic search strategy identifies informative semantic paths. (c) Multi-semantic structural modeling - Multi-step residual graph convolution and hierarchical gated multi-head attention (HGMA) capture deep dependencies. (d) Information bottleneck - Learned embeddings are refined to filter redundant noise. (B) HGMA stacking process: The hierarchical architecture performs weighted aggregation within each attention head, followed by a gating mechanism that integrates information across all heads.

3.2. Node representation initialization module

By simulating biased random walks, Node2Vec captures both local and global structural information and generates low-dimensional dense vectors for each node, serving as input features for downstream GNNs [Figure 2]. First, an undirected weighted bipartite graph is constructed from the drug-target adjacency matrix, where drugs (D1-D4) and targets (T1-T4) form two distinct node types, and edge weights denote known interactions. To prevent data leakage, the bipartite graph used for Node2Vec initialization is dynamically rebuilt during each five-fold cross-validation iteration: all test-set edges are explicitly masked and excluded from the adjacency matrix before random walk generation. Node2Vec is then applied to the masked graph to obtain initial node embeddings. It then simulates fixedlength random walks by interpolating between breadth first search (BFS) and depth first search (DFS). Two hyperparameters control walk preferences: the return parameter p (the likelihood of revisiting the previous node) and the inout parameter q (the tendency to explore local vs. distant nodes), thereby balancing structural equivalence and homophily.

Figure 2. Workflow of Node2Vec for node representation learning.

The resulting walk sequences are treated as “sentences” and fed into a skip-gram model^[34]. Originally designed for natural language processing (NLP), the skip-gram model maximizes word co-occurrence probabilities; in graphs, it captures the co-occurrence of adjacent nodes within the same walk, encoding contextual structure. After training, each node is mapped to a dense low-dimensional embedding that preserves the drug-target graph topology. These embeddings serve as informative initial inputs for subsequent GNNs, enhancing their ability to perceive both topological and semantic features.

3.3. Adaptive metapath selection module

Inspired by AMGDTI^[20], we adopt a dynamic search strategy to model high-order semantic dependencies in heterogeneous graphs. This mechanism automatically generates discriminative meta-paths, constructing a guided graph structure that enhances semantic propagation and feature aggregation. Its key advantage is eliminating manual path design by adaptively identifying optimal meta-path combinations, thereby improving the model’s ability to represent complex semantic relationships.

Specifically, this module constructs a directed acyclic adaptive meta-graph, denoted as M = (V_m, E_m). The node set V_m represents the sequence of node feature states {S₀, S₁, …, S_T} after each propagation step within the heterogeneous network, where the total number of nodes is determined by the predefined propagation steps T. The edge set E_m encodes all possible information propagation strategies. For example, a directed edge labeled "Protein→Disease" from S₀ to S₁ indicates that the feature of a "Disease" node in S₁ is obtained by aggregating the features of "Protein" nodes in S₀. This structure allows any previous state S_i∈{S₀, S₁,…, S_T-1} to influence the current state S_T through skip connections, enabling the model to fully capture complex semantic information embedded in heterogeneous networks.

In addition, the model adaptively determines each edge in the meta-graph by evaluating whether a previous state contributes to the current state and selecting the most appropriate propagation strategy. This approach treats all edge types as potential propagation patterns, enabling dynamic path selection. Additionally, two auxiliary connection types are introduced: L₁ indicates that the current state is identical to the previous state, while L₂ implies that the previous state does not affect the current state. The adaptive meta-graph comprises 12 possible edge types: {L_DP, L_PD, L_DS, L_SD, L_DE, L_ED, L_PE, L_EP, L_DD, L_PP, L₁, L₂}. The first ten correspond to explicit biological relations within the heterogeneous network (e.g., L_DP: Drug → Protein, L_ED: Disease → Drug), while the latter two are auxiliary designs intended to enhance the structural flexibility and semantic expressiveness of the model.

To mathematically formulate the path-selection optimization and ensure reproducibility, we formally define the candidate connection constraints and the selection mechanism. Let C_t,i denote the set of possible connection types from a previous state S_i to the current state S_t. To avoid meaningless aggregations, C_t,i is dynamically constrained based on the propagation step t and the total steps T:

where E_M represents the full set of 12 candidate edges, and R represents the subset of target-related edges. Subsequently, we assign a learnable structural parameter $$\theta_{t, i}^{n}$$ to each possible connection. To balance exploration and exploitation, a random sampling strategy is introduced. The final selected connection $$C_{t, i}^{*}$$ is defined as:

where m is the index of the edge type with the maximum parameter value ($$\theta_{t, i}^{m}=\max \left(\theta_{t, i}^{0}, \ldots, \theta_{t, i}^{n}\right)$$), and rand (C_t,i) denotes uniform random sampling from the candidate set. To encourage exploration early in training, the probability p_i ∈ (0,1) is initialized to a small value and gradually decays to zero over epochs, ensuring structural determinism during inference. For computational efficiency and reproducibility, the adaptive search space is implemented via dynamic binary masks applied to the initial heterogeneous adjacency matrices. Masked aggregations use sparse tensor operations to manage memory overhead in large-scale biomedical networks.

3.4 Multi-Semantic Structural Modeling Module

(1) Multi-step Weighted residual graph convolution module

This module aims to capture the topological information and structural dependencies of nodes along different semantic paths by integrating multi-hop graph propagation with residual learning. It enhances the expressive power of node features while effectively mitigating issues such as gradient vanishing and over-smoothing during deep propagation. Given the input feature matrix $$X \in R^{N \times d_{m}}$$, where N is the number of nodes and d_m is the input dimension, the model first applies a linear transformation to project all node features into a unified hidden space, as defined in Equation (3):

where $$W_{0} \in R^{d_{m} \times d_{h i d}}$$ denotes the learnable weight matrix and b₀ is a bias term. The initial node representation at layer 0 is denoted as h⁽⁰⁾. Subsequently, the model performs a total of steps of graph convolutional propagation. Each step consists of two components. The first component is sequential graph convolution: at step t ∈ {1, 2……, T}, sparse adjacency propagation is performed as follows.

where $$A_{seq}^{(t)}$$ is the adjacency matrix for the sequential path, Op(·) denotes sparse adjacency propagation, and $$h_{seq}^{(t)}$$ represents the output of the graph convolution at step t. We introduce residual connections at each propagation step to mitigate gradient vanishing and feature over-smoothing. Specifically, at step t, all intermediate representations from previous steps s ∈ {0,1,…..,t-1} are incorporated. Each of these representations is propagated using its corresponding adjacency matrix $$A_{res}^{(t,s)}$$, and then combined via a learnable weighted summation, as defined in Equation (5):

where $$\alpha_{s}^{(t)}$$ denotes a learnable scalar residual weight at step t during training, $$A_{res}^{(t,s)}$$ represents the adjacency matrix used for residual propagation from step s at step t, and h^(s) denotes the node representation obtained after the s-th propagation step. To adaptively balance the information flow across different propagation steps, the residual weights $$\alpha_{s}^{(t)}$$ are implemented as learnable parameters. Specifically, these weights are initialized to a constant value of 1.0 to ensure stable and sufficient signal flow during the initial stages of training. During training, $$\alpha_{s}^{(t)}$$ is jointly optimized with the network backbone using the NAdam optimizer via backpropagation. This dynamic adjustment allows the model to adaptively weight the contributions of higher-order dependencies while effectively mitigating the over-smoothing problem commonly associated with deep GNNs.

The final node representation at step t is obtained by summing the sequential propagation $$\mathrm{h}_{s e q}^{(t)}$$ and residual aggregation results $$\mathrm{h}_{r e s}^{(t)}$$, as defined in Equation (6):

After T propagation steps, the final node representation is obtained as $$\mathrm{h}_{{agg }}^{(t)}$$ To improve stability and accelerate convergence, batch normalization (BN) and a non-linear activation function are applied to the final output $$\mathrm{h}_{{agg }}^{(t)}$$ to enhance the model’s representational capacity, defined as follows:

where σ is the Sigmoid Linear Unit (SiLu) activation function^[35], BN denotes batch normalization^[36], and $${h_{1}^{(T)}}$$ represents the final node embedding obtained from the l-th semantic path after T propagation steps.

(2) Hierarchical gated multi-head attention module

To capture local structural dependencies and integrate multi-view semantic information, the HGMA module uses a hierarchical gated multi-head attention mechanism with two layers. The first layer performs weighted aggregation along distinct semantic paths within each attention head. The second layer then fuses information across heads via a gating mechanism. Concretely, after multi-path residual GCN propagation, the representations of each node across all semantic paths are collected. The final representations from all L paths are stacked along the path dimension into a 3D tensor as follows:

where $${h_{1}^{(T)}}$$ denotes the final node representation under the l-th semantic path, and B denotes the number of nodes. Let L be the number of semantic paths and d the hidden dimension. This tensor is then fed into the attention layers to learn adaptive fusion weights across paths. The first layer applies a path-level attention mechanism to capture representation differences of the same node across different paths. Specifically, for the h-th attention head, a feedforward neural network nonlinearly maps the path representations. A shared linear transformation followed by a Tanh activation function^[37] is applied to all path representations H, producing transformed representations of each path in the attention space as follows:

where $$W_{h}^{(1)} \in R^{d \times d_{a}}$$ is a learnable attention parameter, and d_a denotes the attention dimension, $$S^{(h)} \in R^{B \times L \times d_{a}}$$. Next, an additional linear transformation compresses each path representation. A softmax operation^[38] then normalizes these weights, yielding the attention coefficients:

where $$W_{h}^{(2)} \in R^{d_{a} \times 1}$$ is a learnable attention parameter, and $$ \alpha_{l}^{(h)} \in R^{B \times L \times 1}$$ is the attention weight tensor representing the attention scores of each sample over different paths, with the scores normalized to sum to one across all paths. Subsequently, a weighted sum over all path representations is computed to obtain the aggregated node representation under the corresponding attention head as follows:

where ⊙ denotes element-wise multiplication, and h_l denotes the node representations under the l-th semantic path obtained from Eq. (6). After the first-level attention, each attention head h = {1,…,M} outputs an aggregated node representation o^(h). The representations are then stacked by the formula:

To further regulate the contribution of each attention head to the final representation, a gating mechanism^[39] is introduced to adaptively weight and fuse the outputs of all attention heads. Specifically, mean pooling is first applied along the feature dimension d to each attention head’s output to obtain an average activation value, reflecting the overall contribution of each head to the node representation. This value is then mapped to the range [0,1] via a sigmoid function^[37], producing the gating weights G as follows:

where σ(•) denotes the sigmoid function, which maps the input logit to a probability score in the range (0, 1). Finally, the gating weights G are multiplied element-wise with the attention head outputs, and summed along the head dimension to obtain the final fused representation as follows:

where ⊙ denotes element-wise multiplication, and H_final denotes the final fused node representation obtained by aggregating the outputs of all attention heads through a learnable gating mechanism.

3.5. Information bottleneck module

To learn compact and discriminative drug-target representations, we integrate the IB principle^[13,40] into our framework. IB extracts target-relevant information from inputs by balancing compression and prediction. We adopt a variational implementation, modeling each node representation as a latent probabilistic distribution. Variational inference approximates the posterior, and a Kullback-Leibler (KL) divergence term^[41] regularizes it toward a standard normal prior. This mechanism retains discriminative features and filters redundancy. It guides the model to learn robust and compact embeddings. Specifically, for each drug and target node, the encoder outputs the mean μ and log-variance logσ² of the latent representation, which parameterize a Gaussian distribution as follows:

where diag denotes the operation of converting a vector into a diagonal matrix. Since direct sampling from this distribution does not support gradient backpropagation, the reparameterization trick^[42] is employed to enable differentiable sampling of the latent variables:

where ε denotes a random variable sampled from the standard normal distribution, and ⊙ represents element-wise multiplication. The sampled drug and target representations, Z_s and Z_t, are then used to compute the interaction prediction score, defined as their inner product:

The prediction error is measured using the Binary Cross-Entropy (BCE) loss^[43] between the predicted interaction score and the ground truth label:

where y_i is the ground truth label, s_i is the predicted interaction score, N is the total number of training samples, and σ is the sigmoid function. To regulate the degree of information compression, the KL divergence is introduced as a regularization term, encouraging the latent variable distribution to approximate a unit Gaussian:

The final loss function is formulated as:

where L_BCE is the BCE loss, β is a hyperparameter controlling the strength of the IB regularization, $$L_{K L}^{(S)}$$ and $$L_{K L}^{(t)}$$ denote the KL divergence loss for the drug and target representations, respectively. Theoretically, β acts as a Lagrange multiplier that controls the trade-off between the compression of input information and the preservation of predictive sufficiency. A carefully selected β ensures that the model filters out redundant structural noise inherent in heterogeneous networks while retaining discriminative features for DTI prediction.

4.1. Datasets

To evaluate the proposed method, we used two public benchmark datasets: the Luo dataset^[14] and the Zheng dataset^[44]. The Luo dataset comprises four biomedical entity types (drugs, proteins, diseases, side effects) and multiple relation types (e.g., drug-target, disease-protein, drug-side effect), offering a heterogeneous network with diverse structural information [Table 1]. The Zheng dataset provides rich attribute features—chemical substructures and substituents for drugs, and Gene Ontology (GO) terms for proteins—along with associated edges (e.g., drug-substructure, protein-GO), enabling fine-grained semantic modeling [Table 2].

4.2. Experimental settings

For reproducibility, all code and datasets are available at https://github.com/chenzh-23/HGMAIB. The models were developed with Python 3.8, PyTorch 1.11+cu113, and SciPy 1.10.1. Data are presented as mean ± standard deviation (SD); statistical significance was assessed by an independent two-sample t test (P < 0.05). Training and evaluation ran on a cloud server with an NVIDIA RTX 3090 GPU. HGMAIB was trained using the NAdam optimizer^[45] (learning rate = 0.005, weight decay = 0) for 100 epochs, with 4 attention heads and hidden dimensions of 64 (Luo dataset) or 256 (Zheng dataset). Node2Vec generated initial embeddings (walk length = 100, 10 walks/node, p = q = 1). The IB loss weight β was set to 0.005.

A fivefold crossvalidation strategy was adopted. In each fold, 60% of the samples were used for training, 20% for validation (hyperparameter tuning), and 20% for testing. To address the severe imbalance between known and unknown interactions, negative samples were randomly undersampled to match positive samples per fold. Two standard evaluation metrics widely used in previous studies for assessing binary classification models in DTI prediction were adopted: the Area Under the Receiver Operating Characteristic Curve (AUC)^[46] and the Area Under the Precision-Recall Curve (AUPRC)^[47].

5.1. Comparison with baselines

To comprehensively evaluate HGMAIB, we compare it with twelve baseline methods spanning diverse modeling paradigms. For a fair comparison, architectural hyperparameters (e.g., number of layers, embedding dimensions) follow each baseline’s original optimal settings. Training hyperparameters (learning rate, weight decay, early stopping patience) were systematically retuned for each baseline on the Luo and Zheng datasets using validation set performance within our five-fold cross-validation framework. The baselines include:

• Network-based DTI methods: DTINet^[14] and NeoDTI^[16].

• GNN-based DTI models: GCN-DTI^[17], EEG-DTI^[18], and IMCHGAN^[19].

• Representation enhancement and contrastive learning-based methods: CE-DTI^[23], SGCL-DTI^[24], MIDTI^[27], and SHGCL-DTI^[25].

• Recent state-of-the-art heterogeneous graph frameworks: AMGDTI^[20], DSS-DTI^[26], and DHGT-DTI^[21].

As shown in Table 3, HGMAIB consistently achieves the best performance across all evaluation metrics on both benchmark datasets, significantly outperforming all baseline methods. Specifically, HGMAIB attains values of 0.991 ± 0.002 and 0.990 ± 0.002 on the Luo dataset, and 0.988 ± 0.002 and 0.984 ± 0.001 on the Zheng dataset, demonstrating its superior predictive accuracy and robustness.

Compared with early network-based methods (DTINet, NeoDTI), HGMAIB achieves substantial gains, revealing the limitations of shallow feature projection and simple network integration. Against GNN-based models (GCN-DTI, IMCHGAN), HGMAIB improves performance by explicitly modeling heterogeneous semantic paths rather than relying solely on homogeneous aggregation. It also surpasses contrastive learning methods (CE-DTI, SGCL-DTI, MIDTI, SHGCL-DTI), which lack redundancy suppression; in contrast, HGMAIB’s information bottleneck retains task-relevant features, yielding more discriminative representations. Among recent heterogeneous frameworks, DSS-DTI and DHGT-DTI capture multi-scale or dual-view dependencies, but HGMAIB further integrates hierarchical gated multi-head attention with IB-guided refinement, jointly modeling multi-semantic structures for more robust and accurate DTI prediction. Collectively, these results demonstrate HGMAIB’s ability to capture complex heterogeneous semantics and generate highly discriminative representations.

5.2. Ablation study

To validate the contribution of each component, we designed four ablation experiments targeting the multi-step weighted residual graph convolution, HGMA, IB, and adaptive meta-path search. The results are shown in Figure 3.

Figure 3. Performance comparison of ablation experiments: (A) Results on the Luo dataset; (B) results on the Zheng dataset.

• HGMAIB w/o HGMA: This variant replaces the HGMA module with a single-head attention mechanism, while keeping the remaining architecture unchanged.

• HGMAIB w/o IB: In this variant, the IB loss is substituted with the conventional BCE loss, and all other modules are preserved.

• HGMAIB w/o Multi-hop GCN: This variant replaces the multi-step graph convolution module with a basic first-order graph convolution, removing residual connections and deep structural propagation, with the rest of the framework kept intact.

• HGMAIB w/o Adaptive Meta-path: This variant removes the adaptive meta-path search module and instead adopts a fixed predefined meta-path, namely Drug → Disease → Protein → Protein, as the structural input for message propagation, while keeping all other components unchanged.

The ablation results confirm that removing any component degrades performance. On the Luo dataset, replacing hierarchical gated multi-head attention with single-head attention lowers the AUC to 0.988 and the AUPRC to 0.985, highlighting the importance of multi-head attention with hierarchical gating for multi-semantic aggregation. Replacing the IB loss with standard BCE loss yields a slight performance decrease (AUC 0.987, AUPRC 0.984), validating IB’s role in suppressing redundancy. Removing the adaptive meta-path selection and adopting a fixed semantic path (Drug → Disease → Protein → Protein) further degrades performance (AUC 0.985, AUPRC 0.983). Replacing the multi-step graph convolution and residual connections with a single-layer convolution causes a sharp performance drop on the sparse Luo dataset (AUC and AUPRC both fall to 0.848). With only 1,923 edges among 708 drugs and 1,512 proteins (density ≈ 0.18%), deep multi-hop propagation and residual learning are essential to capture higher-order dependencies. In contrast, on the denser Zheng dataset (11,819 edges, density ≈ 0.69%, nearly four times denser than Luo), the performance loss is much milder (AUC 0.977, AUPRC 0.973). The Zheng dataset contains rich local attributes (881 chemical substructures, 4,098 GO terms), which provide sufficient 1-hop semantic signals, partly alleviating the need for deep propagation. These results confirm that each component of HGMAIB is indispensable, and that the benefit of deep structural propagation depends on the inherent complexity of the biomedical network.

5.3. Effect of node embedding methods

To justify the use of Node2Vec for node initialization in HGMAIB, we compared it with LINE and GraphSAGE on the Luo dataset. All other components (network architecture, training procedure, hyperparameters) were kept identical. As shown in Table 4, Node2Vec achieves the highest predictive performance, outperforming both alternatives. This indicates that Node2Vec more effectively captures the structural and semantic information of heterogeneous nodes in biomedical networks, which is essential for accurate DTI prediction.

5.4. Parameter sensitivity analysis

Parameter sensitivity analysis was conducted on the Luo dataset to evaluate the impact of three key hyperparameters: the number of attention heads, learning rate, and the β coefficient. The number of attention heads (tested in {2, 4, 8, 16}) achieved peak performance with four heads [Figure 4A], indicating that a moderate size optimally balances feature aggregation and computational efficiency. The learning rate (tested in {5e-4, 1e-3, 5e-3, 1e-2}) yielded the best results at 5e-3 [Figure 4B], balancing convergence speed and stability—too small a value slows training, while too large a value causes instability.

Figure 4. The performance of HGMAIB on the Luo dataset under different parameter settings: (A) Number of attention heads; (B) Learning rate; (C) β coefficient.

The β parameter determines the weight of the IB loss and plays a key role in balancing representation learning and regularization. A small β may lead to under-regularization and overfitting, whereas an excessively large β can constrain the model and impair learning. β was evaluated over the set {1e-3, 5e-3, 1e-2, 5e-2}, with optimal performance observed at 5e-3, achieving a favorable trade-off between effective representation learning and appropriate regularization [Figure 4C].

5.5. t-SNE visualization of node embeddings

To evaluate HGMAIB’s representation capability, t-SNE was applied to the Zheng dataset, projecting drug (blue) and target (red) embeddings into a two-dimensional space. As shown in Figure 5A, the initial embeddings exhibit substantial overlap with no distinct clusters, indicating limited semantic discriminability. After training [Figure 5B], the embeddings form compact intra-class clusters with clear inter-class separation and well-defined boundaries. This improvement demonstrates that HGMAIB effectively captures heterogeneous semantic dependencies and topological correlations: the hierarchical gated multi-head attention adaptively aggregates multi-level semantics, while the IB filters redundant signals and preserves task-relevant features. Consequently, HGMAIB produces discriminative, biologically meaningful embeddings, enhancing interpretability and generalization in DTI prediction. Overall, these results confirm HGMAIB’s ability to learn robust representations from complex heterogeneous graphs.

Figure 5. t-SNE visualization of drug and target embeddings on the Zheng dataset. (A) Initial embeddings before training; (B) Learned embeddings after training with the HGMAIB model.

5.6. Computational cost analysis

To improve the completeness of our evaluation and justify the computational cost of the proposed complex modules against baseline methods, we provide a detailed theoretical complexity analysis and an empirical footprint of HGMAIB. Because existing baseline methods are implemented across varied frameworks, making direct empirical runtime comparisons highly hardware-dependent, we focus on asymptotic complexity and actual resource consumption.

The computational complexity of HGMAIB is primarily composed of three phases. In the multi-path graph representation learning phase, multi-step sequential propagation with residual aggregation over P meta-paths incurs a complexity of O(T² × |E| × D + P × N × D), where N is the number of nodes, |E| is the number of edges, D is the hidden dimension, and T is the propagation steps. In the hierarchical attention aggregation phase, path-level and head-level gated attention across M heads contributes O(N × P × D × M + N × M × D). Finally, the IB-based feature compression requires O(N × D²) operations. Consequently, the overall time complexity scales linearly with the number of edges and attention heads, avoiding exponential computational overhead. The space complexity (parameter size and feature storage) is strictly bounded by O(|E|+N × D + P × N × D + N × P × M).

Empirically, to further evaluate the practical efficiency of HGMAIB against baseline scales, we recorded the computational resource consumption during training. On the Luo dataset, each training fold processes approximately 2,300 meta-path-guided subgraph instances (averaging 3,570 nodes and 8.1 million edges per subgraph). Evaluated on a single NVIDIA RTX 3090 GPU, HGMAIB achieves stable training with an average training time of approximately 15 seconds per fold and a remarkably low peak GPU memory usage of 0.38 GB. These empirical results clearly indicate that, despite incorporating advanced modules such as multi-step residual propagation and hierarchical multi-path attention, the parameter footprint and computational overhead of HGMAIB remain highly competitive with basic GNNs. This demonstrates a highly favorable and justifiable trade-off between complex model expressiveness and computational cost in large-scale heterogeneous biomedical networks.