Static IR Drop intelligent prediction system based on heterogeneous feature fusion

Abstract

The invention discloses a static IR Drop intelligent prediction system based on heterogeneous feature fusion, and aims to solve the problems that a traditional IR Drop analysis method is high in calculation complexity and an existing deep learning method cannot effectively capture global spatial features and unit instance topological information of a power transmission network (PDN). According to the framework, double branches of a convolutional neural network (CNN) and a graph neural network (GNN) are combined, and effective extraction and feature fusion compensation of PDN multi-scale global to local space power features are realized through a long-distance and local detail encoder (LLE) and a hierarchical and adjacent compensation group (HACG) module of the CNN branches; pDN topological features of heterogeneous neighbors of different orders are adaptively aggregated through a unit instance voltage aware (CVA) module of a GNN branch. Experimental results show that compared with an existing advanced method, the framework has remarkable advantages in prediction precision, and prediction errors are greatly reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of integrated circuit (IC) design and analysis, and particularly relates to a static IR Drop intelligent prediction system based on heterogeneous feature fusion. Background Art

[0002] In the design of ultra-deep submicron integrated circuits, the IR voltage drop analysis of the power delivery network (PDN) is a core link to ensure chip performance and reliability. The IR voltage drop is caused by the resistance of the current flowing through the PDN, which may lead to voltage fluctuations, timing violations, and even functional failures. Traditional analysis methods are based on numerical simulations (such as the modified nodal analysis, MNA), which require solving high-dimensional linear equations (GV = J), and the computational complexity increases exponentially with the design scale, especially inefficient in non-uniform power grids. Existing acceleration methods (such as the multigrid method, boundary element method) can partially alleviate the computational burden, but still have problems of high memory occupancy and long computational time for large-scale designs.

[0003] In recent years, deep learning methods based on convolutional neural networks (CNNs) (such as IREDGe, MAUnet) have achieved fast IR voltage drop prediction through image-to-image mapping. However, such methods have the following limitations. Due to the local perception characteristics of the convolutional kernel, existing CNN models are difficult to capture the long-distance current superposition effect and the global spatial distribution law of the PDN, resulting in insufficient prediction accuracy for regional hotspots. In addition, the actual current path of the PDN is determined by a non-Euclidean topological structure. When the CNN abstracts the circuit as an image, a single pixel may contain multiple unit instances, resulting in the loss of topological connection relationships and unit-level current interference information. Existing methods rely on single-modal features (image or topology), and their adaptability to complex PDN designs is insufficient. When migrating to new processes or designs, a large amount of labeled data is required for retraining, and the model generalization ability is poor.

[0004] At the same time, graph neural networks (GNNs) have shown potential in circuit topology analysis (such as congestion prediction), but their application in IR voltage drop prediction still faces challenges. Traditional GNNs mostly focus on first-order neighborhood aggregation, ignoring the influence of higher-order neighborhoods on voltage propagation, and it is difficult to comprehensively characterize the multi-order dependence relationships in complex current paths. In addition, existing methods have not effectively designed a differential feature fusion mechanism for heterogeneous edge relationships (such as actual connections and virtual adjacencies), resulting in insufficient integrity and adaptability of topological feature extraction. These problems limit the application potential of existing technologies in efficiently and accurately predicting the IR voltage drop distribution.

[0005] To address the above problems, the present invention proposes an Image-Graph Heterogeneous Fusion Framework (IGHF). By collaborating the CNN and GNN branches, and combining multi-scale spatial features with topological awareness, it significantly improves the IR drop prediction accuracy and generalization performance, providing an efficient and reliable power integrity analysis tool for VLSI design. Summary of the Invention

[0006] Object of the Invention: The object of the present invention is to propose a static IR Drop intelligent prediction system based on heterogeneous feature fusion. By combining the CNN branch and the Graph Neural Network (GNN) branch, it effectively captures the global spatial features and topological information of the PDN, thereby improving the accuracy of IR drop prediction.

[0007] To achieve the above object, the technical solution of the present invention is as follows: A static IRDrop intelligent prediction system based on heterogeneous feature fusion, the system includes

[0008] A data preprocessing and input construction module, used to convert the original chip layout and netlist files into feature images and graph structures;

[0009] The CNN branch, adopting a power multi-scale fusion U-shaped network architecture, including a Long-range and Local Detail Encoder (LLE) and a Hierarchical and Adjacent Compensation Group (HACG) module, is used to extract multi-scale global-to-local PDN spatial features;

[0010] The GNN branch, including a Cell Instance Voltage Awareness module (CVA), is used to perceive the non-Euclidean connection relationship of the PDN and extract topological features;

[0011] A heterogeneous feature fusion module, used to align and fuse the CNN features and GNN features to generate the final IR drop prediction result.

[0012] Specifically as follows:

[0013] The content includes the following steps:

[0014] The present invention first converts the chip layout data into a feature image: Based on spatial coordinate mapping, it extracts the power power, leakage power, and minimum path resistance feature maps, and uses a Permutation Importance (PI) filter to screen the input image features, excluding non-critical features such as switching power and cell frequency for analysis, and retaining features such as total power, leakage power, and minimum path resistance to enhance the analysis convergence and reduce redundant features.

[0015] Based on the.dspf file, an undirected bidirectional heterogeneous graph is constructed to represent the actual non-Euclidean PDN topology. This graph contains all cell instances as vertices, and the connection relationships between them define two edge relationships - the actual physical connection edge (R l) and the virtual space adjacent edge R d , where the virtual edges are dynamically generated by an Euclidean distance threshold (||v i ,v j || 2 ≤δ), thus constructing a non-Euclidean heterogeneous graph data structure.

[0016] In the CNN branch based on multi-scale global-local spatial feature extraction, first, a Long-distance and Local-detail Encoder (LLE) is used to capture multi-scale global and local PDN spatial power features. The LLE combines a Long-distance Module (LRM) and a Local-detail Module (LDM). The LRM is composed of Long-distance Blocks (LRBs), and each LRB consists of a perception network and a Convolutional Feed-Forward Network (FFN). The former introduces a 7×7 large kernel depthwise separable convolution to significantly increase the effective receptive field and contains more extensive power and current distribution information; the latter uses fewer channels and more efficient and dense 1×1 layers to manage the computational workload. The overall design is an inverted bottleneck residual structure to reduce memory costs and add skip connections to avoid gradient vanishing.

[0017] The Local-detail Module (LDM) uses two layers of 3×3 small kernel convolutions and Leaky ReLU activation functions to extract fine-grained local current features; multiple LDMs are stacked to capture multi-scale details.

[0018] The features output by the Long-distance Module (LRM) and the Local-detail Module (LDM) are fused using a 1×1 small kernel convolution operation as the fusion operation to integrate global and local information and form a richer feature representation.

[0019] In the decoder part, a lightweight Group Aggregation Bridge (GAB) is used to design a Hierarchical and Adjacent Compensation Group (HACG) to adaptively rescale and guide the fusion and compensation of encoder features at different scales. The HACG includes two sub-modules: Hierarchical Compensation (HC) and Adjacent Compensation (AC). The HC sub-module first designs multiple groups of dilated convolutions with different dilation rates for the top layer of the decoder, superimposing the feature maps from different encoder levels to more comprehensively model the voltage fluctuation trend. In the specific implementation, the top layer of the decoder combines the outputs from all other encoder levels and adaptively extracts information through multiple groups of dilated convolutions with different dilation rates. This process is achieved through a lightweight Group Aggregation Bridge (GAB) module, which combines depthwise separable convolution and bilinear interpolation to align the feature sizes of the low layer and the high layer and adaptively extracts information through four groups of convolutional groups with different dilation rates.

[0020] The AC sub-module mainly addresses the inevitable local information degradation problem in the downsampling layer. By performing GAB interaction on adjacent encoder feature maps, it adaptively rescales and compensates the corresponding decoder layer. Specifically, GAB interaction is performed on adjacent encoder feature maps to guide the IR down prediction from the high layer to the low layer. Different from traditional direct jump connections, AC reduces the loss of features in the upsampling process by performing feature interaction between adjacent layers.

[0021] In the GNN branch, a Cell Voltage Awareness Module (CVA) is designed: First, through the heterogeneous graph attention layer, it adaptively rescales and aggregates important information from heterogeneous edge connections. For the actual connection edge R l and the virtual adjacency edge R d , it learns the key interactions between nodes to obtain the attention factor, and its average value is also used as the attention factor for the weights of the two heterogeneous edge connections in the propagation layer. For each type of edge relationship (r ∈ {R I , R d}), the attention weight between node v i and its neighbor v j is calculated:

[0022]

[0023] The attention weight is normalized by Softmax, is the attention score between v i and v j in type r, N i represents the neighbor set of v i , as an element of the matrix is the attention weight of v i to v j in type r; after normalization, the neighbor features are weighted and aggregated by edge type to obtain the output feature

[0024]

[0025] and are the input and output of the l-th layer attention layer respectively, r represents the edge type in the relation set R, is the hyperparameter matrix of type r, and the matrix is the attention weight matrix in type r.

[0026] Learn the voltage representation from neighbors through adjacent virtual and physical connections, combining voltage-related features of neighbors at different distances. The MixHop method is adopted, which allows learning the relationships between neighbors at different distances and mixing them through different operators to extract meaningful signals, even in extremely sparse connections. The formula is:

[0027]

[0028] is the adjacency matrix with self-connections, is the mean of the attention weights of all edge types, is the learnable weight.

[0029] Align and fuse the image features extracted by the CNN branch and the graph features extracted by the GNN branch. Specifically, the final graph sequence of the GNN branch is combined with the image output of the CNN branch through a linear fusion method to generate the final IRDrop prediction sequence, making full use of the advantages of both features to improve the accuracy and robustness of the prediction.

[0030] Beneficial effects: The proposed IGHF framework in the present invention effectively solves the problems of traditional CNN methods in IR drop prediction, namely, the difficulty in capturing global features and the lack of PDN topology awareness, through the combination of the CNN branch and the GNN branch. It achieves:

[0031] 1. Significantly improve the prediction accuracy: Compared with the prior art, this framework can significantly improve the accuracy of IR drop prediction, outperforming existing state-of-the-art methods on multiple evaluation metrics. Experiments show that on the public dataset CircuitNet-ICISC, the MAE (Mean Absolute Error) of IGHF is reduced by 24.6% compared with the SOTA method MAUnet (0.378mV vs. 0.501mV), and reduced by 55.0% compared with IREDGe (0.378mV vs. 0.840mV); the PCC (Pearson Correlation Coefficient) reaches 0.973, superior to MAUnet (0.961) and IREDGe (0.927).

[0032] 2. Enhance the robustness of hot spot area prediction: The AMMAE (Average Maximum MAE) index is reduced by 10.5% compared with MAUnet (24.790mV vs. 27.717mV), indicating that IGHF has higher prediction stability for the worst-case scenario (hot spot area).

[0033] 3. Efficient Modeling of Non-Euclidean PDN Topologies: Traditional CNNs cannot directly handle irregularly connected PDN topologies. The cell voltage sensing (CVA) module in the GNN branch solves the limitation of traditional GCNs that only rely on first-order neighbors by fusing self-loop, first-order, and second-order neighbor features through MixHop graph convolution. Experiments show that when only using the GNN branch (without CNN), the MAE is 1.171 mV, significantly outperforming the global performance of pure CNN (0.389 mV), verifying the necessity of topology modeling. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 FIG. is the structural diagram of the IGHF framework,

[0035] Figure 2 FIG. is the structural diagram of the LLE module,

[0036] Figure 3 FIG. is the structural diagram of the HACG module. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0037] The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0038] Embodiment: Refer to Figures 1 - 3 ,, a static IR Drop intelligent prediction system based on heterogeneous feature fusion, the system includes

[0039] A data preprocessing and input construction module for converting the original chip layout and netlist files into feature images and graph structures;

[0040] The CNN branch adopts a power multi-scale fusion U-shaped network architecture, including a long-range and local detail encoder (LLE) and a hierarchical and adjacent compensation group (HACG) module for extracting multi-scale global-to-local PDN spatial features;

[0041] The GNN branch includes a cell instance voltage sensing module (CVA) for sensing the non-Euclidean connection relationship of the PDN and extracting topological features;

[0042] A heterogeneous feature fusion module for aligning and fusing CNN features and GNN features to generate the final IR drop prediction result.

[0043] Among them, the data preprocessing and input construction module is specifically used for:

[0044] Generating a feature image according to the spatial unit coordinate mapping, including features such as total power, leakage power, and minimum path resistance;

[0045] Constructing an unweighted bidirectional heterogeneous graph based on the.dspf file, the graph includes all cell instances and their connection relationships, as well as virtual edges based on the Euclidean distance between cells.

[0046] Among them, the long-range and local detail encoder (LLE) of the CNN branch includes:

[0047] The long-range module (LRM) improves the receptive field through large-kernel depth convolution and captures global PDN features;

[0048] The local detail module (LDM) extracts fine-grained local PDN features through small-kernel convolution;

[0049] The branch fusion layer is used to fuse the features extracted by the LRM and LDM.

[0050] Among them, the long-range module (LRM) specifically includes:

[0051] The perception network introduces large-kernel depth convolution to significantly improve the effective receptive field and contains more extensive power and current distribution information;

[0052] The convolutional feed-forward network (FFN) uses more efficient and dense 1×1 layers to manage the computational workload, including feature dimensions and model non-linearity.

[0053] Among them, the hierarchical and adjacent compensation group (HACG) module of the CNN branch includes:

[0054] The hierarchical compensation (HC) sub-module is used to combine encoder feature maps at different semantic levels and realizes the fusion and interaction of multi-scale information through multiple groups of dilated convolutions;

[0055] The adjacent compensation (AC) sub-module is used to interact with adjacent encoder feature maps, adaptively rescale and compensate the corresponding decoder layers, and reduce information loss during the upsampling process.

[0056] Among them, the cell instance voltage perception module (CVA) of the GNN branch includes:

[0057] The attention layer designs a heterogeneous cell attention mechanism to adaptively rescale and aggregate important information from different types of heterogeneous edge connections;

[0058] The propagation layer learns the voltage representation from neighbor cells through adjacent virtual and actual physical connections and combines voltage-related features of neighbors at different distances using the MixHop method.

[0059] Embodiment 2: Refer to Figure 1 , a static IR Drop intelligent prediction algorithm based on heterogeneous feature fusion, and the specific implementation steps are as follows:

[0060] S1: We use the public CircuitNet-ICISC benchmark dataset, which provides more than 7,000 samples of five open designs at the 28nm process node. Each design contains different layouts, synthesized circuit netlists, and different cell utilizations. The training set and test set are divided into a ratio of 8:2.

[0061] S2: Extract features from the chip layout file and netlist file, including total power consumption, spatial distribution of leakage power consumption, and minimum path resistance features, to form a 320×320 pixel grayscale image. Use the permutation importance algorithm (PI) to screen key features, and randomly permute each channel 100 times. If the MAE change of the model after permutation exceeds the threshold, the feature is retained, otherwise it is removed (such as switch power consumption, effective path resistance).

[0062] S3: Based on the chip's .dspf file, each standard cell instance is a graph node, and the node attributes include total power consumption, leakage power consumption, and minimum path resistance (consistent with the image input). Construct the actual physical connection edge (R l ): If two cells are directly connected by metal wires, add a bidirectional edge. Construct virtual space adjacent edge R d : Calculate the Euclidean distance of the cell center coordinates. If the distance is ≤δ, add a bidirectional virtual edge.

[0063] S4: Use the `HeteroData` object of the PyTorch Geometric library to store nodes and edges, and the node feature dimension is 3.

[0064] S5: In CNN, the power multi-scale fusion Unet architecture is adopted, and the long-range-local encoder LLE contains 4 levels of long-range modules (LRM) and local detail modules (LDM). In the long-range module (LRM), LRM is composed of long-range blocks (LRB), and LRB is composed of a perception network and a convolutional feedforward network (FFN). The perception network adopts an inverted residual structure. It first extracts the global current distribution features through a 3×3 convolution and a large-core deep convolution (7×7 core) to reduce the computational overhead, and finally normalizes through a layer. The convolutional feedforward network uses two 1×1 layers and a GeLU layer to reduce the amount of calculation. In the local detail module (LDM), two small-core convolutions (3×3 cores) and Leaky ReLU activation functions are stacked to capture unit-level current details. The output features of LRM and LDM are fused step by step through the branch fusion layer (3×3 convolution). The overall encoding structure is as follows Figure 2 shown.

[0065] S6: In the decoder's hierarchy and adjacent compensation group HACG ( Figure 3) The hierarchical compensation (HC) module completes multi-level feature integration of encoded features at different scales through the group aggregation bridge (GAB). The adjacent compensation (AC) module uses the group aggregation bridge (GAB) to aggregate and compensate for the information loss during the upsampling process. Finally, it is concatenated with the feature map obtained by trilinear interpolation in the decoder and aggregated through convolution.

[0066] S7: Convert the heterogeneous graph generated in step S2 and the CNN input into sequences as the input of the GNN branch. Align the node features with the image features of the CNN branch through spatial coordinates.

[0067] S8: In the design of the cell instance voltage perception module (CVA), in the attention layer, use the heterogeneous graph attention network (HGAT) activated by Leaky ReLU to calculate the attention scores for each edge type:

[0068]

[0069] S9: Calculate the attention weights for different edge classes through Softmax normalization. The formula is as follows:

[0070]

[0071] Aggregate the node features by weighting them with the attention weights to generate a preliminary topological representation.

[0072] S10: Use MixHop graph convolution to fuse the self-loop, first-order, and second-order neighbor features.

[0073]

[0074] S10: Align and fuse the image features extracted by the CNN branch and the graph features extracted by the GNN branch, and generate the final IR reduction prediction result through a linear fusion module. The prediction result includes the instance sequence and the image output, and their sum is used as the total loss for supervised learning to train the model.

[0075] S11: In the specific implementation process, use a loss function that combines L1 / L2 losses. By combining these two losses, the accuracy and stability of the prediction can be comprehensively considered, and the training effect of the model can be improved. Use the Adam optimizer and perform 5 times of linear warm-up and cosine annealing (1.5×10 -3 ) to (1×10 -5 ).

[0076] S12: Pre-train the CNN branch on 320×320 images for 100 epochs. During this process, a large amount of image data is used to train the CNN network so that it can learn the multi-scale spatial feature representation of the PDN. The purpose of pre-training is to enable the CNN branch to converge quickly in subsequent joint training and provide good initial feature extraction capabilities.

[0077] S13: After the pre-training is completed, freeze the parameters of the CNN branch, then add the GNN branch and the fusion block, and jointly train the GNN branch for 50 rounds. The purpose of doing this is to maintain the effective feature representation already learned by the CNN branch, and at the same time supplement the topological information perception ability of the PDN by introducing the GNN branch, laying the foundation for subsequent joint training. In the training stage, the model generates instance sequences and image outputs, and the sum of the outputs of the two is used as the total loss for supervised learning to simplify the training process.

[0078] S14: Compare the proposed IGHF with two excellent CNN-based methods, including MAUnet and IREDGe. Adopt and comprehensively evaluate accuracy and graph evaluation metrics, including Pearson correlation coefficient (PCC), coefficient of determination R 2 , mean absolute error (MAE) (mV), and average maximum MAE (AMMAE) (mV)}. MAE is used to evaluate the accuracy of predictions. AMMAE is used to evaluate the average error of the maximum IR drop, thereby measuring our prediction performance in the hot spot area.

[0079] S15: Compare the performance of three prediction models (IGHF, IREDGe, MAUnet) on five RTL hardware designs (ZERO-RISCY, RISCY, RISCY-FPU, VORTEX, NVDLA) and the comprehensive results. The results show that the IGHF model is significantly better than the other two models in all metrics (PCC, R 2 , MAE, AMMAE), especially in terms of reducing errors: its comprehensive MAE (0.378) and AMMAE (24.790) are 55% and 40% lower than IREDGe, and 24% and 20% lower than MAUnet respectively. The IREDGe model performs the worst. For example, the MAE on the NVDLA hardware is as high as 5.750, far exceeding IGHF (1.311) and MAUnet (1.374), and the AMMAE on the VORTEX hardware reaches 392.454, revealing the lack of generalization ability for complex hardware. Although MAUnet is inferior to IGHF, its comprehensive PCC (0.961) and R 2(0.874) is close to the IGHF level, indicating a certain competitiveness in the correlation index. From the perspective of hardware differences, the prediction errors of VORTEX and NVDLA are significantly higher than those of the RISCY series of hardware (for example, the AMMAE of IGHF in VORTEX is 267.136, which is 12 times that of RISCY-FPU), suggesting that the complexity or data noise of these two types of hardware may be higher. Generally speaking, IGHF exhibits the best prediction stability and accuracy and is recommended as the first choice for high-precision scenarios.

[0080] It should be noted that the above embodiments are not used to limit the protection scope of the present invention, and equivalent transformations or substitutions made on the basis of the above technical solutions all fall within the protection scope of the claims of the present invention.

Claims

1. A static IR Drop intelligent prediction system based on heterogeneous feature fusion, characterized in that: include: Data preprocessing and input construction module, used to convert raw chip layout and netlist files into feature images and graph structures; The CNN branch adopts a power multi-scale fusion U-shaped network architecture, which includes a long-range and local detail encoder (LLE) and a hierarchical and adjacent compensation group (HACG) module to extract multi-scale global-to-local PDN spatial features; The GNN branch includes a cell instance voltage awareness module (CVA) to perceive the non-Euclidean connectivity of the PDN and extract topological features; The heterogeneous feature fusion module is used to align and fuse CNN features and GNN features to generate the final IR reduction prediction results.

2. The static IR Drop intelligent prediction system based on heterogeneous feature fusion according to claim 1 is characterized in that: The data preprocessing and input construction module is specifically used for: Generate feature images based on spatial unit coordinate mapping, including features such as total power, leakage power, and minimum path resistance; A weightless bidirectional heterogeneous graph is constructed based on the .dspf file, which contains all unit instances and their connection relationships, as well as virtual edges based on the Euclidean distance between units.

3. The static IR Drop intelligent prediction system based on heterogeneous feature fusion according to claim 1 is characterized in that: The long-range and local detail encoder (LLE) of the CNN branch includes: Long-range module (LRM), which improves the receptive field through large-kernel deep convolution and captures global PDN features; Local Detail Module (LDM), extracts fine-grained local PDN features through small kernel convolution; The branch fusion layer is used to fuse the features extracted by LRM and LDM.

4. The static IR Drop intelligent prediction system based on heterogeneous feature fusion according to claim 3 is characterized in that: The Long Range Module (LRM) specifically includes: The perception network introduces large-kernel deep convolution to significantly improve the effective receptive field and include more extensive power and current distribution information; Convolutional Feedforward Networks (FFNs) use more efficient and dense 1×1 layers to manage the computational workload, including feature dimensions and model nonlinearities.

5. The static IR Drop intelligent prediction system based on heterogeneous feature fusion according to claim 1 is characterized in that: The Hierarchical and Adjacent Compensation Group (HACG) module of the CNN branch includes: Hierarchical Compensation (HC) submodule, which is used to combine encoder feature maps at different semantic levels and achieve fusion interaction of multi-scale information through multiple sets of dilated convolutions; The adjacent compensation (AC) submodule is used to adaptively rescale and compensate the corresponding decoder layers by interacting with adjacent encoder feature maps to reduce the information loss during upsampling.

6. The static IR Drop intelligent prediction system based on heterogeneous feature fusion according to claim 1 is characterized in that: The cell instance voltage awareness module (CVA) of the GNN branch includes: Attention layer, designing a heterogeneous unit attention mechanism to adaptively rescale and aggregate important information from different types of heterogeneous edge connections; The propagation layer learns voltage representations from neighboring cells through adjacent virtual and actual physical connections, and adopts the MixHop method to combine voltage-related features of neighbors at different distances.

7. The static IR Drop intelligent prediction system based on heterogeneous feature fusion according to claim 1 is characterized in that: In the GNN branch, a cell voltage awareness module (CVA) is designed: first, through the heterogeneous graph attention layer, the important information from the heterogeneous edge connections is adaptively rescaled and aggregated. l With virtual adjacent edge R d , learn the key interactions between nodes, obtain the attention factor, and use its average value as the attention factor of the two heterogeneous edge connection weights in the propagation layer. I ,R d }), calculate node v i With neighbors v j The attention weights are: Attention weights through Softmax Normalization, is type r in v i and v j The attention score between i Indicates v i The neighbor set of As a matrix An element of type r in v i v j Attention weights; after normalization, neighbor features are weighted and aggregated according to edge type to obtain output features and are the input and output of the lth attention layer, r represents the edge type in the relation set R, is a hyperparameter matrix of type r, the matrix is the attention weight matrix in type r, The voltage representation is learned from neighbors through adjacent virtual and actual physical connections. The voltage-related features of neighbors at different distances are combined. The MixHop method is used to allow learning the relationship between neighbors at different distances and mixing them through different operators to extract meaningful signals, which can be captured even in extremely sparse connections. The formula is: is an adjacency matrix with self-connection, is the mean of the attention weights of all edge types, are learnable weights.

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