KAA-based graph neural network enhancement method and system

Abstract

The invention discloses a KAA-based graph neural network enhancement method and system, and the method comprises the steps: 1, constructing a unified scoring function frame, representing a scoring function of an attention graph neural network as a combined function composed of a learnable scoring mapping and a parameter-free alignment function, the learnable scoring mapping being used for calculating importance scores among nodes, and the parameter-free alignment function being used for aligning the importance scores among the nodes; the parameter-free alignment function is used for transforming representations of the central node and the neighbor nodes; step 2, constructing a KAN as a calculation unit of learnable score mapping, wherein the KAN is realized through a learnable B-spline parameterization function; step 3, constructing an MRD index for quantitatively evaluating the expression ability of the scoring functions, and measuring the error upper bound of different scoring functions in node importance ranking; and step 4, applying the scoring function fused with the KAA scoring mechanism to neighbor node scoring calculation of the graph neural network. According to the method, the expression ability, the calculation efficiency and the interpretability of the attention map neural network are remarkably improved.

Description

Technical Field

[0001] The present invention relates to a graph neural network enhancement method based on KAA, and in particular to a graph neural network enhancement method and system based on KAA. Background Art

[0002] Graph neural networks (GNNs) have made significant progress in graph data mining in recent years and have been widely used in tasks such as node classification, link prediction, and graph classification. Among them, attention graph neural networks (AGNNs) introduce an attention mechanism that dynamically adjusts information aggregation weights based on the importance of neighboring nodes, improving the model's expressiveness. However, existing attention GNNs primarily use linear transformations or multi-layer perceptrons (MLPs) for scoring calculations, resulting in limited expressiveness, low computational efficiency, and poor interpretability of the scoring function. Summary of the Invention

[0003] The purpose of the present invention is to overcome the defects of the existing technology of attention graph neural network, such as limited expression ability, low computational efficiency and poor interpretability of scoring function, and to provide a graph neural network enhancement method and system based on KAA.

[0004] The purpose of the present invention is achieved through the following technical solutions: A graph neural network enhancement method based on KAA includes the following steps: Step 1: Construct a unified scoring function framework and express the scoring function of the attention graph neural network as a combination of a learnable scoring map and a parameter-free alignment function. The learnable scoring map is used to calculate the importance scores between nodes, and the parameter-free alignment function is used to transform the representation of the central node and its neighboring nodes. Step 2: Construct KAN as the computational unit of the learnable score mapping. KAN is implemented by a learnable B-spline parameterized function. Step 3: Construct the MRD indicator to quantitatively evaluate the expressiveness of the scoring function and measure the upper bound of the error of different scoring functions in node importance ranking; Step 4: Apply the scoring function integrated with the KAA scoring mechanism to the neighbor node score calculation of the graph neural network.

[0005] KAA, Kolmogorov-Arnold Attention, Kolmogorov-Arnold attention mechanism; KAN, Kolmogorov-Arnold Network, Kolmogorov-Arnold network; MRD, Maximum Ranking Distance, maximum ranking distance.

[0006] KAN is a neural network architecture based on the Kolmogorov-Arnold representation theorem and parameterized by a learnable B-spline function. In the KAA scoring mechanism, the score mapping f is implemented using KAN: where (x1,…,x n ) is the input vector, Φ q and φ q,p The present invention adopts the zero-order B-spline function as the basis function, which has stronger expression ability and higher computational efficiency than traditional linear transformation and MLP.

[0007] In order to quantitatively evaluate the expressive power of different scoring functions, the present invention proposes the MRD index, which is defined as Where Π represents the set of all possible ideal sorts, surface The value of MRD represents the sorted set that can be generated by the scoring function f, and RD is the sorting distance metric function. The smaller the MRD value, the stronger the expressive power of the scoring function. Through theoretical analysis, the present invention proves that the MRD values ​​of the linear transformation and MLP scoring functions have upper bounds. The KAN-based scoring function, even for a single-layer structure, can have an MRD value close to 0, indicating that it has almost unlimited expressive power.

[0008] This solution integrates the KAN network into the scoring process of the attention graph neural network to form a KAA scoring mechanism. In the GAT model, the original scoring function Replaced by This design enables the model to more accurately capture the importance relationship between nodes.

[0009] The KAA scoring mechanism of this solution consists of a unified scoring function framework, a KAN-based learnable scoring mapping module, and the MRD evaluation metric. By introducing the KAN network as the core calculation unit of the scoring function, the present invention uses B-spline for parameterization, improving the nonlinear expression ability of the scoring function. Combined with the maximum ranking distance (MRD) metric, the ranking error of the scoring mechanism is quantitatively analyzed, theoretically improving the expression ability of the scoring function. Finally, the KAA scoring mechanism is adapted to the GAT-based and Transformer-based graph neural networks, optimizing the attention calculation process and improving the generalization ability and computational efficiency of the model in complex graph data tasks.

[0010] Preferably, in step 4, a standardization method is used to normalize the score calculation results. The standardization method is used to normalize the scores to ensure the stability and interpretability of the score distribution.

[0011] Preferably, in step 4, the KAA scoring mechanism is also extended to a multi-head attention architecture. To further improve the expressiveness of the model, the present invention extends the KAA scoring mechanism to a multi-head attention architecture. When the number of heads is K, K independent KANs of the same size are applied, i.e., {KAN 1 ,KAN 2 ,…,KAN K}, and then concatenates the obtained K representations to form the final representation. The multi-head structure enables the model to learn multiple different attention modes simultaneously, further improving the expressive power.

[0012] Preferably, the scoring function of the fusion KAA scoring mechanism is calculated using the following mathematical form: Among them, h i ,h j Represents the representation of the central node and neighbor nodes respectively, AF(h i ,h j ) is a parameter-free alignment function that uses vector concatenation, absolute difference, cosine similarity, or dot product. Represents a function composition operator; KAN consists of multiple B-spline functions B k (x) and the score is calculated as follows: Among them, h i ,h j Represents the representation of the central node and neighbor nodes respectively, AF(h i ,h j ) is a parameter-free alignment function that uses vector concatenation, absolute difference, cosine similarity, or dot product. Represents a function composition operator; KAN consists of multiple B-spline functions B k (x) and the score is calculated as follows.

[0013] Preferably, the MRD indicator calculation formula is as follows: where σ s′ represents the node ordering generated by the scoring function s′, π′ is the set of all possible ideal orderings, RD(σ s′ ,π′) is the ranking error metric function, which calculates the deviation between two rankings.

[0014] A graph neural network enhancement system based on KAA, including the following modules: A data input module, used to receive graph data, including node features and adjacency matrix; The scoring calculation module calculates the importance scores of neighbor nodes based on the KAA scoring function; The information aggregation module uses the normalized scores to perform weighted aggregation on the features of neighbor nodes; The training and inference module performs model training based on the Adam optimizer and is used for prediction in the inference phase; The system executes a KAA-based graph neural network enhancement method at runtime.

[0015] Preferably, the KAA-based graph neural network enhancement system also includes a normalization module to perform Softmax normalization on the score calculation results.

[0016] Preferably, the KAA-based graph neural network enhancement system also includes a multi-head attention module, which adopts multiple KAA scoring functions to learn different attention modes.

[0017] Preferably, the score calculation module uses a single-layer or multi-layer KAN network to calculate the score, and its mathematical form is: Among them, h i ,h j They represent the representation of the central node and the neighboring nodes respectively, k represents the summation index, d represents the summation upper limit, represents the total number of B-spline basis functions, AF(h i ,h j ) is a parameter-free alignment function, φ k B-spline or radial basis function is used for parameterization.

[0018] Preferably, the training and reasoning module adopts an adaptive learning rate adjustment strategy, combined with regularization technology, to optimize the training of the parameters of the KAA scoring mechanism to improve the convergence efficiency and generalization ability of the model.

[0019] The present invention utilizes an adaptive learning rate adjustment strategy, combined with various regularization techniques, to optimize the parameter training process of the KAA scoring mechanism. During the inference phase, the characteristics of the KAN architecture are leveraged to achieve efficient model deployment, making it suitable for a variety of practical application scenarios, such as social network analysis, recommender systems, and molecular graph analysis.

[0020] Compared with the existing technology, the present invention has the following significant advantages: First, the expressive ability of the KAA scoring mechanism is significantly better than that of traditional linear transformation and MLP scoring functions, and can more accurately capture the complex relationships between nodes; Second, the KAA scoring mechanism can be seamlessly integrated into almost all existing attention graph neural networks, and has strong versatility and adaptability; Third, experimental results show that the KAA-enhanced graph neural network has achieved significant performance improvements on multiple benchmark datasets, with the performance of some tasks improved by more than 20%; Finally, the KAA scoring mechanism provides a more intuitive explanation of attention distribution through the visualization of B-spline functions, enhancing the interpretability of the model.

[0021] This paper uses an adaptive learning rate adjustment strategy, combined with various regularization techniques, to optimize the parameter training process of the KAA scoring mechanism. During the inference phase, the characteristics of the KAN architecture are utilized to achieve efficient model deployment, suitable for various practical application scenarios such as social network analysis, recommender systems, and molecular graph analysis.

[0022] In summary, the Kolmogorov-Arnold attention-based graph neural network enhancement method proposed in this paper significantly improves the expressive power, computational efficiency and interpretability of attention graph neural networks by introducing the KAN network as the core computing unit of the scoring function, providing a new research direction and technical path for the development of graph neural networks. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is an overall block diagram of the present invention. DETAILED DESCRIPTION

[0024] The present invention will be further described and illustrated below in conjunction with specific embodiments. The embodiments are merely illustrative of the present disclosure and do not limit its scope. The technical features of the various embodiments of the present invention may be combined accordingly, provided that there is no conflict between them.

[0025] The accompanying drawings are merely schematic illustrations of the present invention and are not necessarily drawn to scale. Some of the blocks shown in the accompanying drawings are functional entities that do not necessarily correspond to physically or logically separate entities. These functional entities may be implemented in software, in one or more hardware modules or integrated circuits, or in different networks and / or processor devices and / or microcontroller devices.

[0026] The flowcharts shown in the accompanying drawings are merely illustrative and do not necessarily include all steps. For example, some steps may be decomposed, while some steps may be combined or partially combined, so the actual execution order may change according to actual circumstances.

[0027] Example: A graph neural network enhancement method based on KAA includes the following steps: Step 1: Construct a unified scoring function framework and express the scoring function of the attention graph neural network as a combination of a learnable scoring map and a parameter-free alignment function. The learnable scoring map is used to calculate the importance scores between nodes, and the parameter-free alignment function is used to transform the representation of the central node and its neighboring nodes. To explain this in detail, we first introduce the necessary formula symbols. represents a graph where Represent the node set and edge set respectively. The node feature can be represented as a matrix in is node v i The features of , d is the dimension of the original node features. A∈{0,1} N×N represents the adjacency matrix, where A i,j =1, if (v i ,v j )=ε. Given a GNN model f, the node representation h i It can be obtained layer by layer through the following expression: in Indicates v at layer l i Node representation of AGG(·) represents an aggregation function, such as summation (GCN) or averaging (GraphSAGE). UPDATE(·) represents a feature transformation function, such as linear transformation or MLP.

[0028] The GNN model with attention introduces an attention mechanism in the aggregation function AGG(·) to adaptively j Assign different weight coefficients α j , which can be expressed as: where α j It is obtained by normalizing the result of the scoring function. Here, the scoring function s(·) calculates the importance score of the adjacent nodes based on the representation of the central node and the adjacent nodes. The scoring functions of the existing attention GNN model can be divided into two categories: GAT-based and Transformer-based. Their representative scoring functions are as follows: For GAT-based scoring functions, many variants replace the concatenation of two representations with alternative operations, such as vector addition or subtraction. In contrast, Transformer-based scoring functions often introduce additional scaling factors. This scheme reduces the above two scoring functions to the following unified form: in is an alignment function without learnable parameters, such as vector concatenation or dot product. Its purpose is to combine the representations of the central node and the neighboring nodes. In addition, It is a score mapping with learnable parameters, typically consisting of multiple linear transformations and possibly some activation functions.

[0029] Step 2: Construct KAN as the computational unit of the learnable score mapping. KAN is implemented by a learnable B-spline parameterized function. The KAN network used in this scheme has an input dimension of n in , the output dimension is n out When the following form is satisfied: x i is the value corresponding to the i-th dimension of x, and φ i,j is a learnable nonlinear function, usually parameterized by B-spline functions or radial basis functions. The specific mapping method is optional in this solution.

[0030] This solution proposes Kolmogorov-Arnold Attention (KAA), which replaces the Ψ of the original scoring function with the KAN network. The specific form is as follows: After obtaining the scores of the node pairs, this aspect will calculate the specific aggregation weight according to the previous formula. This design is very flexible, making KAA applicable to almost all existing GNN models with attention.

[0031] KAA can also be extended to multi-head attention, further improving its performance. When the number of attention heads is K, this scheme applies K independent KANs of the same size {KAN 1 ,…,KAN K} Obtain K different weight coefficients. Then, concatenate the obtained K representations to form the final representation.

[0032] Step 3: Construct the MRD indicator to quantitatively evaluate the expressiveness of the scoring function and measure the upper bound of the error of different scoring functions in node importance ranking; Specifically, the scoring function of the graph neural network with attention generates scores for all neighbor nodes, forming an importance ranking of the neighbor nodes. This scheme formally defines the importance ranking, which has the following definition: Given a scoring function s(·), a central node h i and all its neighbor nodes An importance ranking σ is A permutation of , where σ is a bijective mapping satisfy: Unlike static and dynamic attention, which only focus on identifying the most important neighbors, importance ranking captures the relative importance of all neighboring nodes, providing a more comprehensive evaluation. In practice, under ideal conditions, scoring functions may not always achieve the optimal importance ranking; instead, they try to get as close to the optimal ranking as possible.

[0033] In order to quantitatively evaluate the difference between two rankings, this scheme defines the quantitative gap between two importance rankings as follows: Given two rankings σ1 and σ2 of N nodes, the ranking distance (RD) between them can be calculated by the following formula: in, Returns node v i actual ranking.

[0034] In practical scenarios, the optimal ranking can be any permutation of adjacent nodes. Therefore, the expressive power of the scoring function lies in its ability to generate all possible rankings.

[0035] Based on the node importance ranking and ranking distance, this scheme introduces the concept of maximum ranking distance to quantitatively measure the expressive power of different scoring functions: Given a set of scoring functions A central node has a representation h i , whose neighbor nodes have representation For any We denote the obtained importance ranking as σ s At the same time, all The permutation set of π is a bijection. The maximum ranking distance (MRD) is expressed as follows: Step 4: Apply the scoring function integrated with the KAA scoring mechanism to the neighbor node score calculation of the graph neural network.

[0036] KAA, Kolmogorov-Arnold Attention, Kolmogorov-Arnold attention mechanism; KAN, Kolmogorov-Arnold Network, Kolmogorov-Arnold network; MRD, Maximum Ranking Distance, maximum ranking distance.

[0037] KAN is a neural network architecture based on the Kolmogorov-Arnold representation theorem and parameterized by a learnable B-spline function. In the KAA scoring mechanism, the score mapping f is implemented using KAN: where (x1,…,x n ) is the input vector, Φ q and φ q,p This scheme uses the zero-order B-spline function as the basis function, which has stronger expression ability and higher computational efficiency than traditional linear transformation and MLP.

[0038] In order to quantitatively evaluate the expressive power of different scoring functions, this scheme proposes the MRD indicator, which is defined as Where Π represents the set of all possible ideal sorts, represents the set of sorts generated by the scoring function f, and RD is the sorting distance metric. Smaller MRD values ​​indicate greater expressive power of the scoring function. Through theoretical analysis, this approach demonstrates that the MRD values ​​of linear transformation and MLP scoring functions have upper bounds. Furthermore, the KAN-based scoring function, even with a single-layer structure, can achieve an MRD value close to 0, demonstrating its nearly unlimited expressive power.

[0039] This solution integrates the KAN network into the scoring process of the attention graph neural network to form a KAA scoring mechanism. In the GAT model, the original scoring function Replaced by This design enables the model to more accurately capture the importance relationship between nodes.

[0040] See also Figure 1As shown in the overall block diagram, this scheme first constructs a unified scoring function framework, and uniformly expresses the scoring function of the existing attention graph neural network as a combination of a learnable scoring mapping and a parameter-free alignment function; then introduces the KAN network as the core calculation unit of the scoring mapping, and parameterizes it through the B-spline function to improve the nonlinear expression ability of the scoring function; at the same time, the maximum ranking distance (MRD) indicator is proposed to quantitatively analyze the ranking error of the scoring mechanism, and theoretically improve the expression ability of the scoring function; finally, the KAA scoring mechanism is adapted to the GAT-based and Transformer-based graph neural networks, optimizing the attention calculation process and improving the generalization ability and computational efficiency of the model in complex graph data tasks.

[0041] In step 4, the score calculation results are normalized using a standardization method. The scores are normalized using a standardization method to ensure the stability and interpretability of the score distribution.

[0042] In step 4, the KAA scoring mechanism is also extended to a multi-head attention architecture. To further improve the expressiveness of the model, this solution extends the KAA scoring mechanism to a multi-head attention architecture. When the number of heads is K, K independent KANs of the same size are applied, i.e. {KAN 1 ,KAN 2 ,…,KAN K}, and then concatenates the obtained K representations to form the final representation. The multi-head structure enables the model to learn multiple different attention modes simultaneously, further improving the expressive power.

[0043] This embodiment verifies the specific function of MRD of this scheme through the following example calculation.

[0044] Without loss of generality, this example assumes that the chosen central node is connected to all other nodes in the graph, and All AF(h i ,h j ) is aggregated into an alignment matrix represented as Where N is the number of nodes. At the same time, this example assumes that P is a full-rank circulant matrix The first d columns of N are derived, where N = d 2 (i.e. N>>d).

[0045] (1) Linear Variation Attention MDR Calculation. Most existing GNNs with attention can be classified into this category. Many actual scoring function implementations use multiple continuous learned linear transformations, but theoretically, this does not enhance the expressive power more than using a single fully learned linear transformation, because multiple transformations are equivalent to a single transformation represented by their product. Given an alignment matrix For the form s(hi ,h j )=W·AF(h i ,h j ), Its MRD satisfies the following inequality: (2) MLP attention MDR calculation. Although MLP is a universal approximator under ideal conditions, in practical applications, its expressive power is often limited by its limited width and depth. Given the alignment matrix For the form s(h i ,h j )=w2·(ReLU(W1·AF(h i ,h j )))'s scoring function, where and Its MRD satisfies the following inequality: where λ = d 3 -3d 2 +2d.

[0046] (3) KAA attention MDR calculation. Finally, this example calculates the MRD of the KAA proposed in this scheme. The score mapping in KAA is KAN, which has a representation theorem similar to MLP. Given the alignment matrix For the form The scoring function, where each φ k Composed of d modified zero-order B-spline functions Its MRD satisfies the following inequality: In summary, the following conclusions can be drawn from this example: This example also proves that in practical scenarios with limited parameters, the KAA proposed in this scheme exhibits the strongest expressive power.

[0047] In order to demonstrate the effectiveness of this solution, this embodiment uses the following specific experiments to verify the improvement of this solution on the existing model.

[0048] (1) Data description This example validates the effectiveness of KAA in node-level applications in node classification and link prediction tasks. For the node classification task, four citation network datasets of varying sizes were selected: Cora, CiteSeer, PubMed, and ogbn-arxiv, as well as two product network datasets: Amazon-Computers and Amazon-Photo. The goal of citation networks is to identify the research field of a paper, while product networks involve the classification of products. For the link prediction task, this example selected three citation network datasets: Cora, CiteSeer, and PubMed, to predict whether there are edges between pairs of nodes. Furthermore, for graph-level tasks, this example considered two main categories: graph classification tasks and graph regression tasks. For graph classification, this example selected four datasets from bioinformatics and cheminformatics: PPI, MUTAG, ENZYMES, and PROTEINS. The downstream tasks of these datasets involve predicting the properties of proteins or molecules. For graph regression, this example selected two datasets: ZINC and QM9. Both ZINC and QM9 are molecular datasets.

[0049] (2) Evaluation indicators This experiment uses the following metrics to evaluate model performance: For node classification and graph classification tasks excluding the PPI dataset, this experiment compares the classification accuracy of each method. A higher accuracy indicates more accurate classification. For link prediction, this experiment compares the ROC-AUC metric obtained by each method. A higher ROC-AUC indicates more accurate link prediction. For graph regression, this experiment compares the MAE loss of each method. A lower MAE loss indicates more accurate characterization and better model performance. For graph classification tasks on the PPI dataset, this experiment uses the F1 evaluation metric. A higher F1 indicates more accurate classification.

[0050] (3) Comparison method This experiment selected three GAT-based GNN models with attention as benchmark models. These models have different alignment functions: GAT, GLCN, and CFGAT. In addition, this experiment also selected two Transformer-based benchmark models with different scoring functions: GT and SAN. In the experiment, KAA technology will be applied to each benchmark model, and the experimental results will be compared with the original model results. At the same time, all methods will be compared with the results of GCN, GraphSAGE, and GIN. The node task test results are shown in Table 1, and the graph task test results are shown in Table 2: Table 1: Node task results Table 2: Graph task results The experimental results in Table 1 show that the KAA-enhanced models outperform the original models on all datasets for node-level tasks, with an average improvement of 1.63%. This clearly demonstrates the effectiveness of KAA in enhancing the performance of attention-based GNN models on node-level tasks. For GAT-based models, the original attention-based models fail to outperform all non-attentional models on any dataset or task. This phenomenon suggests that the additional parameters in the existing scoring function fail to effectively improve performance. However, after applying KAA, the performance of these models improves significantly. All KAA-enhanced GAT models outperform the non-attentional models on all tasks and datasets. In contrast, the Transformer-based models perform poorly on the node-level tasks involved. In this case, the benefits of KAA are even more pronounced. Specifically, the KAA-enhanced models achieve an average performance improvement of 2.70% across all tasks and datasets. Overall, KAA can universally enhance the performance of attention-based GNN models on node-level tasks, even narrowing the performance gap between different models.

[0051] The experimental results in Table 2 show that the KAA-enhanced model outperforms the original model on all graph-level datasets. Notably, KAA achieves even more significant performance improvements on graph-level tasks than on node-level tasks. Specifically, KAA achieves an average performance improvement of 7.71% across all graph-level tasks, with improvements exceeding 10% observed in one-third of the tasks and exceeding 5% in two-thirds of the tasks. This significant performance improvement underscores the effectiveness of KAA on graph-level tasks. For GAT-based models, we find significant performance gains with KAA on certain datasets, such as GLCN on the PPI dataset and GAT on the QM9 dataset. In these cases, KAA significantly improves the performance of attention-based GNN models, achieving over 20% improvements. For Transformer-based models, which typically perform better on graph-level tasks, KAA still achieves an average performance improvement of 2.72%. Overall, KAA's outstanding performance on graph-level tasks further demonstrates the significant performance improvement of integrating KAN into the scoring function.

[0052] Based on the same inventive concept, this embodiment also provides a KAA-based graph neural network enhancement system, including the following modules: A data input module, used to receive graph data, including node features and adjacency matrix; The scoring calculation module calculates the importance scores of neighbor nodes based on the KAA scoring function; The information aggregation module uses the normalized scores to perform weighted aggregation on the features of neighbor nodes; The training and inference module performs model training based on the Adam optimizer and is used for prediction in the inference phase; The system executes a KAA-based graph neural network enhancement method at runtime.

[0053] The KAA-based graph neural network enhancement system also includes a normalization module to perform Softmax normalization on the scoring calculation results.

[0054] The KAA-based graph neural network enhancement system also includes a multi-head attention module, which uses multiple KAA scoring functions to learn different attention patterns.

[0055] The scoring calculation module uses a single-layer or multi-layer KAN network to calculate the score, and its mathematical form is: Among them, φ k (x) is parameterized using B-spline or radial basis function.

[0056] The training and inference module adopts an adaptive learning rate adjustment strategy combined with regularization technology to optimize the parameters of the KAA scoring mechanism and improve the convergence efficiency and generalization ability of the model.

[0057] As for the system embodiment, since it basically corresponds to the method embodiment, the relevant parts can be referred to the partial description of the method embodiment, and the implementation methods of the remaining modules will not be repeated here. The system embodiment described above is only illustrative, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of the present invention. Ordinary technicians in this field can understand and implement it without paying any creative work.

[0058] Embodiments of the system of the present invention can be applied to any device with data processing capabilities, such as a computer or other device. System embodiments can be implemented through software, hardware, or a combination of software and hardware. For example, a software implementation, as a logical device, is implemented by a processor of any device with data processing capabilities, reading corresponding computer program instructions from non-volatile memory into internal memory and executing them.

[0059] The above-described embodiments merely illustrate several implementations of the present invention, and while the descriptions are relatively specific and detailed, they are not to be construed as limiting the scope of the present invention. Persons skilled in the art will readily appreciate that variations and modifications may be made without departing from the spirit of the present invention, and all such variations and modifications fall within the scope of protection of the present invention.

Claims

1. A graph neural network enhancement method based on KAA, characterized by: The following steps are involved: Step 1: Construct a unified scoring function framework and express the scoring function of the attention graph neural network as a combination of a learnable scoring map and a parameter-free alignment function. The learnable scoring map is used to calculate the importance scores between nodes, and the parameter-free alignment function is used to transform the representation of the central node and its neighboring nodes. Step 2: Construct KAN as the computational unit of the learnable score mapping. KAN is implemented by a learnable B-spline parameterized function. Step 3: Construct the MRD indicator to quantitatively evaluate the expressiveness of the scoring function and measure the upper bound of the error of different scoring functions in node importance ranking; Step 4: Apply the scoring function integrated with the KAA scoring mechanism to the neighbor node score calculation of the graph neural network.

2. The KAA-based graph neural network enhancement method according to claim 1, characterized in that: In step 4, a standardization method is used to normalize the result of the score calculation.

3. The KAA-based graph neural network enhancement method according to claim 1, characterized in that: In step 4, the KAA scoring mechanism is also extended to a multi-head attention architecture.

4. The KAA-based graph neural network enhancement method according to claim 1, characterized in that: The scoring function of the fusion KAA scoring mechanism is calculated using the following mathematical form: Among them, h i ,h j Represents the representation of the central node and neighbor nodes respectively, AF(h i ,h j ) is a parameter-free alignment function that uses vector concatenation, absolute difference, cosine similarity, or dot product. Represents a function composition operator; KAN consists of multiple B-spline functions B k (x) and the score is calculated as follows: Among them, h i ,h j Represents the representation of the central node and neighbor nodes respectively, AF(h i ,h j ) is a parameter-free alignment function that uses vector concatenation, absolute difference, cosine similarity, or dot product. Represents a function composition operator; KAN consists of multiple B-spline functions B k (x) and the score is calculated as follows.

5. The KAA-based graph neural network enhancement method according to claim 4, characterized in that: The MRD indicator calculation formula is as follows: where σ s′ represents the node ordering generated by the scoring function s′, π′ is the set of all possible ideal orderings, RD(σ s′ ,π′) is the ranking error metric function, which calculates the deviation between two rankings.

6. A graph neural network enhancement system based on KAA, characterized by: Includes the following modules: A data input module, used to receive graph data, including node features and adjacency matrix; The scoring calculation module calculates the importance scores of neighbor nodes based on the KAA scoring function; The information aggregation module uses the normalized scores to perform weighted aggregation on the features of neighbor nodes; The training and inference module performs model training based on the Adam optimizer and is used for prediction in the inference phase; The system executes the KAA-based graph neural network enhancement method as described in claim 1 during operation.

7. The KAA-based graph neural network enhancement system according to claim 6, characterized in that: It also includes a normalization module to perform Softmax normalization on the score calculation results.

8. The KAA-based graph neural network enhancement system according to claim 6, characterized in that: It also includes a multi-head attention module that adopts multiple KAA scoring functions to learn different attention modes.

9. The KAA-based graph neural network enhancement system according to claim 6, characterized in that: The scoring calculation module uses a single-layer or multi-layer KAN network to calculate the score, and its mathematical form is: Among them, h i ,h j They represent the representation of the central node and the neighboring nodes respectively, k represents the summation index, d represents the summation upper limit, represents the total number of B-spline basis functions, AF(h i ,h j ) is a parameter-free alignment function, φ k B-spline or radial basis function is used for parameterization.

10. A KAA-based graph neural network enhancement system according to 6, characterized in that: The training and inference module adopts an adaptive learning rate adjustment strategy combined with regularization technology to optimize the parameters of the KAA scoring mechanism and improve the convergence efficiency and generalization ability of the model.

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