Fair graph neural network training method and system based on two-dimensional structure entropy

Abstract

The invention relates to the technical field of intelligent decision making, in particular to a fair graph neural network training method and system based on two-dimensional structure entropy, and the method comprises the steps: S1, obtaining graph data; s2, constructing an initial weighted adjacency matrix and an initial anchor adjacency matrix; s3, acquiring a learning view and an anchor view according to the current weighted adjacency matrix and the current anchor adjacency matrix; s4, obtaining the two-dimensional structure entropy of the learning view, and calculating the loss of the two-dimensional structure entropy; s5, respectively extracting node representations of the learning view and the anchor view, and calculating symmetric normalized temperature scaling cross entropy loss; s6, obtaining the total optimization loss, training the graph neural network, updating the weighted adjacency matrix and the anchor adjacency matrix, returning to S3 until a preset iteration ending condition is met, and obtaining a trained graph neural network; and S7, inputting the new graph data into the trained graph neural network, and outputting a classification result of whether the user breaks the contract or not. According to the method, the false alarm rate can be effectively controlled while the group fairness is ensured.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of intelligent decision-making, in particular to a fair graph neural network training method and system based on two-dimensional structure entropy. BACKGROUND

[0002] In the financial credit approval system, banks rely on graph neural networks (GNN) to analyze the social relationships of users to assess the default risk. For example, if there is a high-risk individual in the friend circle of a user, the system may mark him as a "potential default". However, existing models often have the phenomenon of over-rejection of users in certain regions, leading to a series of technical operational problems such as increased compliance risk, increased customer attrition rate, and increased probability of regulatory penalties. Traditional GNN aggregates neighbor information through a message passing mechanism to update node representation, but this mechanism amplifies the inherent bias in the graph topology. To alleviate this problem, existing technologies have proposed a variety of fairness-aware GNN methods, mainly including the following categories: such as FairGNN which eliminates sensitive attribute information through adversarial learning, FairVGNN which suppresses bias propagation through dynamic masking, and FairSIN which neutralizes sensitive information through heterogeneous neighbor estimation. These methods mainly focus on optimizing group fairness indicators such as statistical parity (∆SP) and equal opportunity (∆EO).

[0003] However, the above methods have a key defect: while pursuing fairness, they often significantly increase the false positive rate (FPR) of negative samples. For example, in the credit approval scenario, the model may incorrectly determine a large number of creditworthy users as "high risk", triggering an automatic rejection mechanism and causing capital misallocation and customer attrition. This phenomenon of improving fairness with high FPR, i.e. the model achieves prediction consistency across groups by significantly increasing the overall positive class prediction probability, thus formally meeting the fairness indicators, severely damages the practicality and compliance of the system.

[0004] Therefore, existing fair GNN methods lack an effective balance mechanism between fairness and classification performance, especially in controlling FPR. How to improve fairness while effectively controlling FPR and avoiding the phenomenon of "all predictions as positive" false fairness has become a technical problem that needs to be solved in current high-risk decision-making systems. SUMMARY

[0005] The application aims to provide a fair graph neural network training method and system based on two-dimensional structure entropy, to solve the problems of high false positive rate, inconsistent cross-group decision, compliance risk caused by algorithm discrimination and the like caused by graph structure bias amplification in the prior art, so as to reduce the regulatory compliance risk of financial institutions caused by algorithm discrimination and improve the operation stability of the intelligent decision system.

[0006] To achieve the above-mentioned purpose, the application provides the following solutions.

[0007] The application provides a fair graph neural network training method based on two-dimensional structure entropy, comprising:

[0008] S1, obtaining graph data by taking users as a node set, social relationships as an adjacency matrix and user information as node features;

[0009] S2, constructing an initial weighted adjacency matrix and an initial anchor adjacency matrix by taking the graph data as node input information of a graph neural network;

[0010] S3, obtaining a learning view and an anchor view according to a current weighted adjacency matrix and a current anchor adjacency matrix;

[0011] S4, obtaining two-dimensional structure entropy of the learning view and calculating two-dimensional structure entropy loss;

[0012] S5, extracting node representations of the learning view and the anchor view respectively and calculating symmetric normalized temperature scaling cross-entropy loss;

[0013] S6, obtaining an optimization total loss according to the two-dimensional structure entropy loss, the symmetric normalized temperature scaling cross-entropy loss and cross-entropy loss, training the graph neural network, updating the weighted adjacency matrix and the anchor adjacency matrix and returning to S3 until a preset iteration end condition is reached to obtain a trained graph neural network;

[0014] S7, inputting new graph data into the trained graph neural network and outputting a classification result of whether a user defaults.

[0015] Optionally, the initial weighted adjacency matrix is:

[0016] ;

[0017] wherein, is the initial weighted adjacency matrix, is a sigmoid function, is an initialized trainable parameter of an edge between node i and node j;

[0018] The initial anchor adjacency matrix is : wherein, A is an adjacency matrix.

[0019] Optionally, obtaining the two-dimensional structural entropy of the learning view includes:

[0020] The nodes are divided into several sensitive groups based on their sensitive attributes, and the two-dimensional structural entropy of the sensitive groups is calculated based on the learning view.

[0021] The two-dimensional structural entropy for:

[0022] ;

[0023] in, For the learning view, k is the group count of sensitive attributes. Maximum number of groups for sensitive attributes Indicates sensitive attribute subgroups The sum of edge weights, This represents the sum of the edge weights of the learned view at round t. Represents a node The sum of edge weights, Indicates from The sum of the weights of the cross-group edges that originate from.

[0024] Optionally, extracting the node representations of the learning view and the anchor view respectively includes:

[0025] The learning view and the anchor view are extracted by a shared graph neural network encoder, and the node embeddings are mapped by a projection head to obtain the node representations of the learning view and the anchor view.

[0026] Optionally, calculating the symmetric normalized temperature-scaled cross-entropy loss includes:

[0027] ;

[0028] in, To calculate the symmetric normalized temperature-scaled cross-entropy loss for round t, where n is the total number of nodes, , Let p be the positive sample node representing the anchor view and the learning view, respectively. Indicates temperature parameter, Indicates cosine similarity. The negative sample nodes q are represented by the anchor view and the learning view, respectively.

[0029] Optionally, the optimized total loss include:

[0030] ;

[0031] in, and For hyperparameters, To calculate the cross-entropy loss at round t, To calculate the symmetric normalized temperature-scaled cross-entropy loss for round t, To calculate the two-dimensional structural entropy loss at round t.

[0032] Optionally, updating the weighted adjacency matrix and the anchor adjacency matrix includes:

[0033] The weighted adjacency matrix is ​​updated by updating the trainable parameters, wherein the trainable parameters are updated. : In the formula, Indicates the learning rate. For gradient, To calculate the two-dimensional structural entropy loss at round t;

[0034] The anchor adjacency matrix is ​​updated as follows: In the formula, To calculate the anchor adjacency matrix for round t, For parameters, To calculate the anchor adjacency matrix for round t-1, To calculate the weighted adjacency matrix for round t.

[0035] This invention also provides a fair graph neural network training system based on two-dimensional structural entropy, comprising:

[0036] The data acquisition module is used to acquire graph data by using users as a set of nodes, social relationships as an adjacency matrix, and user information as node features.

[0037] The adjacency matrix construction module is used to construct an initial weighted adjacency matrix and an initial anchor adjacency matrix by taking the graph data as the node input information of the graph neural network.

[0038] The graph construction module is used to obtain the learning view and anchor view based on the current weighted adjacency matrix and the current anchor adjacency matrix;

[0039] The 2D structure entropy loss calculation module is used to obtain the 2D structure entropy of the learning view and calculate the 2D structure entropy loss.

[0040] The contrastive learning module is used to extract the node representations of the learning view and the anchor view respectively, and calculate the symmetric normalized temperature scaling cross-entropy loss.

[0041] The graph neural network training module is used to obtain the optimized total loss based on the two-dimensional structure entropy loss, the symmetric normalized temperature scaling cross-entropy loss, and the cross-entropy loss, to train the graph neural network, update the weighted adjacency matrix and the anchor adjacency matrix, and obtain the trained graph neural network.

[0042] The decision output interface is used to input new graph data into the trained graph neural network and output the classification result of whether the user has defaulted.

[0043] The beneficial effects of this invention are as follows:

[0044] Significantly reduced false positive rate: By introducing a two-dimensional structural entropy constraint, this invention significantly reduces the false positive rate for non-target groups while ensuring the overall classification accuracy of the model. This reduces financial losses and decreased customer satisfaction caused by incorrectly rejecting high-quality customers.

[0045] Strong theoretical support: Theorem proofs provide theoretical bounds for fairness indices and FPR;

[0046] Strong structural adaptability: The graph structure learner can automatically adjust the edge weights according to the distribution of sensitive attributes without manual intervention;

[0047] Highly scalable: suitable for various high-risk decision-making scenarios such as credit approval and recruitment screening. Attached Figure Description

[0048] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0049] Figure 1 This is a flowchart of a fair graph neural network training method based on two-dimensional structural entropy, according to an embodiment of the present invention. Detailed Implementation

[0050] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0051] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0052] This embodiment proposes a fair graph neural network training method based on two-dimensional structural entropy, including:

[0053] S1. Obtain graph data by treating users as a set of nodes, social relationships as an adjacency matrix, and user information as node features;

[0054] S2. Using graph data as the node input information of the graph neural network, construct the initial weighted adjacency matrix and the initial anchor adjacency matrix;

[0055] S3. Based on the current weighted adjacency matrix and the current anchor adjacency matrix, obtain the learning view and the anchor view;

[0056] S4. Obtain the two-dimensional structural entropy of the learning view and calculate the two-dimensional structural entropy loss;

[0057] S5. Extract the node representations of the learning view and the anchor view respectively, and calculate the symmetric normalized temperature scaling cross-entropy loss.

[0058] S6. Based on the two-dimensional structure entropy loss, symmetric normalized temperature scaling cross-entropy loss, and cross-entropy loss, obtain the optimized total loss, train the graph neural network, update the weighted adjacency matrix and anchor adjacency matrix, return to S3 until the preset iteration termination condition is reached, and obtain the trained graph neural network.

[0059] S7. Input the new graph data into the trained graph neural network and output the classification result of whether the user has violated the contract.

[0060] Furthermore, obtain the input graph data. ,in For a set of nodes (such as users). It is an adjacency matrix (such as social relationships). This is a node feature matrix (e.g., income, age, occupation). It is based on the node's sensitive attributes. (e.g., gender, region) Divide the nodes into at least two sensitive groups. Initialize trainable parameters for each edge. An initial weighted adjacency matrix is ​​constructed using the sigmoid function. ,satisfy:

[0061] ;

[0062] in, This is the initial weighted adjacency matrix. For the sigmoid function, Initialize trainable parameters for the edge between node i and node j;

[0063] Initial anchor adjacency matrix : , where A is the adjacency matrix.

[0064] Furthermore, obtaining the two-dimensional structural entropy of the learning view includes:

[0065] The nodes are divided into several sensitive groups based on their sensitive attributes, and the two-dimensional structural entropy about the sensitive groups is calculated based on the learning view.

[0066] Two-dimensional structural entropy for:

[0067] ;

[0068] in, For the learning view, k is the group count of sensitive attributes. Maximum number of groups for sensitive attributes Indicates sensitive attribute subgroups The sum of edge weights, This represents the sum of the edge weights of the learned view at round t. Represents a node The sum of edge weights, Indicates from The sum of the weights of the cross-group edges that start from the beginning, where t is the round of calculation.

[0069] Furthermore, the node representations of the learning view and the anchor view are extracted separately, including:

[0070] The learning view and anchor view are extracted by using a shared graph neural network encoder, and the node embeddings are mapped by a projection head to obtain the node representations of the learning view and anchor view.

[0071] Specifically, a shared graph neural network encoder is used. and projector head Extract the node representations from both views, specifically:

[0072] , ;

[0073] , ;

[0074] in, and These are the node representations for the anchor view and the learning view, respectively. and The node embeddings for the anchor view and the learning view are respectively. It is a weighted adjacency matrix.

[0075] Furthermore, symmetric normalized temperature-scaled cross-entropy loss for:

[0076] .

[0077] Furthermore, optimize the total loss. include:

[0078] ;

[0079] in, and For hyperparameters, To calculate the cross-entropy loss at round t, To calculate the symmetric normalized temperature-scaled cross-entropy loss for round t, To calculate the two-dimensional structural entropy loss at round t.

[0080] Specifically, cross-entropy loss is used as the classification loss for the target graph neural network model in the node classification task, that is:

[0081] ;

[0082] In the formula, The output of the classifier for the embedding of nodes in the anchor view. The true category label of the node, i.e. , For classifiers, Embed nodes for anchor views.

[0083] Furthermore, updating the weighted adjacency matrix and the anchor adjacency matrix includes:

[0084] The weighted adjacency matrix is ​​updated by updating the trainable parameters, wherein the trainable parameters are updated. : In the formula, Indicates the learning rate. For gradient, To calculate the two-dimensional structural entropy loss at round t;

[0085] Based on the anchor adjacency matrix: In the formula, To calculate the anchor adjacency matrix for round t, For parameters, To calculate the anchor adjacency matrix for round t-1, To calculate the weighted adjacency matrix for round t.

[0086] This embodiment provides a theoretical and mechanistic approach to simultaneously constrain fairness and false positive rate, aiming to solve the "FPR shortcut" problem in existing technologies. It effectively controls the false positive rate while ensuring group fairness, and avoids the false fairness phenomenon caused by "all predictions being positive".

[0087] The method of this embodiment will be further described below with reference to the accompanying drawings:

[0088] Fair graph neural network training methods based on two-dimensional structural entropy include:

[0089] Obtain the anchor adjacency matrix and initialize the structure learner ;

[0090] The weighted adjacency matrix is ​​initialized and its two-dimensional structural entropy is calculated through sensitive attribute self-organization as the loss to train the structural learner. By sharing GNN parameters and projection head parameters, the contrastive learning loss between the anchor adjacency matrix and the weighted adjacency matrix is ​​further calculated. Finally, the cross-entropy loss of the GNN model on the anchor view is calculated, and the sum of the three losses is used as the overall loss function to train the model, thereby obtaining a fair perception GNN with a low false positive rate.

[0091] like Figure 1 As shown, taking the Credit card dataset as an example, the steps of the fair graph neural network training method based on two-dimensional structural entropy are as follows:

[0092] S1: Initialization phase. Input graph data. Here, V represents the node set (e.g., users), A represents the adjacency matrix (e.g., social relationships), and X represents the node feature matrix. The node feature vector of the node feature matrix consists of demographic features, repayment behavior features, consumption pattern features, income features, age features, occupation features, and credit risk label features. These features serve as the node input signals of the graph neural network. After being encoded by the embedding layer, they participate in graph convolution operations together with the learnable weighted adjacency matrix to generate an implicit representation of user credit risk. Node label Y (whether the user defaults), binary sensitive attribute S (e.g., gender, region); initialize learnable parameters. Construct the initial weighted adjacency matrix Set up the anchor adjacency matrix Initialize the GCN encoder Projector head Classifier .

[0093] S2: Further, during the iterative training phase:

[0094] S21: Specifically, in each calculation round t, construct the anchor view. With learning view ;

[0095] S22: Computational Learning View Two-dimensional structural entropy Calculate the entropy loss of the two-dimensional structure:

[0096] ;

[0097] In the formula, Represents a node The sum of edge weights, Indicates sensitive attribute subgroups The sum of edge weights, Indicates from The sum of the weights of the cross-group edges from which the starting point is located. This represents the sum of the edge weights of the learned view when calculating round t;

[0098] S23: Backpropagation Update : In the formula The learning rate is used to achieve adaptive reweighting of graph structures and enhance information flow across sensitive groups.

[0099] S24: Further calculate the anchor view by sharing GNN parameters and projection head parameters. and learning view The contrast loss;

[0100] Specifically, a shared GCN encoder is used to extract node embeddings: , The projected representation of the node is obtained through mapping by the projection head: , In this embodiment, the comparison loss is calculated using the symmetric normalized temperature-scaled cross-entropy loss (NT-Xent loss):

[0101] ;

[0102] in, To calculate the symmetric normalized temperature-scaled cross-entropy loss for round t, where n is the total number of nodes, , Let p be the positive sample node representing the anchor view and the learning view, respectively. Indicates temperature parameter, Indicates cosine similarity. The negative sample nodes q are represented by the anchor view and the learning view, respectively. To avoid consuming too much spatiotemporal resources in calculating the contrastive loss, the batch size for each contrastive learning session is set to 2000.

[0103] S25: Furthermore, cross-entropy loss is used as the classification loss for the target graph neural network model on the node classification task, that is:

[0104] In the formula The output of the classifier for the embedding of nodes in the anchor view, i.e. ;

[0105] S26: Further, through joint optimization , and This allows the model to improve fairness while reducing the FPR (Fairness Per Principle), i.e., using the Adam algorithm to update the model parameters using gradients to optimize the total loss. ,in for:

[0106] In the formula and For hyperparameters;

[0107] S27: Further, through the structural bootstrapping module, the anchor view anchor adjacency matrix Update, specifically ,in In this embodiment, it is 0.9999. This prevents "inheritance deviation" caused by the anchor view being fixed.

[0108] S3: Inference phase, fix the model parameters, input new graph data, perform forward inference, and output node classification results.

[0109] This embodiment uses the Credit dataset for evaluation, which contains 30,000 users, with gender as the sensitive attribute. The GNN backbone of this embodiment uses a two-layer GCN with 32 hidden layers, two MLP layers as projectors, and one MLP layer as a classifier, with a learning rate of... The hyperparameter is 0.01. and The parameters were 0.5 and 3, respectively, with a temperature parameter of 0.1 and 700 training epochs. The experimental results are shown in Table 1, comparing the performance of our proposed method (FairGSE) with existing mainstream fair graph neural network methods in terms of area under the ROC curve (AUC), false positive rate (FPR), statistical equality difference (ΔSP), and chance equality difference (ΔEO). The ROC (Receiver Operating Characteristic) curve is a commonly used tool for evaluating the performance of classification models. Our proposed method, while maintaining high classification performance, significantly reduced the false positive rate (FPR = 41.45%, better than all compared methods), and achieved ΔSP and ΔEO of 5.09 and 3.37, respectively, outperforming most baseline models. In particular, compared to FairSIN (with an FPR as high as 99.76%), our proposed method effectively avoids the "all predictions are positive" FPR shortcut problem, demonstrating its practical value in high-risk decision-making scenarios.

[0110] Table 1

[0111]

[0112] Furthermore, compared to existing optimal fair graph neural network methods, the FPR is reduced by 58.45%, from 99.76% to 41.45%, effectively avoiding the "FPR shortcut" problem: theoretical proof shows that maximizing the two-dimensional structural entropy can simultaneously constrain the upper bounds of ∆SP, ∆EO and FPR, fundamentally preventing the model from achieving false fairness through "all predictions being positive".

[0113] On the Pokec_n social network dataset, ΔSP reaches 0.90 and ΔEO reaches 1.38, both of which are at the best or second best level. It achieves the best AUC metric on multiple datasets, with an AUC of 74.53% on the Credit dataset.

[0114] This embodiment also provides a fair graph neural network training system based on two-dimensional structural entropy, including:

[0115] The data acquisition module is used to acquire graph data by using users as a set of nodes, social relationships as an adjacency matrix, and user information as node features.

[0116] The adjacency matrix construction module is used to construct the initial weighted adjacency matrix and the initial anchor adjacency matrix by taking graph data as the node input information of the graph neural network.

[0117] The graph construction module is used to obtain the learning view and anchor view based on the current weighted adjacency matrix and the current anchor adjacency matrix;

[0118] The 2D structure entropy loss calculation module is used to obtain the 2D structure entropy of the learning view and calculate the 2D structure entropy loss.

[0119] The contrastive learning module is used to extract node representations from the learning view and the anchor view respectively, and to calculate the symmetric normalized temperature scaling cross-entropy loss.

[0120] The graph neural network training module is used to obtain the optimized total loss based on the two-dimensional structure entropy loss, the symmetric normalized temperature scaling cross-entropy loss, and the cross-entropy loss, to train the graph neural network, update the weighted adjacency matrix and the anchor adjacency matrix, and obtain the trained graph neural network.

[0121] The decision output interface is used to input new graph data into the trained graph neural network and output the classification result of whether the user has violated the agreement.

Claims

1. A fair graph neural network training method based on two-dimensional structural entropy, characterized in that, include: S1. Obtain graph data by treating users as a set of nodes, social relationships as an adjacency matrix, and user information as node features; S2. Using the graph data as the node input information of the graph neural network, construct the initial weighted adjacency matrix and the initial anchor adjacency matrix; S3. Based on the current weighted adjacency matrix and the current anchor adjacency matrix, obtain the learning view and the anchor view; S4. Obtain the two-dimensional structural entropy of the learning view and calculate the two-dimensional structural entropy loss; S5. Extract the node representations of the learning view and the anchor view respectively, and calculate the symmetric normalized temperature scaling cross-entropy loss. S6. Based on the two-dimensional structure entropy loss, the symmetric normalized temperature scaling cross-entropy loss, and the cross-entropy loss, obtain the optimized total loss, train the graph neural network, update the weighted adjacency matrix and anchor adjacency matrix, return to S3 until the preset iteration termination condition is reached, and obtain the trained graph neural network. S7. Input the new graph data into the trained graph neural network and output the classification result of whether the user has violated the contract.

2. The fair graph neural network training method based on two-dimensional structural entropy according to claim 1, characterized in that, The initial weighted adjacency matrix is: ； in, This is the initial weighted adjacency matrix. For the sigmoid function, Initialize trainable parameters for the edge between node i and node j; The initial anchor adjacency matrix : , where A is the adjacency matrix.

3. The fair graph neural network training method based on two-dimensional structural entropy according to claim 1, characterized in that, Obtaining the two-dimensional structural entropy of the learning view includes: The nodes are divided into several sensitive groups based on their sensitive attributes, and the two-dimensional structural entropy of the sensitive groups is calculated based on the learning view. The two-dimensional structural entropy for: ； in, For the learning view, k is the group count of sensitive attributes. Maximum number of groups for sensitive attributes Indicates sensitive attribute subgroups The sum of edge weights, This represents the sum of the edge weights of the learned view at round t. Represents a node The sum of edge weights, Indicates from The sum of the weights of the cross-group edges that originate from.

4. The fair graph neural network training method based on two-dimensional structural entropy according to claim 1, characterized in that, Extracting the node representations of the learning view and the anchor view respectively includes: The learning view and the anchor view are extracted by a shared graph neural network encoder, and the node embeddings are mapped by a projection head to obtain the node representations of the learning view and the anchor view.

5. The fair graph neural network training method based on two-dimensional structural entropy according to claim 1, characterized in that, Calculating the symmetric normalized temperature-scaled cross-entropy loss includes: ； in, To calculate the symmetric normalized temperature-scaled cross-entropy loss for round t, where n is the total number of nodes, , Let p be the positive sample node representing the anchor view and the learning view, respectively. Indicates temperature parameter, Indicates cosine similarity. The negative sample nodes q are represented by the anchor view and the learning view, respectively.

6. The fair graph neural network training method based on two-dimensional structural entropy according to claim 1, characterized in that, The total optimization loss include: ； in, and For hyperparameters, To calculate the cross-entropy loss at round t, To calculate the symmetric normalized temperature-scaled cross-entropy loss for round t, To calculate the two-dimensional structural entropy loss at round t.

7. The fair graph neural network training method based on two-dimensional structural entropy according to claim 2, characterized in that, Updating the weighted adjacency matrix and anchor adjacency matrix includes: The weighted adjacency matrix is ​​updated by updating the trainable parameters, wherein the trainable parameters are updated. : In the formula, Indicates the learning rate. For gradient, To calculate the two-dimensional structural entropy loss at round t; The anchor adjacency matrix is ​​updated as follows: In the formula, To calculate the anchor adjacency matrix for round t, For parameters, To calculate the anchor adjacency matrix for round t-1, To calculate the weighted adjacency matrix for round t.

8. A fair graph neural network training system based on two-dimensional structural entropy, used to implement the fair graph neural network training method based on two-dimensional structural entropy as described in any one of claims 1-7, characterized in that, include: The data acquisition module is used to acquire graph data by using users as a set of nodes, social relationships as an adjacency matrix, and user information as node features. The adjacency matrix construction module is used to construct an initial weighted adjacency matrix and an initial anchor adjacency matrix by taking the graph data as the node input information of the graph neural network. The graph construction module is used to obtain the learning view and anchor view based on the current weighted adjacency matrix and the current anchor adjacency matrix; The 2D structure entropy loss calculation module is used to obtain the 2D structure entropy of the learning view and calculate the 2D structure entropy loss. The contrastive learning module is used to extract the node representations of the learning view and the anchor view respectively, and calculate the symmetric normalized temperature scaling cross-entropy loss. The graph neural network training module is used to obtain the optimized total loss based on the two-dimensional structure entropy loss, the symmetric normalized temperature scaling cross-entropy loss, and the cross-entropy loss, to train the graph neural network, update the weighted adjacency matrix and the anchor adjacency matrix, and obtain the trained graph neural network. The decision output interface is used to input new graph data into the trained graph neural network and output the classification result of whether the user has defaulted.

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