A loan default detection method based on task aggregation and hyperparameter optimization

Abstract

This application relates to a loan default detection method based on task aggregation and hyperparameter optimization. This method constructs corresponding structural feature vectors from the feature vectors of samples in the loan default detection task, and constructs corresponding attribute feature vectors from the labels of the samples. It calculates a comprehensive similarity based on the label similarity and structural feature similarity between the sub-task to be tested and historical sub-tasks. Then, it calculates task aggregation weights based on the comprehensive similarity, and aggregates the structural feature vectors of each historical sub-task in the neighborhood of the sub-task to be tested using these weights. Finally, it fuses the two prediction results obtained from the attribute feature vector of the sub-task to be tested and the aggregated structural feature vector to obtain the final loan default prediction result for the sub-task to be tested. This method fully explores the feature relationships between sub-tasks and improves the accuracy and robustness of default detection by fusing prediction results based on structural feature inference and label attribute inference.

Description

Technical Field

[0001] This application relates to the field of loan default detection technology, and in particular to a loan default detection method based on task aggregation and hyperparameter optimization. Background Technology

[0002] Traditional loan risk assessment methods typically rely on large amounts of historical data and fixed feature engineering strategies. However, in practical applications, due to the rapid iteration of new loan products and the limited sample size in some small-sample scenarios (such as microloans and short-term credit loans), traditional methods face problems such as poor generalization ability and declining prediction accuracy. Furthermore, existing meta-learning methods generally face challenges in multi-task, multi-label loan default detection scenarios, including difficulties in task aggregation, insufficient feature fusion, and poor hyperparameter adaptability.

[0003] Therefore, there is an urgent need for a small-sample loan default detection method that can fully explore the feature relationships between sub-tasks and dynamically adjust the learning strategy to improve the model's adaptability to new tasks and its predictive accuracy. Summary of the Invention

[0004] Therefore, it is necessary to provide a loan default detection method based on task aggregation and hyperparameter optimization, including: S1: Treat the loan default detection task as a subtask, and each subtask shares the parameters of the basic learner; S2: Calculate the structural feature vector of the corresponding subtask based on the feature vectors of all samples in any subtask, and statistically analyze the labels of all samples in the subtask to be tested to obtain the attribute feature vector of the corresponding subtask. S3: Calculate the label similarity between the sub-task to be tested and the historical sub-tasks based on the labels of the samples in the sub-tasks; calculate the structural feature similarity between the sub-task to be tested and the historical sub-tasks based on the structural feature vectors of the sub-tasks; calculate the comprehensive similarity between the sub-task to be tested and the historical sub-tasks based on label similarity and structural feature similarity. S4: Calculate the task aggregation weight based on comprehensive similarity, and aggregate the structural feature vectors of each historical subtask in the neighborhood of the subtask to be tested based on the task aggregation weight; pass the attribute feature vector and the aggregated structural feature vector through the prediction model respectively, and fuse the two prediction results to obtain the final loan default prediction result of the subtask to be tested.

[0005] Beneficial effects: This method constructs corresponding structural feature vectors from the feature vectors of samples in the loan default detection task, and constructs corresponding attribute feature vectors from the labels of the samples; it calculates comprehensive similarity based on the label similarity and structural feature similarity between the subtask to be tested and historical subtasks; then, it calculates task aggregation weights based on comprehensive similarity, and aggregates the structural feature vectors of each historical subtask in the neighborhood of the subtask to be tested using task aggregation weights; finally, it fuses the two prediction results obtained from the attribute feature vector of the subtask to be tested and the aggregated structural feature vector to obtain the final loan default prediction result of the subtask to be tested; this method fully explores the feature relationships between subtasks, and improves the accuracy and robustness of default detection by fusing prediction results based on structural feature inference and label attribute inference. Attached Figure Description

[0006] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0007] Figure 1 This is a flowchart of the loan default detection method based on task aggregation and hyperparameter optimization in the embodiments of this application. Detailed Implementation

[0008] To make the above-mentioned objectives, features, and advantages of this application more apparent and understandable, the specific embodiments of this application are described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of this application. However, this application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of this application. Therefore, this application is not limited to the specific embodiments disclosed below.

[0009] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0010] like Figure 1 As shown, this embodiment provides a loan default detection method based on task aggregation and hyperparameter optimization, including: S1: Treat the loan default detection task as a subtask, and each subtask shares the parameters of the base learner.

[0011] Each sub-task is constructed based on a differentiated combination of loan products and customer groups, reflecting the need for heterogeneous risk assessment in financial business due to differences in region, product category, or user characteristics.

[0012] S2: Calculate the structural feature vector of the corresponding subtask based on the feature vectors of all samples in any subtask, and statistically analyze the labels of all samples in the subtask to be tested to obtain the attribute feature vector of the corresponding subtask.

[0013] Specifically, the elements in the feature vector of the sample include customer information, loan product information, historical performance information, and customer behavior data; Customer information includes occupation type, income level, and education level; Loan product information includes loan amount, loan term, and repayment method; Historical performance information includes the number of times a contract has been overdue and any modifications to the contract. Customer behavior data includes the number of recent loan applications (within the last 12 months), loan renewal records, and the frequency of customer service interactions; The label of a sample includes whether the sample defaulted on a loan within the set observation window. If so, the label value of the sample is 1; otherwise, the label value is 0.

[0014] The label is an objective marker of historical events, independent of subjective classification standards or scoring systems. The model's learning objective is to identify the likelihood of default in a sample based on the structural feature similarity between samples across tasks, thereby achieving loan default detection. This embodiment does not assume a direct or deterministic mapping between any feature and the label; therefore, it aims to model based on structural differences in multi-task data, exploring cross-task transferability under small sample conditions.

[0015] For each subtask, the same base learner is used for initialization, and the parameters of the base learner are shared across different subtasks, with rapid adjustments made on each subtask.

[0016] Furthermore, the formula for calculating the structural feature vector of a subtask is as follows: ; in, This represents the structural feature vector of the i-th subtask; This represents the customer information features of the i-th subtask; This represents the loan product information feature of the i-th subtask; This represents the historical performance information characteristics of the i-th subtask; This represents the customer behavior data characteristics of the i-th subtask; This represents the mean; Indicates variance; Indicates the mode; Represents entropy; Indicates the maximum value; Indicates standard deviation; Indicates income level; Indicates occupation type; Indicates the level of education; Indicates the loan amount; Indicates the loan term; Indicate the repayment method; Indicates the number of times the payment has been overdue in the past; This indicates that the contract has been modified. Indicates the number of recent loan applications; Indicates loan renewal records; This indicates the frequency of customer service interactions.

[0017] The aforementioned structural feature vectors reflect the feature distribution and behavioral performance of samples in each subtask. They are not directly used to predict label results, but only to describe the structural differences between subtasks, and are used for subsequent task aggregation and generation of meta-network parameters.

[0018] Furthermore, the formula for calculating the attribute feature vector of a subtask is: ; in, This represents the attribute feature vector of the i-th subtask; Indicates the tag value; This indicates the proportion of samples that violated the rules in the subtask; This represents the proportion of samples that did not violate the rules in the subtask; This represents the mean; Indicates standard deviation; This represents the mean loan amount corresponding to the sample of defaults; The standard deviation of the loan amount corresponding to the sample of defaults; This represents the sample difficulty feature vector of the i-th subtask in loan default detection, used to quantify the numerical volatility of default samples in the loan amount dimension in the subtask, so as to characterize the modeling difficulty or prediction complexity of the task. This represents the statistical feature vector of the label distribution in the i-th subtask, used to measure the differences in the proportion of default samples and the heterogeneity of the label distribution state in the subtasks, specifically used to describe the similarities and differences in the label distribution structure among the subtasks.

[0019] The attribute feature vector is obtained by statistical analysis of the label information of samples in the subtask and is used to characterize the label distribution state of the task.

[0020] S3: Calculate the label similarity between the subtask to be tested and the historical subtasks based on the labels of the samples in the subtasks; calculate the structural feature similarity between the subtask to be tested and the historical subtasks based on the structural feature vectors of the subtasks; calculate the comprehensive similarity between the subtask to be tested and the historical subtasks based on label similarity and structural feature similarity.

[0021] Specifically, the formula for calculating the label similarity between the subtask to be tested and the historical subtasks is as follows: ; in, Indicates the subtask to be tested With historical subtasks Tag similarity between them; Indicates the subtask to be tested The number of tags; Representing historical subtasks The number of tags; Indicates the subtask to be tested The label value of the a-th sample in the dataset; Representing historical subtasks The label value of the b-th sample; Indicates the subtask to be tested The tag set in; Representing historical subtasks The tag set in; This represents the L2 norm.

[0022] The formula for calculating the structural feature similarity between the subtask to be tested and the historical subtasks is as follows: ; in, Indicates the subtask to be tested With historical subtasks Structural feature similarity between them; Indicates the subtask to be tested The structural feature vector; Representing historical subtasks The structural feature vector; This represents the L2 norm.

[0023] Furthermore, the formula for calculating the comprehensive similarity between the subtask to be tested and the historical subtasks is as follows: ; ; in, Indicates the subtask to be tested With historical subtasks The overall similarity between them; Indicates the weighting coefficient; Indicates the subtask to be tested With historical subtasks Structural feature similarity between them; Indicates the subtask to be tested With historical subtasks Tag similarity between them; Indicates variance.

[0024] S4: Calculate the task aggregation weight based on comprehensive similarity, and aggregate the structural feature vectors of each historical subtask in the neighborhood of the subtask to be tested based on the task aggregation weight; pass the attribute feature vector and the aggregated structural feature vector through the prediction model respectively, and fuse the two prediction results to obtain the final loan default prediction result of the subtask to be tested.

[0025] Specifically, the formula for calculating the aggregated structural feature vector is as follows: ; ; in, Indicates the subtask to be tested The aggregated structural feature vector; m represents the subtask to be tested. Historical subtasks within the neighborhood Quantity; Indicates the subtask to be tested With historical subtasks Task aggregation weights between; Representing historical subtasks The structural feature vector; Indicates the subtask to be tested With historical subtasks The overall similarity between them; Indicates the subtask to be tested With the k-th historical subtask The overall similarity between them.

[0026] By combining structural feature similarity and label similarity, historical subtasks similar to the target subtask are dynamically selected for feature aggregation and expansion, effectively improving learning stability under small sample conditions. Through the aggregation operation of structural feature vectors, structural feature vectors from historically similar subtasks are introduced into small-sample subtasks with limited sample size, thereby alleviating the problem of decreased model generalization ability caused by sample sparsity. Aggregating structural feature vectors not only improves the stability of the input space but also enhances the accuracy of the meta-learner during hyperparameter initialization. This aggregation method further enhances the model's adaptability to heterogeneous tasks, optimizes convergence speed and robustness in multi-task transfer scenarios, and effectively supports the improvement of the credibility of default prediction results.

[0027] To optimize the aggregation results, an aggregation objective function is introduced to minimize the weighted difference between similar tasks. The aggregation objective function is expressed as: ; in, Indicates the aggregate objective function; Indicates the subtask to be tested Quantity; Indicates the subtask to be tested The aggregated structural feature vector; m represents the subtask to be tested. Historical subtasks within the neighborhood Quantity; Indicates the subtask to be tested With historical subtasks Task aggregation weights between; Representing historical subtasks The structural feature vector; The L2 norm is represented; by optimizing the aggregation objective function, the robustness of subtask aggregation and the expressive power of the aggregated structural feature vector are further improved.

[0028] Furthermore, the formula for calculating the final loan default prediction result of the sub-task is as follows: ; ; ; ; ; ; in, Indicates the subtask to be tested Final loan default prediction results; Indicates the contribution weighting coefficient; This represents a prediction model based on aggregated structural feature vectors; This represents a prediction model based on attribute feature vectors; Indicates the subtask to be tested The aggregated structural feature vector; Indicates the subtask to be tested Attribute feature vectors; This represents the first weight generation function based on the structural feature vector; This represents the weight parameters of the first weight generation function; This represents the bias term of the first weight generation function; This represents the second weight generation function based on the attribute feature vector; This represents the weight parameters of the second weight generation function; This represents the bias term of the second weight generation function; Indicates the subtask to be tested The structural feature vector; Represents a non-linear activation function; Represents the prediction model The weights; Represents the prediction model The bias; Represents the prediction model The weights; Represents the prediction model The bias.

[0029] Unlike traditional default detection methods that train directly based on all features, this embodiment designs two independent modeling paths: a prediction model based on aggregated structural feature vectors and a prediction model based on attribute feature vectors. The prediction model based on aggregated structural feature vectors focuses on characterizing the distribution features of customer attributes, loan product characteristics, and behavioral records, making it suitable for risk classification tasks using explicit variables. The prediction model based on attribute feature vectors focuses on the distribution of default labels themselves, uncovering implicit risk patterns reflected in the probability of risk occurrence and the volatility of loan amounts from a historical statistical perspective. The two models complement each other, outputting the final result through a weighted fusion method during the prediction phase, balancing structural stability and label sensitivity, thereby significantly improving risk identification capabilities under small sample conditions.

[0030] In this embodiment, the method further includes dividing the samples in any subtask into a training set and a validation set proportionally, and dynamically adjusting the learning rate and weight decay coefficient of the corresponding subtask based on the attribute feature vector of the subtask. The adjustment formula is as follows: ; ; in, This represents the adjusted learning rate for the i-th subtask; This represents the weight decay coefficient of the i-th subtask after adjustment; Indicates the initial learning rate; This represents the initial weight decay coefficient; This represents the learnable first parameter vector. This represents the learnable second parameter vector. The two parameter vectors are used to adjust the sensitivity of the hyperparameters to different subtasks. Indicates transpose; Let represent the attribute feature vector of the i-th subtask; the learning rate and weight decay coefficient are dynamically adjusted based on the attribute feature vector of the subtask, so that the training process is more adaptable to the characteristics of different loan products.

[0031] Meta-learning is performed on the sub-tasks, and the base learner within the sub-task is updated using the adjusted learning rate and weight decay coefficient on the training set of the corresponding sub-task. The update formula is as follows: ; in, This represents the updated parameters of the base learner within the i-th subtask; This represents the parameters of the base learner before it was updated; Let represent the training set for the i-th subtask; Represents the basic learner; This represents the training loss for the i-th subtask; Indicates training loss The gradient; The validation loss is calculated using the updated base learner from each subtask on the validation set of all subtasks, and the parameters of the meta-network are updated based on the validation loss. The update formula is as follows: ; in, This represents the updated parameters of the meta-network; This represents the parameters before the meta-network update; Indicates the meta-learning rate; Indicates the number of subtasks; This represents the verification set for the i-th subtask; This represents the base learner updated within the i-th subtask; Let represent the verification loss of the i-th subtask; This represents the gradient of the validation loss for all subtasks; The updated meta-network guides the basic learner to learn novel default detection tasks. Based on the structural and attribute feature vectors of each subtask, the meta-network adaptively generates optimization parameters such as meta-learning rate and regularization term, thereby improving the model's generalization ability and convergence efficiency under heterogeneous tasks. This allows the method to adapt to the task heterogeneity problem caused by different customer types, product attributes, and historical behavior differences in loan business. Even under small sample conditions, it can still effectively improve the accuracy and reliability of default risk detection, and is applicable to various segmented credit scenarios such as consumer finance, credit loans, and micro and small enterprise loans.

[0032] It is worth noting that the novel default detection task refers to a loan default detection task that has emerged in the time dimension or data distribution dimension and whose specific feature distribution differs from the historical sub-task. It is essentially a special case of the historical sub-task, that is, it can be a loan default detection task with sparse sample size and / or one that the meta-network has never directly fitted.

[0033] The loan default detection method based on task aggregation and hyperparameter optimization provided in this embodiment has the following beneficial effects: This method constructs corresponding structural feature vectors from the feature vectors of samples in a loan default detection task, and constructs corresponding attribute feature vectors from the labels of the samples. It calculates a comprehensive similarity based on the label similarity and structural feature similarity between the subtask to be tested and historical subtasks. Then, based on the comprehensive similarity, it calculates task aggregation weights, and aggregates the structural feature vectors of each historical subtask within the neighborhood of the subtask to be tested using these weights. Finally, it fuses the two prediction results obtained from the attribute feature vector of the subtask to be tested and the aggregated structural feature vector to arrive at the final loan default prediction result for the subtask to be tested. This method fully explores the feature relationships between subtasks and improves the accuracy and robustness of default detection by fusing prediction results based on structural feature inference and label attribute inference.

[0034] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0035] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A loan default detection method based on task aggregation and hyperparameter optimization, characterized in that, include: S1: Treat the loan default detection task as a subtask, and each subtask shares the parameters of the basic learner; S2: Calculate the structural feature vector of the corresponding subtask based on the feature vectors of all samples in any subtask, and statistically analyze the labels of all samples in the subtask to be tested to obtain the attribute feature vector of the corresponding subtask. S3: Calculate the label similarity between the subtask to be tested and the historical subtasks based on the labels of the samples in the subtasks, and calculate the structural feature similarity between the subtask to be tested and the historical subtasks based on the structural feature vectors of the subtasks. The comprehensive similarity between the subtask to be tested and the historical subtasks is calculated based on label similarity and structural feature similarity. S4: Calculate the task aggregation weight based on comprehensive similarity, and aggregate the structural feature vectors of each historical subtask in the neighborhood of the subtask to be tested based on the task aggregation weight; pass the attribute feature vector and the aggregated structural feature vector through the prediction model respectively, and fuse the two prediction results to obtain the final loan default prediction result of the subtask to be tested.

2. The loan default detection method based on task aggregation and hyperparameter optimization according to claim 1, characterized in that, The elements in the feature vector of the sample include customer information, loan product information, historical performance information, and customer behavior data; Customer information includes occupation type, income level, and education level; Loan product information includes loan amount, loan term, and repayment method; Historical performance information includes the number of times a contract has been overdue and any modifications to the contract. Customer behavior data includes the number of recent loan applications, loan renewal records, and frequency of customer service interactions; The label of a sample includes whether the sample defaulted on a loan within the set observation window. If so, the label value of the sample is 1; otherwise, the label value is 0. 3.The loan default detection method based on task aggregation and hyper-parameter optimization according to claim 2, characterized in that, The formula for calculating the structural feature vector of a subtask is: ； wherein, represents a structural feature vector of the i-th subtask; represents customer information features of the i-th subtask; represents loan product information features of the i-th subtask; represents historical repayment information features of the i-th subtask; represents customer behavior data features of the i-th subtask; represents a mean value; represents a variance; represents a mode; represents an entropy; represents a maximum value; represents a standard deviation; represents an income interval rank; represents a profession type; represents an education rank; represents a loan amount; represents a loan term; represents a repayment method; represents a historical delinquency times; represents a contract modification condition; represents a recent loan application times; represents a loan renewal record; represents a customer service interaction frequency. 4.The loan default detection method based on task aggregation and hyper-parameter optimization according to claim 2, wherein, The formula for calculating the attribute feature vector of a subtask is: ； wherein, denotes the attribute feature vector of the i-th subtask; denotes the label value; denotes the proportion of samples in default in the subtask; denotes the proportion of samples not in default in the subtask; denotes the mean value; denotes the standard deviation; denotes the mean value of the loan amount corresponding to the sample in default; denotes the standard deviation of the loan amount corresponding to the sample in default; denotes the sample difficulty feature vector of the i-th subtask in loan default detection; denotes the statistical feature vector of the label distribution in the i-th subtask. 5.The loan default detection method based on task aggregation and hyper-parameter optimization according to claim 1, wherein, The formula for calculating the label similarity between the subtask to be tested and the historical subtasks is as follows: ； wherein, denotes the label similarity between the subtask to be tested and the historical subtask ; denotes the number of labels of the subtask to be tested ; denotes the number of labels of the historical subtask ; denotes the label value of the a-th sample in the subtask to be tested ; denotes the label value of the b-th sample in the historical subtask ; denotes the label set in the subtask to be tested ; denotes the label set in the historical subtask ; denotes the L2 norm.

6. The loan default detection method based on task aggregation and hyperparameter optimization according to claim 1, characterized in that, The formula for calculating the structural feature similarity between the subtask to be tested and the historical subtasks is as follows: ； in, Indicates the subtask to be tested With historical subtasks Structural feature similarity between them; Indicates the subtask to be tested The structural feature vector; Representing historical subtasks The structural feature vector; This represents the L2 norm.

7. The loan default detection method based on task aggregation and hyperparameter optimization according to claim 1, characterized in that, The formula for calculating the overall similarity between the subtask to be tested and the historical subtasks is as follows: ； ； in, Indicates the subtask to be tested With historical subtasks The overall similarity between them; Indicates the weighting coefficient; Indicates the subtask to be tested With historical subtasks Structural feature similarity between them; Indicates the subtask to be tested With historical subtasks Tag similarity between them; Indicates variance.

8. The loan default detection method based on task aggregation and hyperparameter optimization according to claim 1, characterized in that, The formula for calculating the aggregated structural feature vector is: ； ； in, Indicates the subtask to be tested The aggregated structural feature vector; m represents the subtask to be tested. Historical subtasks within the neighborhood Quantity; Indicates the subtask to be tested With historical subtasks Task aggregation weights between; Representing historical subtasks The structural feature vector; Indicates the subtask to be tested With historical subtasks The overall similarity between them; Indicates the subtask to be tested With the k-th historical subtask The overall similarity between them.

9. The loan default detection method based on task aggregation and hyperparameter optimization according to claim 1, characterized in that, The formula for calculating the final loan default prediction result of the subtask is as follows: ； ； ； ； ； ； in, Indicates the subtask to be tested Final loan default prediction results; Indicates the contribution weighting coefficient; This represents a prediction model based on aggregated structural feature vectors; This represents a prediction model based on attribute feature vectors; Indicates the subtask to be tested The aggregated structural feature vector; Indicates the subtask to be tested Attribute feature vectors; This represents the first weight generation function based on the structural feature vector; This represents the weight parameters of the first weight generation function; This represents the bias term of the first weight generation function; This represents the second weight generation function based on the attribute feature vector; This represents the weight parameters of the second weight generation function; This represents the bias term of the second weight generation function; Indicates the subtask to be tested The structural feature vector; Represents a non-linear activation function; Represents the prediction model The weights; Represents the prediction model The bias; Represents the prediction model The weights; Represents the prediction model The bias.

10. The loan default detection method based on task aggregation and hyperparameter optimization according to claim 1, characterized in that, This also includes dividing the samples in any subtask into training and validation sets proportionally, and dynamically adjusting the learning rate and weight decay coefficient of the corresponding subtask based on the attribute feature vector of the subtask. The adjustment formula is as follows: ； ； in, This represents the adjusted learning rate for the i-th subtask; This represents the weight decay coefficient of the i-th subtask after adjustment; Indicates the initial learning rate; This represents the initial weight decay coefficient; Represents the first parameter vector; Represents the second parameter vector; Indicates transpose; This represents the attribute feature vector of the i-th subtask; Meta-learning is performed on the sub-tasks, and the base learner within the sub-task is updated using the adjusted learning rate and weight decay coefficient on the training set of the corresponding sub-task. The update formula is as follows: ； in, This represents the updated parameters of the base learner within the i-th subtask; This represents the parameters of the base learner before it was updated; Let represent the training set for the i-th subtask; Represents the basic learner; This represents the training loss for the i-th subtask; Indicates training loss The gradient; The validation loss is calculated using the updated base learner from each subtask on the validation set of all subtasks, and the parameters of the meta-network are updated based on the validation loss. The update formula is as follows: ； in, This represents the updated parameters of the meta-network; This represents the parameters before the meta-network update; Indicates the meta-learning rate; Indicates the number of subtasks; This represents the verification set for the i-th subtask; This represents the base learner updated within the i-th subtask; Let represent the verification loss of the i-th subtask; This represents the gradient of the validation loss for all subtasks; The updated meta-network guides the basic learner to learn novel default detection tasks.

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