Risk assessment method, electronic equipment and storage medium

Abstract

The embodiment of the invention provides a risk assessment method, electronic equipment and a storage medium. The method comprises the steps of obtaining target feature data of a to-be-assessed object; and inputting the target feature data into a risk assessment model to obtain a risk assessment result of the to-be-assessed object, the risk assessment model being obtained based on a trained KAN network, and the KAN network being constructed and initialized based on a trained logistic regression model. According to the embodiment of the invention, the prediction performance can be remarkably improved.

Description

Technical Field

[0001] This application relates to the field of data processing technology, and in particular to a risk assessment method, electronic device, and storage medium. Background Technology

[0002] With the rapid development of fintech, risk assessment in the financial sector has become a crucial part of the core business processes of banks and financial institutions. Accurate risk prediction can not only effectively reduce losses for financial institutions but also improve capital allocation efficiency and promote the healthy development of the financial market. Traditional risk assessment mainly relies on expert experience and simple statistical methods. However, with the rise of big data and artificial intelligence technologies, machine learning models have gradually become the mainstream technical means for risk assessment.

[0003] Currently, the risk assessment field mainly employs the following types of machine learning models: logistic regression models, tree ensemble models, and traditional neural network models. Logistic regression models offer good mathematical interpretability, but their linear assumptions lead to insufficient predictive performance in risk assessment. Tree ensemble models, by constructing and integrating multiple decision trees, can capture complex data patterns and often outperform logistic regression models; however, they struggle to maintain high predictive performance while providing sufficient model interpretability. Traditional neural network models typically employ random initialization strategies, which lack prior knowledge guidance specific to the problem, potentially leading to unstable training, slow convergence, and ultimately unsatisfactory performance. Therefore, improving predictive performance while ensuring model interpretability is a crucial technical challenge. Summary of the Invention

[0004] In view of the above problems, embodiments of this application are proposed to provide a risk assessment method, electronic device, and storage medium that overcomes or at least partially solves the above problems.

[0005] According to a first aspect of the embodiments of this application, a risk assessment method is provided, comprising: Obtain the target feature data of the object to be evaluated; The target feature data is input into the risk assessment model to obtain the risk assessment result of the object to be assessed. The risk assessment model is based on the trained KAN network, which is constructed and initialized based on the trained logistic regression model.

[0006] According to a second aspect of the embodiments of this application, a risk assessment method is provided, comprising: Obtain target feature data of the user to be evaluated, wherein the target feature data is related to the evaluation of credit risk; The target feature data is input into the credit risk assessment model to obtain the credit risk assessment result of the user to be assessed. The credit risk assessment model is based on a trained KAN network, which is constructed and initialized based on a trained logistic regression model. The logistic regression model and the KAN network are trained on a credit dataset. The credit risk assessment result is used to indicate the probability of the user to be assessed defaulting or complying with the agreement.

[0007] According to a third aspect of the embodiments of this application, an electronic device is provided, including: a processor, a memory, and a computer program stored in the memory and executable on the processor, wherein the computer program, when executed by the processor, implements the risk assessment method as described in the first or second aspect.

[0008] According to a fourth aspect of the embodiments of this application, a computer-readable storage medium is provided, on which a computer program is stored, which, when executed by a processor, implements the risk assessment method as described in the first or second aspect.

[0009] According to a fifth aspect of the embodiments of this application, a computer program product is provided, including a computer program or computer instructions, which, when executed by a processor, implement the risk assessment method as described in the first or second aspect.

[0010] The risk assessment method, electronic device, and storage medium provided in this application embodiment input the target feature data of the object to be assessed into a risk assessment model to obtain the risk assessment result of the object to be assessed. The risk assessment model is based on a trained KAN network, which is constructed and initialized based on a trained logistic regression model. By constructing and initializing the KAN network using a trained logistic regression model, the trained KAN network can maintain the inherent interpretability of the model and clearly show the specific contribution of each feature to the final prediction result, meeting the strict requirements for model transparency. Compared with the logistic regression model, it introduces a non-linear feature representation, which can significantly improve prediction performance.

[0011] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, the following are specific embodiments of this application. Attached Figure Description

[0012] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of this application.

[0013] Figure 1 This is a flowchart illustrating the steps of a risk assessment method provided in an embodiment of this application; Figure 2 This is a flowchart of the training process of the KAN network in the embodiments of this application; Figure 3 This is a flowchart of another risk assessment method provided in the embodiments of this application; Figure 4 This is a schematic diagram of a risk assessment system provided in an embodiment of this application; Figure 5 This is a structural block diagram of a risk assessment device provided in an embodiment of this application; Figure 6 This is a structural block diagram of another risk assessment device provided in the embodiments of this application; Figure 7 This is a structural block diagram of an electronic device provided in an embodiment of this application. Detailed Implementation

[0014] It should be noted that the feature data obtained in this application are accessed, collected, stored and used for subsequent analysis and processing after the user or relevant data owner has been clearly informed of the content of the data collection, the purpose of the data, the processing method and other information, and with the consent and authorization of the user or relevant data owner. Furthermore, the application can provide the user or relevant data owner with the means to access, correct or delete the data, as well as the method to revoke consent or authorization.

[0015] Exemplary embodiments of the present application will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present application are shown in the drawings, it should be understood that the present application may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this application will be thorough and complete, and will fully convey the scope of the present application to those skilled in the art.

[0016] In recent years, significant progress has been made in research on technologies based on artificial intelligence, such as computer vision, deep learning, machine learning, image processing, and image recognition. Artificial intelligence (AI) is an emerging science and technology that studies and develops theories, methods, technologies, and application systems to simulate and extend human intelligence. AI is a comprehensive discipline involving numerous technologies, including chips, big data, cloud computing, the Internet of Things, distributed storage, deep learning, machine learning, and neural networks. Computer vision, as an important branch of AI, specifically enables machines to recognize the world. Computer vision technologies typically include face recognition, liveness detection, fingerprint recognition and anti-counterfeiting verification, biometric recognition, face detection, pedestrian detection, object detection, image processing, image recognition, image semantic understanding, image retrieval, text recognition, video processing, video content recognition, 3D reconstruction, virtual reality, augmented reality, simultaneous localization and mapping (SLAM), computational photography, and robot navigation and localization. With the research and advancement of artificial intelligence technology, this technology has been applied in numerous fields, such as security and prevention, urban management, traffic management, building management, park management, facial recognition access control, facial recognition attendance, logistics management, warehouse management, robotics, intelligent marketing, computational photography, mobile imaging, cloud services, smart homes, wearable devices, autonomous driving, autonomous driving, smart healthcare, facial recognition payment, facial recognition unlocking, fingerprint unlocking, identity verification, smart screens, smart TVs, cameras, mobile internet, live streaming, beauty filters, cosmetics, medical aesthetics, and intelligent temperature measurement.

[0017] Currently, the risk assessment field mainly uses the following types of machine learning models: logistic regression models, tree ensemble models, and traditional neural network models.

[0018] Logistic Regression (LR) models, as traditional linear classification models, are widely used in risk assessment. LR models linearly combine input features and use the sigmoid function to map the results to the 0-1 interval, outputting the probability of default. Logistic regression models have good mathematical interpretability, clearly demonstrating the contribution of each feature to default risk.

[0019] Gradient boosting-based tree ensemble models such as XGBoost and LightGBM perform exceptionally well on tabular data, automatically handling feature interactions and nonlinear relationships, and achieving good predictive performance in various risk assessment applications. These models, by constructing and ensembling multiple decision trees, can capture complex data patterns and, in most cases, achieve slightly better performance than logistic regression (LR) models.

[0020] Traditional neural networks such as the Multilayer Perceptron (MLP) have also been applied to risk assessment, learning feature representations through multilayer nonlinear transformations. However, on tabular data, neural networks typically perform worse than tree models specifically designed for tabular data.

[0021] Each of the above models has certain problems.

[0022] Logistic regression models suffer from performance bottlenecks. While existing logistic regression models offer good interpretability, their linear assumptions limit their expressive power. In complex risk assessment scenarios (such as credit scenarios), they often fail to fully exploit nonlinear relationships and interactions between features in the data, resulting in significant room for improvement in predictive performance. Particularly concerning is the Kolmogorov-Smirnov (KS) score, a key performance indicator, where traditional logistic regression models struggle to meet business requirements.

[0023] Tree-based ensemble models face a trade-off between interpretability and performance. While tree-based models (such as XGBoost and LightGBM) exhibit excellent predictive performance, their complex structures, involving numerous decision trees and intricate feature segmentation rules, result in poor interpretability. Consequently, in certain domains, such as finance, it is difficult to clearly explain the model's decision-making logic, creating application barriers in that specific environment. Current technologies struggle to provide sufficient model interpretability while maintaining high predictive performance.

[0024] To address the interpretability issue of tree-based models, posterior interpretation methods such as SHAP (SHapley Additive ex Planations) can be used for interpretability analysis. SHAP, based on the Shapley value concept from game theory, assigns an importance score to each feature, thereby explaining the model's predictions. However, SHAP also has significant limitations: first, it only provides post-hoc explanations and cannot fundamentally change the black-box nature of the model itself; second, SHAP has high computational complexity, especially for large-scale datasets and complex models, significantly increasing computational time costs. Therefore, existing techniques struggle to provide sufficient intrinsic model interpretability while maintaining high predictive performance.

[0025] Traditional neural networks suffer from model initialization and training stability issues. Traditional neural network models typically employ random initialization strategies, which lack prior knowledge specific to the problem, potentially leading to unstable training, slow convergence, and ultimately suboptimal performance. Particularly in applications like credit risk assessment, where model stability is paramount, the lack of effective model initialization methods becomes a significant factor limiting performance improvement.

[0026] There is a lack of effective model fusion strategies. Current technologies lack effective fusion mechanisms between different types of models (such as linear and nonlinear models). Simple model fusion methods often fail to fully utilize the advantages of each model and struggle to achieve significant performance improvements. How to organically combine the interpretability advantages of logistic regression models with the nonlinear fitting capabilities of deep learning models remains a pressing technical challenge.

[0027] The aforementioned problems severely restrict the application effectiveness of risk assessment models in actual business operations, and there is an urgent need for a new technical solution that can maintain good interpretability while significantly improving predictive performance.

[0028] Figure 1 This is a flowchart illustrating the steps of a risk assessment method provided in an embodiment of this application. This method can be applied to electronic devices such as mobile phones, computers, and servers. Figure 1 As shown, the method may include: Step 101: Obtain the target feature data of the object to be evaluated; Step 102: Input the target feature data into the risk assessment model to obtain the risk assessment result of the user to be assessed. The risk assessment model is based on the trained KAN network, which is constructed and initialized based on the trained logistic regression model.

[0029] The risk assessment method provided in this application involves inputting the target feature data of the object to be assessed into a risk assessment model to obtain the risk assessment result of the object to be assessed. The risk assessment model is based on a trained KAN network, which is constructed and initialized based on a trained logistic regression model. By constructing and initializing the KAN network using the trained logistic regression model, the trained KAN network can clearly demonstrate the specific contribution of each feature to the final prediction result, maintain the model's inherent interpretability, and meet the strict requirements for model transparency. Moreover, since the KAN network is constructed and initialized based on the logistic regression model, it introduces a non-linear feature representation compared to the logistic regression model after training. The non-linear feature representation is more complex than the linear feature representation and can more accurately represent the impact of feature data on the output, thus significantly improving prediction performance.

[0030] The risk assessment method provided in this application can assess the risk of any specific scenario, and is particularly applicable to common financial scenarios such as credit scoring, credit limit increase, anti-fraud and marketing in credit scenarios. For example, it can be used for credit risk assessment in credit scenarios and insurance fraud risk assessment in insurance scenarios. In addition, it can also be used for other scenarios that can be assessed using logistic regression models, such as risk assessment of some disasters (such as risk assessment of natural disasters).

[0031] In step 101 above, the target feature data can be the input feature data selected when training the logistic regression model. For example, in a credit scenario, the target feature data can include data such as the income and age of the object to be assessed. The object to be assessed is the object to be subject to risk assessment; for example, in a credit scenario, the object to be assessed can be a credit applicant.

[0032] In step 102 above, the risk assessment model can be an analytical expression converted from the trained KAN network. This analytical expression can clearly show the specific contribution of each feature to the final prediction result, meeting the strict requirements for model transparency.

[0033] Kolmogorov-Arnold Networks (KANs) are a novel neural network architecture whose core idea originates from the Kolmogorov-Arnold representation theorem. By introducing learnable activation functions onto the weights (edges), this network overturns the node activation pattern of traditional multilayer perceptrons, significantly improving the model's ability to approximate complex functions and fit mathematical formulas.

[0034] The KAN network is built and initialized based on the trained logistic regression model. The initialized KAN network has the exact same output as the logistic regression model.

[0035] Figure 2 This is a flowchart of the training process of the KAN network in the embodiments of this application, such as... Figure 2 As shown, the training process of the KAN network includes: Step 201: Based on the training dataset, train the activation function parameters of the initialized KAN network to obtain the trained KAN network. During the training of the initialized KAN network, keep the basic structural parameters of the KAN network fixed.

[0036] The KAN network structure is constructed based on a logistic regression model, and the basic structural parameters and activation function parameters of the constructed KAN network are initialized based on the logistic regression parameters of the trained logistic regression model.

[0037] Before training the model, data preprocessing is required. The system can receive feature data of the evaluation object, which can be represented by an n-dimensional feature vector. The dataset, containing feature data from multiple evaluation objects, is divided into a training dataset, a validation dataset, and an out-of-time (OOT) dataset. Each dataset contains feature data and risk labels; in a credit scenario, risk labels indicate whether a default has occurred. Screening metrics can be used across these datasets to filter the features of the input model. For example, in a credit scenario, metrics such as Weight of Evidence (WoE) and Population Stability Index (PSI) can be used to filter and refine the features of the input model across these datasets.

[0038] An initial logistic regression model is constructed on the training dataset after feature selection, and the feature weight vector is learned using the maximum likelihood estimation method. And the bias term b. The mathematical expression of the logistic regression model is:

[0039] Where P(y=1|X) represents the default probability given the feature vector X, and sigmoid is a logistic function.

[0040] Based on the weight vectors obtained from the training, the input model features are further filtered according to the collinearity of each feature. The filtering method is to delete features with negative weights in the logistic regression model, and then retrain the logistic regression model using the remaining features. The process of training the logistic regression model and filtering features is repeated until the trained logistic regression model does not contain any weights with negative numbers, resulting in the trained logistic regression model. The weight coefficients and bias terms of each input feature are obtained, forming a complete linear classification function.

[0041] After the logistic regression model is trained, a KAN network corresponding to the logistic regression model is constructed, and the basic structural parameters and activation function parameters of the constructed KAN network are initialized according to the logistic regression parameters of the trained logistic regression model.

[0042] Extract the mathematical expression of the trained logistic regression model, i.e., extract all feature weights and bias parameters. Based on the mathematical expression of the logistic regression model, construct the corresponding KAN network structure, and initialize the basic structural parameters and activation function parameters of the constructed KAN network based on the logistic regression parameters such as feature weights and bias parameters.

[0043] After initializing the KAN network, selective parameter fine-tuning is performed on the training dataset (after feature selection during logistic regression model training) to obtain the trained KAN network. During selective parameter fine-tuning, the basic structural parameters of the KAN network can be kept constant while the activation function parameters are optimized. The basic structural parameters determine the network structure of the KAN network. These parameters are inherited from the initialization settings of the logistic regression model, ensuring the network's fundamental linear properties are preserved. Based on the training dataset, the learnable activation function parameters are adaptively adjusted using gradient descent, allowing the activation function on each edge to gradually evolve from an initial linear mapping to a more complex nonlinear function representation. The basic structural parameters can include node bias parameter `node_bias`, node scaling parameter `node_scale`, child node bias parameter `subnode_bias`, and child node scaling parameter `subnode_scale`. The activation function parameters may include: activation function coefficient matrix (act_fun.coef), activation function mask vector (act_fun.mask), base scaling parameter (act_fun.scale_base), spline scaling parameter (act_fun.scale_sp), and the mask parameter of the symbolic function (symbolic_fun.mask) and affine transformation parameter (symbolic_fun.affine).

[0044] Through a selective parameter optimization strategy, the KAN network can automatically learn and capture nonlinear relationships and feature interaction patterns in the data while maintaining the interpretability of the logistic regression model. The entire optimization process is based on the backpropagation algorithm to achieve end-to-end automatic learning, autonomously adjusting the learnable activation function parameters according to the gradient information of the loss function, without the need for manual setting or intervention in the optimization process.

[0045] After initializing the KAN network in the manner described above, the initialized KAN network can be fine-tuned based on the training dataset. For example, the Adam Optimizer can be used to update the parameters, with a learning rate of 0.001 (the learning rate may need to be adjusted appropriately depending on the amount of data), and the number of training epochs can be 100-200.

[0046] After optimization, the KAN network can be evaluated using out-of-time sample datasets to calculate evaluation metrics, such as KS scores and AUC values ​​in credit scenarios. The optimized KAN network can then be used for risk assessment, outputting risk assessment results while maintaining the interpretability of the model's decision-making process.

[0047] Compared to traditional logistic regression methods, the embodiments of this application show improved KS scores on the OOT dataset, representing a significant performance improvement in the field of risk assessment. This enables more accurate identification of high-risk objects and can reduce credit losses for financial institutions in credit scenarios. Unlike traditional tree-based models, the KAN network-based method of this application maintains inherent interpretability similar to logistic regression models. The learning process of each side function is transparent, clearly demonstrating the specific contribution of each feature to the final prediction result, meeting the strict requirements for model transparency. The embodiments of this application solve the technical challenge of balancing performance and interpretability in traditional methods, significantly improving prediction performance while maintaining model interpretability, providing financial institutions with a technical solution that meets both business performance requirements and regulatory requirements. The embodiments of this application use a logistic regression model for intelligent initialization of the KAN network, avoiding training instability issues that may be caused by random initialization (ablation experiments have confirmed that randomly initialized KANs have almost no predictive effect on risk control OOT data), improving the reliability and convergence speed of model training, and reducing the technical risks of model development and deployment.

[0048] In some embodiments of this application, the logistic regression model includes a linear component, an exponential function, and a sigmoid function; The KAN network includes an input layer, a first network layer, a second network layer, and a third network layer; The number of input nodes in the input layer is the same as the number of input features in the linear part; The first network layer corresponds to the linear part, the second network layer corresponds to the exponential function, and the third network layer corresponds to the sigmoid function.

[0049] Mathematical expression based on the above logistic regression model The linear part is The exponential function is c = exp(-a), the sigmoid function is 1 / (1 + c), and c > 0.

[0050] Based on the logistic regression parameters of the trained logistic regression model, a corresponding KAN network structure is constructed. Besides the input layer, the KAN network can employ a three-layer architecture, with each layer containing multiple nodes connected by learnable side functions (i.e., activation functions). The input layer of the KAN network can be constructed based on the number of input features in the linear part of the logistic regression model, ensuring that the number of input nodes in the input layer is the same as the number of input features in the linear part. The first network layer of the KAN network is constructed based on the linear part of the logistic regression model; the second network layer is constructed based on the exponential function of the logistic regression model; and the third network layer is constructed based on the sigmoid function of the logistic regression model. The third network layer is the output layer, a single-node binary classification structure. The side functions between the first and second network layers are initialized to exponential functions, and the side functions between the second and third network layers are initialized to sigmoid functions. These two side functions are the basic structural parameters of the KAN network structure and remain fixed during training, while the side functions between the input layer and the first network layer are trained and optimized.

[0051] By constructing the KAN network based on the logistic regression model, it is easier to initialize the KAN network with the logistic regression parameters of the logistic regression model, maintain the interpretability of the model, and improve the stability of KAN network training.

[0052] In some embodiments of the present invention, the edge function between the input node and the network node in the first network layer is initialized based on the linear function corresponding to the input feature in the linear part.

[0053] The side functions of the first layer of the KAN network are initialized as the corresponding linear functions in logistic regression. Specifically, for the linear part of the logistic regression model... Each feature The corresponding edge functions (i.e., the edge functions between the input node and the network nodes in the first network layer) are initialized as linear functions. This ensures that the initialized KAN network has the exact same output as the logistic regression model. The side functions between the first and second network layers can be initialized in the same way as the KAN network, and the side functions between the second and third network layers can also be initialized. Furthermore, the bias term 'b' of the logistic regression model can be mapped to the corresponding node bias parameters of the KAN network.

[0054] By using a logistic regression model for intelligent initialization of the KAN network, the training instability that may be caused by random initialization is avoided, improving the reliability and convergence speed of model training and reducing the technical risks of model development and deployment.

[0055] In some embodiments of this application, before training the activation function parameters of the initialized KAN network based on the training dataset to obtain the trained KAN network, the method includes: performing preliminary training on the initialized KAN network according to multiple candidate hyperparameters based on the training dataset to obtain a preliminarily trained KAN network corresponding to each candidate hyperparameter; determining a first evaluation index value of the preliminarily trained KAN network on an out-of-time sample dataset for each candidate hyperparameter; and determining the candidate hyperparameter with the largest first evaluation index value as the target hyperparameter for training the initialized KAN network.

[0056] Among them, the evaluation index is a metric used to evaluate the risk assessment performance of the model. For example, in a credit scenario, the evaluation index may include KS and / or AUC, that is, the first evaluation index value may include the first KS value and / or the first AUC value.

[0057] During the fine-tuning of the KAN network, some key hyperparameters (such as the learning rate) have a significant impact on the final model's performance. To ensure the model's generalization ability on out-of-time (OOT) datasets, a systematic hyperparameter search can be performed before formal training.

[0058] A grid search strategy can be used to iterate through hyperparameters such as the learning rate. Several candidate learning rate values ​​(e.g., 1e-2, 5e-3, 1e-3, 5e-4, 1e-4, etc.) can be set as candidate hyperparameters. For each candidate hyperparameter, the KAN network training process is executed, i.e., initializing the KAN network and loading logistic regression parameters, performing fine-tuning of the KAN network, resulting in a pre-trained KAN network corresponding to each candidate hyperparameter. For each candidate hyperparameter, an evaluation metric value is calculated on an out-of-time sample dataset to obtain the first evaluation metric value, which serves as the evaluation basis for that candidate hyperparameter; the candidate hyperparameter with the largest first evaluation metric value is retained. Finally, the hyperparameter that performs best on the out-of-time sample dataset is selected as the final target hyperparameter. This target hyperparameter can then be used to perform final training of the KAN network on the training dataset, improving the model's stability and generalization performance.

[0059] This step effectively avoids underfitting or overfitting of the model due to improper settings of hyperparameters such as the learning rate, and further enhances the model's risk assessment capability under different time distributions.

[0060] In some embodiments, multiple KAN networks with different initialization strategies can be trained, and the trained KAN networks can be integrated for prediction using a weighted average or voting mechanism to further improve the prediction accuracy and stability of the model.

[0061] Taking credit risk assessment as an example, after training the initial KAN network, performance can be evaluated on out-of-time (OOT) datasets: prediction probability calculation: for the input feature vector X, the KAN network outputs the default probability P_KAN(y=1|X); performance index calculation: calculate key evaluation indicators such as KS value and area under the curve (AUC); model deployment: deploy the trained KAN network to the production environment to perform real-time risk assessment on new credit applications.

[0062] In some embodiments of this application, the step of training the activation function parameters of the initialized KAN network based on the training dataset to obtain a trained KAN network includes: training the activation function parameters of the initialized KAN network using reinforcement learning based on the training dataset to obtain a trained KAN network.

[0063] When training an initialized KAN network based on a training dataset, in addition to traditional supervised training, reinforcement learning can also be used. Reinforcement learning aims to further improve the model's evaluation metrics (such as KS and AUC values) and generalization ability on out-of-time (OOT) datasets, especially its performance on evaluation metrics. Compared to traditional supervised fine-tuning methods (such as SFT), reinforcement learning can directly guide the model to learn a better output policy through the reward function.

[0064] In the credit scenario, the reward function of the reinforcement learning method may include KS and / or AUC (Area Under the Curve). AUC is defined as the area enclosed by the ROC (Receiver Operating Characteristic curve) and the coordinate axis.

[0065] In some embodiments, when training an initialized KAN network using reinforcement learning, the following steps can be followed: 1. Definition of State Space The current state of the agent is defined as a batch feature vector X_train_batch from the training set, i.e.: state = X_train_batch ∈ R^{B×n} where B is the batch size and n is the feature dimension.

[0066] 2. Definition of Action Space The KAN model is used as the policy network to generate the default probability output p = P(y=1|X) for each sample. That is, each sample in the current batch is input into the KAN network to obtain the risk assessment probability of each sample (such as the default probability in a credit scenario). Based on this probability, Bernoulli distribution sampling is performed to obtain the model's action: action∈ {0,1}^B, where action_i ~ Bernoulli(p_i), and each action represents the KAN network's binary classification prediction of whether the sample has risk.

[0067] 3. Definition of reward function The reward function is the overall prediction performance of the current KAN model on the training dataset, and it is calculated as follows: The feature vector X_train is input into the current KAN model, which generates the predicted probability p_train = sigmoid(KAN(X_train)). The predicted probability is converted into a binary classification prediction result y_pred_train = 1 (p_train>0.5). The predicted probability is compared with the true label y_true_train, and the KS value or AUC is calculated as the reward function. Taking the KS value as the reward function as an example, the reward function reward corresponding to this batch can be expressed as: reward = KS(y_true_train, y_pred_train).

[0068] 4. Policy Gradient Training Training is performed using a policy gradient method (e.g., REINFORCE), with KS and / or AUC as the reward function, aiming to maximize the expected value of KS or AUC. The specific steps are as follows: Calculate the log-probability of all sampling actions in the current batch:

[0069] in, Represents the i-th sample (input features are...) Sampling action () The corresponding logarithmic probability; Construct the loss function using the global reward function reward, and subtract the baseline to reduce variance: loss = - log(p) × (reward - baseline); The trainable parameters (i.e. activation function parameters) of the KAN model are updated using the gradient descent algorithm.

[0070] By training the initial KAN network using reinforcement learning, the KAN network can be guided to learn a better output strategy, thereby improving the model's predictive performance.

[0071] In some embodiments of this application, the step of training the activation function parameters of the initialized KAN network based on the training dataset to obtain a trained KAN network includes: training the activation function parameters of the initialized KAN network for the current round based on the training dataset, determining and recording the second evaluation index value of the KAN network trained in the current round on the out-of-time sample dataset; iteratively executing the operations of training the activation function parameters of the KAN network for the current round based on the training dataset and determining and recording the second evaluation index value, until the loss function of the KAN network converges and the second evaluation index value converges, thereby obtaining a trained KAN network.

[0072] Among them, the evaluation index is a metric used to evaluate the risk assessment performance of the model. For example, in a credit scenario, the evaluation index may include KS and / or AUC, that is, the second evaluation index value may include a second KS value and / or a second AUC value.

[0073] Since the out-of-time sample dataset and the training dataset are from different time periods, there may be a significant distributional shift between them. During the training of the KAN network (including traditional supervised training and reinforcement learning training), a phenomenon may occur where the loss function on the training dataset does not decrease during training, but the evaluation metric value on the out-of-time sample dataset continues to rise. Therefore, this embodiment suggests: using a larger number of training epochs (e.g., 200-500); using an early-stopping strategy to monitor the second evaluation metric value on the out-of-time sample dataset; recording the second evaluation metric value on the out-of-time sample dataset after each training epoch, and using the trend of the second evaluation metric value curve across epochs as a model tuning metric. Iteratively training the KAN network and recording the second evaluation metric value until the KAN network's loss function converges and the second evaluation metric value converges. This trained KAN network can improve the evaluation metric value on the out-of-time sample dataset, further improving prediction performance.

[0074] Figure 3 This is a flowchart illustrating another risk assessment method provided in this application embodiment. This method can be applied to electronic devices such as mobile phones, computers, and servers. Figure 3 As shown, the method may include: Step 301: Obtain the target feature data of the user to be evaluated, wherein the target feature data is data related to the evaluation of credit risk; Step 302: Input the target feature data into the credit risk assessment model to obtain the credit risk assessment result of the user to be assessed. The credit risk assessment model is based on the trained KAN network. The KAN network is constructed and initialized based on the trained logistic regression model. The logistic regression model and the KAN network are trained on the credit dataset. The credit risk assessment result is used to indicate the probability of the user to be assessed defaulting or complying with the agreement.

[0075] The risk assessment method provided in this application involves inputting the target feature data of the user to be assessed into a credit risk assessment model to obtain the credit risk assessment result of the user. The credit risk assessment model is based on a trained KAN network, which is constructed and initialized based on a trained logistic regression model. By constructing and initializing the KAN network using the trained logistic regression model, the trained KAN network can clearly demonstrate the specific contribution of each feature to the final prediction result, maintain the model's inherent interpretability, and meet the strict requirements of financial regulation for model transparency. Moreover, since the KAN network is constructed and initialized based on the logistic regression model, it introduces a non-linear feature representation compared to the logistic regression model after training. The non-linear feature representation is more complex than the linear feature representation and can more accurately represent the impact of feature data on the output, thus significantly improving prediction performance.

[0076] In step 301 above, the target feature can be an input feature selected when training the logistic regression model, and the target feature can include data such as income and age. The user to be evaluated is the user for whom credit risk assessment is to be conducted; for example, the user to be evaluated can be a credit applicant.

[0077] In step 302 above, the credit risk assessment model can be an analytical expression derived from the trained KAN network. This analytical expression clearly demonstrates the specific contribution of each feature to the final prediction result, meeting the stringent requirements for model transparency. Each sample in the credit dataset includes feature data and labeled data, where the labeled data includes default or compliance data.

[0078] In some embodiments of this application, the training process of the KAN network includes: Based on the training dataset, the activation function parameters of the initialized KAN network are trained to obtain the trained KAN network. During the training of the initialized KAN network, the basic structural parameters of the KAN network are kept fixed. The KAN network structure is constructed based on a logistic regression model, and the basic structural parameters and activation function parameters of the constructed KAN network are initialized based on the logistic regression parameters of the trained logistic regression model.

[0079] In some embodiments, training the activation function parameters of the initialized KAN network based on the training dataset to obtain a trained KAN network includes: training the activation function parameters of the initialized KAN network using reinforcement learning based on the credit dataset to obtain a trained KAN network, wherein the reward function of the reinforcement learning method includes KS and / or AUC.

[0080] The training process of the KAN network (including its construction, initialization, and training) and the reinforcement learning process can be referred to the above embodiments, and will not be repeated here. However, in this credit scenario, the evaluation metrics mentioned above may include the KS value and / or AUC value. During the reinforcement learning process, by using KS and / or AUC as reward functions, the KAN network can be guided to learn a better output policy, thereby improving the model's predictive performance and increasing the KS value and AUC of the model on the OOT dataset.

[0081] Figure 4 This is a schematic diagram of a risk assessment system provided in an embodiment of this application, such as... Figure 4 As shown, the risk assessment system comprises five core components: a data preprocessing module, a logistic regression training module, a KAN network initialization module, a KAN network fine-tuning and optimization module, and a risk prediction module.

[0082] The data preprocessing module is used to receive, clean, feature-engineer, and standardize credit data. It divides the dataset into training, validation, and out-of-time sample datasets and performs feature selection. The data preprocessing module includes a data interface submodule, a data cleaning submodule, a data standardization submodule, and a feature selection submodule. The data interface submodule supports access to multiple data sources, including relational databases, file systems, and real-time data streams.

[0083] The logistic regression training module is used to implement the training and parameter extraction functions of the logistic regression model. The logistic regression training module includes a model training submodule, a parameter extraction submodule, and a performance evaluation submodule. The model training submodule uses the maximum likelihood estimation algorithm, the parameter extraction submodule is responsible for obtaining the weight vector and bias term, and the performance evaluation submodule calculates the benchmark performance index.

[0084] The KAN network initialization module is responsible for the structural design, parameter initialization, and network configuration of the KAN network. It includes a network architecture design submodule, a parameter initialization submodule, and a network configuration submodule. The network architecture design submodule automatically determines the network structure based on the input feature dimensions, while the parameter initialization submodule implements the parameter mapping from the logistic regression model to the KAN network.

[0085] The KAN network fine-tuning and optimization module implements the selective parameter fine-tuning function of the KAN network. This module includes a parameter classification submodule, a gradient calculation submodule, a parameter update submodule, and a performance monitoring submodule. The parameter classification submodule distinguishes between fixed parameters (basic structural parameters) and trainable parameters (activation function parameters). The gradient calculation submodule implements the backpropagation algorithm. The parameter update submodule uses the Adam optimizer for parameter adjustment and combines supervised fine-tuning and reinforcement learning methods for model training. The performance monitoring submodule is responsible for monitoring the model's performance changes on the test set and OOT in each training epoch.

[0086] The risk prediction module is responsible for the final credit risk prediction and output. It includes a prediction calculation submodule and a results visualization submodule. The prediction calculation submodule uses a trained KAN network to calculate risk assessment probabilities (such as the probability of default in a credit scenario), while the results visualization submodule provides interpretability analysis of the model's decisions.

[0087] Unlike the random initialization of traditional neural networks, this application adopts an intelligent initialization strategy based on logistic regression. Through mathematical mapping, it ensures that the initialized KAN network has the same output as the logistic regression model, providing a good starting point for subsequent optimization. This application innovatively proposes a selective parameter fine-tuning mechanism, optimizing only the key parameters that affect the nonlinear mapping capability while keeping the basic structural parameters unchanged. This strategy ensures both performance improvement and maintains the interpretability of the model. By retaining the linear basic structure of the logistic regression model and introducing nonlinearity only at the side function level, the interpretability of the model is successfully maintained. Moreover, depending on the data, the logistic regression model is simplified to different degrees after fine-tuning the KAN network, making the contribution of each feature clearly traceable and meeting financial regulatory requirements.

[0088] Experimental results show that, compared with the traditional logistic regression method, the KS value of the embodiments in this application is improved from 0.327 to 0.339 on a real credit scenario test set, and from 0.065 to 0.090 on the OOT dataset, an improvement of 0.025 points. Meanwhile, the model's interpretability score remains at a higher level than the logistic regression model and significantly outperforms tree-based models such as XGBoost.

[0089] It should be noted that, for the sake of simplicity, the method embodiments are all described as a series of actions. However, those skilled in the art should understand that the embodiments of this application are not limited to the described order of actions, because according to the embodiments of this application, some steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should also understand that the embodiments described in the specification are all preferred embodiments, and the actions involved are not necessarily required by the embodiments of this application.

[0090] Figure 5 This is a structural block diagram of a risk assessment device provided in an embodiment of this application, such as... Figure 5 As shown, the risk assessment device may include: The feature acquisition module 501 is used to acquire the target feature data of the object to be evaluated. The risk assessment module 502 is used to input the target feature data into the risk assessment model to obtain the credit risk assessment result of the object to be assessed. The risk assessment model is based on the trained KAN network, which is constructed and initialized based on the trained logistic regression model.

[0091] Optionally, the device further includes: The KAN network training module is used to train the activation function parameters of an initialized KAN network based on a training dataset to obtain a trained KAN network. During the training of the initialized KAN network, the basic structural parameters of the KAN network are kept fixed. The KAN network structure is constructed based on a logistic regression model, and the basic structural parameters and activation function parameters of the constructed KAN network are initialized based on the logistic regression parameters of the trained logistic regression model.

[0092] Optionally, the logistic regression model includes a linear component, an exponential function, and a sigmoid function; The KAN network includes an input layer, a first network layer, a second network layer, and a third network layer; The number of input nodes in the input layer is the same as the number of input features in the linear part; The first network layer corresponds to the linear part, the second network layer corresponds to the exponential function, and the third network layer corresponds to the sigmoid function.

[0093] Optionally, the edge function between the input node and the network node in the first network layer is initialized based on the linear function corresponding to the input feature in the linear part.

[0094] Optionally, the basic structure parameters include: node offset parameters, node scaling parameters, child node offset parameters, and child node scaling parameters.

[0095] Optionally, the KAN network training module is specifically used for: Based on the training dataset, the activation function parameters of the initialized KAN network are trained using reinforcement learning to obtain the trained KAN network.

[0096] Optionally, the device further includes a hyperparameter search module, the hyperparameter search module being used for: Based on the training dataset, the initialized KAN network is initially trained according to multiple candidate hyperparameters to obtain the initially trained KAN network corresponding to each candidate hyperparameter. For each of the candidate hyperparameters, determine the first evaluation index value of the preliminarily trained KAN network on the out-of-time sample dataset; The candidate hyperparameter with the largest value of the first evaluation index is determined as the target hyperparameter for training the initialized KAN network.

[0097] Optionally, the KAN network training module is specifically used for: Based on the training dataset, after training the activation function parameters of the initialized KAN network for the current round, the second evaluation index value of the KAN network after the current round of training on the out-of-time sample dataset is determined and recorded. Iteratively execute the operation of training the activation function parameters of the KAN network in the current round based on the training dataset and determining and recording the value of the second evaluation index, until the loss function of the KAN network converges and the value of the second evaluation index converges, thus obtaining the trained KAN network.

[0098] For the specific implementation process of the functions corresponding to each module and unit in the device provided in this application embodiment, please refer to... Figure 1 The specific implementation process of the functions corresponding to each module and unit of the device is not described in detail here as shown in the method embodiment.

[0099] The risk assessment device provided in this embodiment inputs the target feature data of the object to be assessed into the risk assessment model to obtain the risk assessment result of the object to be assessed. The risk assessment model is based on a trained KAN network, which is constructed and initialized based on a trained logistic regression model. By constructing and initializing the KAN network using the trained logistic regression model, the trained KAN network can clearly show the specific contribution of each feature to the final prediction result, maintain the inherent interpretability of the model, and meet the strict requirements for model transparency. Moreover, since the KAN network is constructed and initialized based on the logistic regression model, it introduces a non-linear feature representation compared to the logistic regression model after training. The non-linear feature representation is more complex than the linear feature representation and can more accurately represent the impact of feature data on the output, which can significantly improve prediction performance.

[0100] Figure 6 This is a structural block diagram of another risk assessment device provided in the embodiments of this application, such as... Figure 6 As shown, the risk assessment device may include: Credit feature acquisition module 601 is used to acquire target feature data of the user to be evaluated, wherein the target feature data is data related to the evaluation of credit risk. The credit risk assessment module 602 is used to input the target feature data into the credit risk assessment model to obtain the credit risk assessment result of the user to be assessed. The credit risk assessment model is based on a trained KAN network. The KAN network is constructed and initialized based on a trained logistic regression model. The logistic regression model and the KAN network are trained on a credit dataset. The credit risk assessment result is used to indicate the probability of the user to be assessed defaulting or complying with the agreement.

[0101] Optionally, the device further includes: The KAN network training module is used to train the activation function parameters of an initialized KAN network based on a training dataset to obtain a trained KAN network. During the training of the initialized KAN network, the basic structural parameters of the KAN network are kept fixed. The KAN network structure is constructed based on a logistic regression model, and the basic structural parameters and activation function parameters of the constructed KAN network are initialized based on the logistic regression parameters of the trained logistic regression model.

[0102] Optionally, the KAN network training module is specifically used for: Based on the credit dataset, the activation function parameters of the initialized KAN network are trained using reinforcement learning to obtain the trained KAN network. The reward function of the reinforcement learning method includes KS and / or AUC.

[0103] The risk assessment device provided in this application embodiment inputs the target feature data of the user to be assessed into a credit risk assessment model to obtain the credit risk assessment result of the user to be assessed. The credit risk assessment model is based on a trained KAN network, which is constructed and initialized based on a trained logistic regression model. By constructing and initializing the KAN network using the trained logistic regression model, the trained KAN network can clearly show the specific contribution of each feature to the final prediction result, maintain the inherent interpretability of the model, and meet the strict requirements of financial supervision for model transparency. Moreover, since the KAN network is constructed and initialized based on the logistic regression model, it introduces a non-linear feature representation compared to the logistic regression model after training. The non-linear feature representation is more complex than the linear feature representation and can more accurately represent the impact of feature data on the output, which can significantly improve prediction performance.

[0104] As the device embodiment is basically similar to the method embodiment, the description is relatively simple, and relevant parts can be found in the description of the method embodiment.

[0105] Figure 7 This is a structural block diagram of an electronic device provided in an embodiment of this application, such as... Figure 7 As shown, the electronic device 700 may include one or more processors 710 and one or more memories 720 connected to the processors 710. The electronic device 700 may also include an input interface 730 and an output interface 740 for communicating with another device or system. Program code executed by the processor 710 may be stored in the memory 720.

[0106] The processor 710 in the electronic device 700 calls the program code stored in the memory 720 to execute the risk assessment method in the above embodiments.

[0107] According to one embodiment of this application, a computer-readable storage medium is also provided, including but not limited to disk storage, CD-ROM, optical storage, etc., wherein a computer program is stored on the computer-readable storage medium, and when the computer program is executed by a processor, it implements the risk assessment method described in the foregoing embodiments.

[0108] According to one embodiment of this application, a computer program product is also provided, including a computer program or computer instructions, which, when executed by a processor, implement the risk assessment method described in the above embodiments.

[0109] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0110] Those skilled in the art will understand that embodiments of this application can be provided as methods, apparatus, or computer program products. Therefore, embodiments of this application can take the form of entirely hardware embodiments, entirely software embodiments, or embodiments combining software and hardware aspects. Furthermore, embodiments of this application can take the form of computer program products implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0111] This application describes embodiments with reference to flowchart illustrations and / or block diagrams of methods, terminal devices (systems), and computer program products according to embodiments of this application. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing terminal device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing terminal device, generate instructions for implementing the flowchart illustrations. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0112] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing terminal device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0113] These computer program instructions can also be loaded onto a computer or other programmable data processing terminal equipment, causing a series of operational steps to be performed on the computer or other programmable terminal equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable terminal equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0114] Although preferred embodiments of the present application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the embodiments of the present application.

[0115] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal device that includes said element.

[0116] The above provides a detailed description of the risk assessment method, electronic device, and storage medium provided in this application. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A risk assessment method, characterized in that, include: Obtain the target feature data of the object to be evaluated; The target feature data is input into the risk assessment model to obtain the risk assessment result of the object to be assessed. The risk assessment model is based on the trained KAN network, which is constructed and initialized based on the trained logistic regression model.

2. The method according to claim 1, characterized in that, The training process of the KAN network includes: Based on the training dataset, the activation function parameters of the initialized KAN network are trained to obtain the trained KAN network. During the training of the initialized KAN network, the basic structural parameters of the KAN network are kept fixed. The KAN network structure is constructed based on a logistic regression model, and the basic structural parameters and activation function parameters of the constructed KAN network are initialized based on the logistic regression parameters of the trained logistic regression model.

3. The method according to claim 2, characterized in that, The logistic regression model includes a linear component, an exponential function, and a sigmoid function. The KAN network includes an input layer, a first network layer, a second network layer, and a third network layer; The number of input nodes in the input layer is the same as the number of input features in the linear part; The first network layer corresponds to the linear part, the second network layer corresponds to the exponential function, and the third network layer corresponds to the sigmoid function.

4. The method according to claim 3, characterized in that, The edge function between the input node and the network node in the first network layer is initialized based on the linear function corresponding to the input feature in the linear part.

5. The method according to any one of claims 2-4, characterized in that, The basic structural parameters include: node offset parameters, node scaling parameters, child node offset parameters, and child node scaling parameters; The activation function parameters include: activation function coefficient matrix, activation function mask vector, basic scaling parameters, spline scaling parameters, and mask and affine transformation parameters of the sign function.

6. The method according to any one of claims 2-4, characterized in that, The process of training the activation function parameters of the initialized KAN network based on the training dataset to obtain the trained KAN network includes: Based on the training dataset, the activation function parameters of the initialized KAN network are trained using reinforcement learning to obtain the trained KAN network.

7. The method according to any one of claims 2-4, characterized in that, Before training the activation function parameters of the initialized KAN network based on the training dataset to obtain the trained KAN network, the following steps are included: Based on the training dataset, the initialized KAN network is initially trained according to multiple candidate hyperparameters to obtain the initially trained KAN network corresponding to each candidate hyperparameter. For each of the candidate hyperparameters, determine the first evaluation index value of the preliminarily trained KAN network on the out-of-time sample dataset; The candidate hyperparameter with the largest value of the first evaluation index is determined as the target hyperparameter for training the initialized KAN network.

8. The method according to any one of claims 2-4, characterized in that, The process of training the activation function parameters of the initialized KAN network based on the training dataset to obtain the trained KAN network includes: Based on the training dataset, after training the activation function parameters of the initialized KAN network for the current round, the second evaluation index value of the KAN network after the current round of training on the out-of-time sample dataset is determined and recorded. Iteratively execute the operation of training the activation function parameters of the KAN network in the current round based on the training dataset and determining and recording the value of the second evaluation index, until the loss function of the KAN network converges and the value of the second evaluation index converges, thus obtaining the trained KAN network.

9. A risk assessment method, characterized in that, include: Obtain target feature data of the user to be evaluated, wherein the target feature data is related to the evaluation of credit risk; The target feature data is input into the credit risk assessment model to obtain the credit risk assessment result of the user to be assessed. The credit risk assessment model is based on a trained KAN network, which is constructed and initialized based on a trained logistic regression model. The logistic regression model and the KAN network are trained on a credit dataset. The credit risk assessment result is used to indicate the probability of the user to be assessed defaulting or complying with the agreement.

10. The method according to claim 9, characterized in that, The training process of the KAN network includes: Based on the training dataset, the activation function parameters of the initialized KAN network are trained to obtain the trained KAN network. During the training of the initialized KAN network, the basic structural parameters of the KAN network are kept fixed. The KAN network structure is constructed based on a logistic regression model, and the basic structural parameters and activation function parameters of the constructed KAN network are initialized based on the logistic regression parameters of the trained logistic regression model.

11. The method according to claim 10, characterized in that, The step of training the activation function parameters of the initialized KAN network based on the training dataset to obtain the trained KAN network includes: Based on the credit dataset, the activation function parameters of the initialized KAN network are trained using reinforcement learning to obtain the trained KAN network. The reward function of the reinforcement learning method includes KS and / or AUC.

12. An electronic device, characterized in that, include: A processor, a memory, and a computer program stored in the memory and executable on the processor, wherein the computer program, when executed by the processor, implements the risk assessment method as described in any one of claims 1-8 or 9-11.

13. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the risk assessment method as described in any one of claims 1-8 or 9-11.

14. A computer program product, characterized in that, It includes a computer program or computer instructions that, when executed by a processor, implement the risk assessment method according to any one of claims 1 to 8 or claims 9 to 11.

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